libtess.debug.js

/**
 * @license
 * Copyright 2000, Silicon Graphics, Inc. All Rights Reserved.
 * Copyright 2015, Google Inc. All Rights Reserved.
 *
 * Permission is hereby granted, free of charge, to any person obtaining a copy
 * of this software and associated documentation files (the "Software"), to
 * deal in the Software without restriction, including without limitation the
 * rights to use, copy, modify, merge, publish, distribute, sublicense, and/or
 * sell copies of the Software, and to permit persons to whom the Software is
 * furnished to do so, subject to the following conditions:
 *
 * The above copyright notice including the dates of first publication and
 * either this permission notice or a reference to http://oss.sgi.com/projects/FreeB/
 * shall be included in all copies or substantial portions of the Software.
 *
 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
 * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
 * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
 * SILICON GRAPHICS, INC. BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
 * WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR
 * IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
 *
 * Original Code. The Original Code is: OpenGL Sample Implementation,
 * Version 1.2.1, released January 26, 2000, developed by Silicon Graphics,
 * Inc. The Original Code is Copyright (c) 1991-2000 Silicon Graphics, Inc.
 * Copyright in any portions created by third parties is as indicated
 * elsewhere herein. All Rights Reserved.
 */
/**
 * @author ericv@cs.stanford.edu (Eric Veach)
 * @author bckenny@google.com (Brendan Kenny)
 */

/**
 * Base namespace.
 * @const
 */
var libtess = {};

/**
 * Whether to run asserts and extra debug checks.
 * @define {boolean}
 */
libtess.DEBUG = true;

/**
 * Checks if the condition evaluates to true if libtess.DEBUG is true.
 * @param {*} condition The condition to check.
 * @param {string=} opt_message Error message in case of failure.
 * @throws {Error} Assertion failed, the condition evaluates to false.
 */
libtess.assert = function(condition, opt_message) {
  if (libtess.DEBUG && !condition) {
    throw new Error('Assertion failed' +
        (opt_message ? ': ' + opt_message : ''));
  }
};

/**
 * The maximum vertex coordinate size, 1e150. Anything larger will trigger a
 * GLU_TESS_COORD_TOO_LARGE error callback and the vertex will be clamped to
 * this value for all tessellation calculations.
 * @const {number}
 */
libtess.GLU_TESS_MAX_COORD = 1e150;
// NOTE(bckenny): value from glu.pl generator

/**
 * Normally the polygon is projected to a plane perpendicular to one of the
 * three coordinate axes before tessellating in 2d. This helps numerical
 * accuracy by forgoing a transformation step by simply dropping one coordinate
 * dimension.
 *
 * However, this can affect the placement of intersection points for non-axis-
 * aligned polygons. Setting TRUE_PROJECT to true will instead project onto a
 * plane actually perpendicular to the polygon's normal.
 *
 * NOTE(bckenny): I can find no instances on the internet in which this mode has
 * been used, but it's difficult to search for. This was a compile-time setting
 * in the original, so setting this as constant. If this is exposed in the
 * public API, remove the ignore coverage directives on
 * libtess.normal.projectPolygon and libtess.normal.normalize_.
 * @const {boolean}
 */
libtess.TRUE_PROJECT = false;

/**
 * The default tolerance for merging features, 0, meaning vertices are only
 * merged if they are exactly coincident
 * If a higher tolerance is needed, significant rewriting will need to occur.
 * See libtess.sweep.TOLERANCE_NONZERO_ as a starting place.
 * @const {number}
 */
libtess.GLU_TESS_DEFAULT_TOLERANCE = 0;

/**
 * The input contours parition the plane into regions. A winding
 * rule determines which of these regions are inside the polygon.
 *
 * For a single contour C, the winding number of a point x is simply
 * the signed number of revolutions we make around x as we travel
 * once around C (where CCW is positive). When there are several
 * contours, the individual winding numbers are summed. This
 * procedure associates a signed integer value with each point x in
 * the plane. Note that the winding number is the same for all
 * points in a single region.
 *
 * The winding rule classifies a region as "inside" if its winding
 * number belongs to the chosen category (odd, nonzero, positive,
 * negative, or absolute value of at least two). The current GLU
 * tesselator implements the "odd" rule. The "nonzero" rule is another
 * common way to define the interior. The other three rules are
 * useful for polygon CSG operations.
 * @enum {number}
 */
libtess.windingRule = {
  // NOTE(bckenny): values from enumglu.spec
  GLU_TESS_WINDING_ODD: 100130,
  GLU_TESS_WINDING_NONZERO: 100131,
  GLU_TESS_WINDING_POSITIVE: 100132,
  GLU_TESS_WINDING_NEGATIVE: 100133,
  GLU_TESS_WINDING_ABS_GEQ_TWO: 100134
};

/**
 * The type of primitive return from a "begin" callback. GL_LINE_LOOP is only
 * returned when GLU_TESS_BOUNDARY_ONLY is true. GL_TRIANGLE_STRIP and
 * GL_TRIANGLE_FAN are no longer returned since 1.1.0 (see release notes).
 * @enum {number}
 */
libtess.primitiveType = {
  GL_LINE_LOOP: 2,
  GL_TRIANGLES: 4,
  GL_TRIANGLE_STRIP: 5,
  GL_TRIANGLE_FAN: 6
};

/**
 * The types of errors provided in the error callback.
 * @enum {number}
 */
libtess.errorType = {
  // TODO(bckenny) doc types
  // NOTE(bckenny): values from enumglu.spec
  GLU_TESS_MISSING_BEGIN_POLYGON: 100151,
  GLU_TESS_MISSING_END_POLYGON: 100153,
  GLU_TESS_MISSING_BEGIN_CONTOUR: 100152,
  GLU_TESS_MISSING_END_CONTOUR: 100154,
  GLU_TESS_COORD_TOO_LARGE: 100155,
  GLU_TESS_NEED_COMBINE_CALLBACK: 100156
};

/**
 * Enum values necessary for providing settings and callbacks. See the readme
 * for details.
 * @enum {number}
 */
libtess.gluEnum = {
  // TODO(bckenny): rename so not always typing libtess.gluEnum.*?

  // NOTE(bckenny): values from enumglu.spec
  GLU_TESS_BEGIN: 100100,
  GLU_TESS_VERTEX: 100101,
  GLU_TESS_END: 100102,
  GLU_TESS_ERROR: 100103,
  GLU_TESS_EDGE_FLAG: 100104,
  GLU_TESS_COMBINE: 100105,
  GLU_TESS_BEGIN_DATA: 100106,
  GLU_TESS_VERTEX_DATA: 100107,
  GLU_TESS_END_DATA: 100108,
  GLU_TESS_ERROR_DATA: 100109,
  GLU_TESS_EDGE_FLAG_DATA: 100110,
  GLU_TESS_COMBINE_DATA: 100111,

  GLU_TESS_MESH: 100112,  //  NOTE(bckenny): from tess.c
  GLU_TESS_TOLERANCE: 100142,
  GLU_TESS_WINDING_RULE: 100140,
  GLU_TESS_BOUNDARY_ONLY: 100141,

  // TODO(bckenny): move this to libtess.errorType?
  GLU_INVALID_ENUM: 100900,
  GLU_INVALID_VALUE: 100901
};

/** @typedef {number} */
libtess.PQHandle;

/* global libtess */

/** @const */
libtess.geom = {};

/**
 * Returns whether vertex u and vertex v are equal.
 * @param {libtess.GluVertex} u
 * @param {libtess.GluVertex} v
 * @return {boolean}
 */
libtess.geom.vertEq = function(u, v) {
  return u.s === v.s && u.t === v.t;
};

/**
 * Returns whether vertex u is lexicographically less than or equal to vertex v.
 * @param {libtess.GluVertex} u
 * @param {libtess.GluVertex} v
 * @return {boolean}
 */
libtess.geom.vertLeq = function(u, v) {
  return (u.s < v.s) || (u.s === v.s && u.t <= v.t);
};

/**
 * Given three vertices u,v,w such that geom.vertLeq(u,v) && geom.vertLeq(v,w),
 * evaluates the t-coord of the edge uw at the s-coord of the vertex v.
 * Returns v.t - (uw)(v.s), ie. the signed distance from uw to v.
 * If uw is vertical (and thus passes thru v), the result is zero.
 *
 * The calculation is extremely accurate and stable, even when v
 * is very close to u or w.  In particular if we set v.t = 0 and
 * let r be the negated result (this evaluates (uw)(v.s)), then
 * r is guaranteed to satisfy MIN(u.t,w.t) <= r <= MAX(u.t,w.t).
 * @param {libtess.GluVertex} u
 * @param {libtess.GluVertex} v
 * @param {libtess.GluVertex} w
 * @return {number}
 */
libtess.geom.edgeEval = function(u, v, w) {
  libtess.assert(libtess.geom.vertLeq(u, v) && libtess.geom.vertLeq(v, w));

  var gapL = v.s - u.s;
  var gapR = w.s - v.s;

  if (gapL + gapR > 0) {
    if (gapL < gapR) {
      return (v.t - u.t) + (u.t - w.t) * (gapL / (gapL + gapR));
    } else {
      return (v.t - w.t) + (w.t - u.t) * (gapR / (gapL + gapR));
    }
  }

  // vertical line
  return 0;
};

/**
 * Returns a number whose sign matches geom.edgeEval(u,v,w) but which
 * is cheaper to evaluate.  Returns > 0, == 0 , or < 0
 * as v is above, on, or below the edge uw.
 * @param {libtess.GluVertex} u
 * @param {libtess.GluVertex} v
 * @param {libtess.GluVertex} w
 * @return {number}
 */
libtess.geom.edgeSign = function(u, v, w) {
  libtess.assert(libtess.geom.vertLeq(u, v) && libtess.geom.vertLeq(v, w));

  var gapL = v.s - u.s;
  var gapR = w.s - v.s;

  if (gapL + gapR > 0) {
    return (v.t - w.t) * gapL + (v.t - u.t) * gapR;
  }

  // vertical line
  return 0;
};

/**
 * Version of VertLeq with s and t transposed.
 * Returns whether vertex u is lexicographically less than or equal to vertex v.
 * @param {libtess.GluVertex} u
 * @param {libtess.GluVertex} v
 * @return {boolean}
 */
libtess.geom.transLeq = function(u, v) {
  return (u.t < v.t) || (u.t === v.t && u.s <= v.s);
};

/**
 * Version of geom.edgeEval with s and t transposed.
 * Given three vertices u,v,w such that geom.transLeq(u,v) &&
 * geom.transLeq(v,w), evaluates the t-coord of the edge uw at the s-coord of
 * the vertex v. Returns v.s - (uw)(v.t), ie. the signed distance from uw to v.
 * If uw is vertical (and thus passes thru v), the result is zero.
 *
 * The calculation is extremely accurate and stable, even when v
 * is very close to u or w.  In particular if we set v.s = 0 and
 * let r be the negated result (this evaluates (uw)(v.t)), then
 * r is guaranteed to satisfy MIN(u.s,w.s) <= r <= MAX(u.s,w.s).
 * @param {libtess.GluVertex} u
 * @param {libtess.GluVertex} v
 * @param {libtess.GluVertex} w
 * @return {number}
 */
libtess.geom.transEval = function(u, v, w) {
  libtess.assert(libtess.geom.transLeq(u, v) && libtess.geom.transLeq(v, w));

  var gapL = v.t - u.t;
  var gapR = w.t - v.t;

  if (gapL + gapR > 0) {
    if (gapL < gapR) {
      return (v.s - u.s) + (u.s - w.s) * (gapL / (gapL + gapR));
    } else {
      return (v.s - w.s) + (w.s - u.s) * (gapR / (gapL + gapR));
    }
  }

  // vertical line
  return 0;
};

/**
 * Version of geom.edgeSign with s and t transposed.
 * Returns a number whose sign matches geom.transEval(u,v,w) but which
 * is cheaper to evaluate.  Returns > 0, == 0 , or < 0
 * as v is above, on, or below the edge uw.
 * @param {libtess.GluVertex} u
 * @param {libtess.GluVertex} v
 * @param {libtess.GluVertex} w
 * @return {number}
 */
libtess.geom.transSign = function(u, v, w) {
  libtess.assert(libtess.geom.transLeq(u, v) && libtess.geom.transLeq(v, w));

  var gapL = v.t - u.t;
  var gapR = w.t - v.t;

  if (gapL + gapR > 0) {
    return (v.s - w.s) * gapL + (v.s - u.s) * gapR;
  }

  // vertical line
  return 0;
};

/**
 * Returns whether edge is directed from right to left.
 * @param {libtess.GluHalfEdge} e
 * @return {boolean}
 */
libtess.geom.edgeGoesLeft = function(e) {
  return libtess.geom.vertLeq(e.dst(), e.org);
};

/**
 * Returns whether edge is directed from left to right.
 * @param {libtess.GluHalfEdge} e
 * @return {boolean}
 */
libtess.geom.edgeGoesRight = function(e) {
  return libtess.geom.vertLeq(e.org, e.dst());
};

/**
 * Calculates the L1 distance between vertices u and v.
 * @param {libtess.GluVertex} u
 * @param {libtess.GluVertex} v
 * @return {number}
 */
libtess.geom.vertL1dist = function(u, v) {
  return Math.abs(u.s - v.s) + Math.abs(u.t - v.t);
};

// NOTE(bckenny): vertCCW is called nowhere in libtess and isn't part of the
// public API.
/* istanbul ignore next */
/**
 * For almost-degenerate situations, the results are not reliable.
 * Unless the floating-point arithmetic can be performed without
 * rounding errors, *any* implementation will give incorrect results
 * on some degenerate inputs, so the client must have some way to
 * handle this situation.
 * @param {!libtess.GluVertex} u
 * @param {!libtess.GluVertex} v
 * @param {!libtess.GluVertex} w
 * @return {boolean}
 */
libtess.geom.vertCCW = function(u, v, w) {
  return (u.s * (v.t - w.t) + v.s * (w.t - u.t) + w.s * (u.t - v.t)) >= 0;
};

/**
 * Given parameters a,x,b,y returns the value (b*x+a*y)/(a+b),
 * or (x+y)/2 if a==b==0. It requires that a,b >= 0, and enforces
 * this in the rare case that one argument is slightly negative.
 * The implementation is extremely stable numerically.
 * In particular it guarantees that the result r satisfies
 * MIN(x,y) <= r <= MAX(x,y), and the results are very accurate
 * even when a and b differ greatly in magnitude.
 * @private
 * @param {number} a
 * @param {number} x
 * @param {number} b
 * @param {number} y
 * @return {number}
 */
libtess.geom.interpolate_ = function(a, x, b, y) {
  // from Macro RealInterpolate:
  //(a = (a < 0) ? 0 : a, b = (b < 0) ? 0 : b, ((a <= b) ? ((b == 0) ? ((x+y) / 2) : (x + (y-x) * (a/(a+b)))) : (y + (x-y) * (b/(a+b)))))
  a = (a < 0) ? 0 : a;
  b = (b < 0) ? 0 : b;

  if (a <= b) {
    if (b === 0) {
      return (x + y) / 2;
    } else {
      return x + (y - x) * (a / (a + b));
    }
  } else {
    return y + (x - y) * (b / (a + b));
  }
};

/**
 * Given edges (o1,d1) and (o2,d2), compute their point of intersection.
 * The computed point is guaranteed to lie in the intersection of the
 * bounding rectangles defined by each edge.
 * @param {!libtess.GluVertex} o1
 * @param {!libtess.GluVertex} d1
 * @param {!libtess.GluVertex} o2
 * @param {!libtess.GluVertex} d2
 * @param {!libtess.GluVertex} v
 */
libtess.geom.edgeIntersect = function(o1, d1, o2, d2, v) {
  // This is certainly not the most efficient way to find the intersection
  // of two line segments, but it is very numerically stable.

  // Strategy: find the two middle vertices in the VertLeq ordering,
  // and interpolate the intersection s-value from these. Then repeat
  // using the TransLeq ordering to find the intersection t-value.
  var z1;
  var z2;
  var tmp;
  if (!libtess.geom.vertLeq(o1, d1)) {
    // Swap(o1, d1);
    tmp = o1;
    o1 = d1;
    d1 = tmp;
  }
  if (!libtess.geom.vertLeq(o2, d2)) {
    // Swap(o2, d2);
    tmp = o2;
    o2 = d2;
    d2 = tmp;
  }
  if (!libtess.geom.vertLeq(o1, o2)) {
    // Swap(o1, o2);
    tmp = o1;
    o1 = o2;
    o2 = tmp;
    // Swap(d1, d2);
    tmp = d1;
    d1 = d2;
    d2 = tmp;
  }

  if (!libtess.geom.vertLeq(o2, d1)) {
    // Technically, no intersection -- do our best
    v.s = (o2.s + d1.s) / 2;

  } else if (libtess.geom.vertLeq(d1, d2)) {
    // Interpolate between o2 and d1
    z1 = libtess.geom.edgeEval(o1, o2, d1);
    z2 = libtess.geom.edgeEval(o2, d1, d2);
    if (z1 + z2 < 0) { z1 = -z1; z2 = -z2; }
    v.s = libtess.geom.interpolate_(z1, o2.s, z2, d1.s);

  } else {
    // Interpolate between o2 and d2
    z1 = libtess.geom.edgeSign(o1, o2, d1);
    z2 = -libtess.geom.edgeSign(o1, d2, d1);
    if (z1 + z2 < 0) { z1 = -z1; z2 = -z2; }
    v.s = libtess.geom.interpolate_(z1, o2.s, z2, d2.s);
  }

  // Now repeat the process for t
  if (!libtess.geom.transLeq(o1, d1)) {
    // Swap(o1, d1);
    tmp = o1;
    o1 = d1;
    d1 = tmp;
  }
  if (!libtess.geom.transLeq(o2, d2)) {
    // Swap(o2, d2);
    tmp = o2;
    o2 = d2;
    d2 = tmp;
  }
  if (!libtess.geom.transLeq(o1, o2)) {
    // Swap(o1, o2);
    tmp = o1;
    o1 = o2;
    o2 = tmp;
    // Swap(d1, d2);
    tmp = d1;
    d1 = d2;
    d2 = tmp;
  }

  if (!libtess.geom.transLeq(o2, d1)) {
    // Technically, no intersection -- do our best
    v.t = (o2.t + d1.t) / 2;

  } else if (libtess.geom.transLeq(d1, d2)) {
    // Interpolate between o2 and d1
    z1 = libtess.geom.transEval(o1, o2, d1);
    z2 = libtess.geom.transEval(o2, d1, d2);
    if (z1 + z2 < 0) { z1 = -z1; z2 = -z2; }
    v.t = libtess.geom.interpolate_(z1, o2.t, z2, d1.t);

  } else {
    // Interpolate between o2 and d2
    z1 = libtess.geom.transSign(o1, o2, d1);
    z2 = -libtess.geom.transSign(o1, d2, d1);
    if (z1 + z2 < 0) { z1 = -z1; z2 = -z2; }
    v.t = libtess.geom.interpolate_(z1, o2.t, z2, d2.t);
  }
};

/* global libtess */

// TODO(bckenny): could maybe merge GluMesh and mesh.js since these are
// operations on the mesh

/** @const */
libtess.mesh = {};

/****************** Basic Edge Operations **********************/


/**
 * makeEdge creates one edge, two vertices, and a loop (face).
 * The loop consists of the two new half-edges.
 *
 * @param {libtess.GluMesh} mesh [description].
 * @return {libtess.GluHalfEdge} [description].
 */
libtess.mesh.makeEdge = function(mesh) {
  // TODO(bckenny): probably move to GluMesh, but needs Make* methods with it

  var e = libtess.mesh.makeEdgePair_(mesh.eHead);

  // complete edge with vertices and face (see mesh.makeEdgePair_)
  libtess.mesh.makeVertex_(e, mesh.vHead);
  libtess.mesh.makeVertex_(e.sym, mesh.vHead);
  libtess.mesh.makeFace_(e, mesh.fHead);

  return e;
};


/**
 * meshSplice(eOrg, eDst) is the basic operation for changing the
 * mesh connectivity and topology. It changes the mesh so that
 *  eOrg.oNext <- OLD( eDst.oNext )
 *  eDst.oNext <- OLD( eOrg.oNext )
 * where OLD(...) means the value before the meshSplice operation.
 *
 * This can have two effects on the vertex structure:
 *  - if eOrg.org != eDst.org, the two vertices are merged together
 *  - if eOrg.org == eDst.org, the origin is split into two vertices
 * In both cases, eDst.org is changed and eOrg.org is untouched.
 *
 * Similarly (and independently) for the face structure,
 *  - if eOrg.lFace == eDst.lFace, one loop is split into two
 *  - if eOrg.lFace != eDst.lFace, two distinct loops are joined into one
 * In both cases, eDst.lFace is changed and eOrg.lFace is unaffected.
 *
 * Some special cases:
 * If eDst == eOrg, the operation has no effect.
 * If eDst == eOrg.lNext, the new face will have a single edge.
 * If eDst == eOrg.lPrev(), the old face will have a single edge.
 * If eDst == eOrg.oNext, the new vertex will have a single edge.
 * If eDst == eOrg.oPrev(), the old vertex will have a single edge.
 *
 * @param {libtess.GluHalfEdge} eOrg [description].
 * @param {libtess.GluHalfEdge} eDst [description].
 */
libtess.mesh.meshSplice = function(eOrg, eDst) {
  // TODO: more descriptive name?

  var joiningLoops = false;
  var joiningVertices = false;

  if (eOrg === eDst) {
    return;
  }

  if (eDst.org !== eOrg.org) {
    // We are merging two disjoint vertices -- destroy eDst.org
    joiningVertices = true;
    libtess.mesh.killVertex_(eDst.org, eOrg.org);
  }

  if (eDst.lFace !== eOrg.lFace) {
    // We are connecting two disjoint loops -- destroy eDst.lFace
    joiningLoops = true;
    libtess.mesh.killFace_(eDst.lFace, eOrg.lFace);
  }

  // Change the edge structure
  libtess.mesh.splice_(eDst, eOrg);

  if (!joiningVertices) {
    // We split one vertex into two -- the new vertex is eDst.org.
    // Make sure the old vertex points to a valid half-edge.
    libtess.mesh.makeVertex_(eDst, eOrg.org);
    eOrg.org.anEdge = eOrg;
  }

  if (!joiningLoops) {
    // We split one loop into two -- the new loop is eDst.lFace.
    // Make sure the old face points to a valid half-edge.
    libtess.mesh.makeFace_(eDst, eOrg.lFace);
    eOrg.lFace.anEdge = eOrg;
  }
};


/**
 * deleteEdge(eDel) removes the edge eDel. There are several cases:
 * if (eDel.lFace != eDel.rFace()), we join two loops into one; the loop
 * eDel.lFace is deleted. Otherwise, we are splitting one loop into two;
 * the newly created loop will contain eDel.dst(). If the deletion of eDel
 * would create isolated vertices, those are deleted as well.
 *
 * This function could be implemented as two calls to __gl_meshSplice
 * plus a few calls to memFree, but this would allocate and delete
 * unnecessary vertices and faces.
 *
 * @param {libtess.GluHalfEdge} eDel [description].
 */
libtess.mesh.deleteEdge = function(eDel) {
  var eDelSym = eDel.sym;
  var joiningLoops = false;

  // First step: disconnect the origin vertex eDel.org.  We make all
  // changes to get a consistent mesh in this "intermediate" state.
  if (eDel.lFace !== eDel.rFace()) {
    // We are joining two loops into one -- remove the left face
    joiningLoops = true;
    libtess.mesh.killFace_(eDel.lFace, eDel.rFace());
  }

  if (eDel.oNext === eDel) {
    libtess.mesh.killVertex_(eDel.org, null);

  } else {
    // Make sure that eDel.org and eDel.rFace() point to valid half-edges
    eDel.rFace().anEdge = eDel.oPrev();
    eDel.org.anEdge = eDel.oNext;

    libtess.mesh.splice_(eDel, eDel.oPrev());

    if (!joiningLoops) {
      // We are splitting one loop into two -- create a new loop for eDel.
      libtess.mesh.makeFace_(eDel, eDel.lFace);
    }
  }

  // Claim: the mesh is now in a consistent state, except that eDel.org
  // may have been deleted.  Now we disconnect eDel.dst().
  if (eDelSym.oNext === eDelSym) {
    libtess.mesh.killVertex_(eDelSym.org, null);
    libtess.mesh.killFace_(eDelSym.lFace, null);

  } else {
    // Make sure that eDel.dst() and eDel.lFace point to valid half-edges
    eDel.lFace.anEdge = eDelSym.oPrev();
    eDelSym.org.anEdge = eDelSym.oNext;
    libtess.mesh.splice_(eDelSym, eDelSym.oPrev());
  }

  // Any isolated vertices or faces have already been freed.
  libtess.mesh.killEdge_(eDel);
};

/******************** Other Edge Operations **********************/

/* All these routines can be implemented with the basic edge
 * operations above.  They are provided for convenience and efficiency.
 */


/**
 * addEdgeVertex(eOrg) creates a new edge eNew such that
 * eNew == eOrg.lNext, and eNew.dst() is a newly created vertex.
 * eOrg and eNew will have the same left face.
 *
 * @param {libtess.GluHalfEdge} eOrg [description].
 * @return {libtess.GluHalfEdge} [description].
 */
libtess.mesh.addEdgeVertex = function(eOrg) {
  // TODO(bckenny): why is it named this?

  var eNew = libtess.mesh.makeEdgePair_(eOrg);
  var eNewSym = eNew.sym;

  // Connect the new edge appropriately
  libtess.mesh.splice_(eNew, eOrg.lNext);

  // Set the vertex and face information
  eNew.org = eOrg.dst();

  libtess.mesh.makeVertex_(eNewSym, eNew.org);

  eNew.lFace = eNewSym.lFace = eOrg.lFace;

  return eNew;
};


/**
 * splitEdge(eOrg) splits eOrg into two edges eOrg and eNew,
 * such that eNew == eOrg.lNext. The new vertex is eOrg.dst() == eNew.org.
 * eOrg and eNew will have the same left face.
 *
 * @param {libtess.GluHalfEdge} eOrg [description].
 * @return {!libtess.GluHalfEdge} [description].
 */
libtess.mesh.splitEdge = function(eOrg) {
  var tempHalfEdge = libtess.mesh.addEdgeVertex(eOrg);
  var eNew = tempHalfEdge.sym;

  // Disconnect eOrg from eOrg.dst() and connect it to eNew.org
  libtess.mesh.splice_(eOrg.sym, eOrg.sym.oPrev());
  libtess.mesh.splice_(eOrg.sym, eNew);

  // Set the vertex and face information
  eOrg.sym.org = eNew.org; // NOTE(bckenny): assignment to dst
  eNew.dst().anEdge = eNew.sym;  // may have pointed to eOrg.sym
  eNew.sym.lFace = eOrg.rFace(); // NOTE(bckenny): assignment to rFace
  eNew.winding = eOrg.winding;  // copy old winding information
  eNew.sym.winding = eOrg.sym.winding;

  return eNew;
};


/**
 * connect(eOrg, eDst) creates a new edge from eOrg.dst()
 * to eDst.org, and returns the corresponding half-edge eNew.
 * If eOrg.lFace == eDst.lFace, this splits one loop into two,
 * and the newly created loop is eNew.lFace. Otherwise, two disjoint
 * loops are merged into one, and the loop eDst.lFace is destroyed.
 *
 * If (eOrg == eDst), the new face will have only two edges.
 * If (eOrg.lNext == eDst), the old face is reduced to a single edge.
 * If (eOrg.lNext.lNext == eDst), the old face is reduced to two edges.
 *
 * @param {libtess.GluHalfEdge} eOrg [description].
 * @param {libtess.GluHalfEdge} eDst [description].
 * @return {!libtess.GluHalfEdge} [description].
 */
libtess.mesh.connect = function(eOrg, eDst) {
  var joiningLoops = false;
  var eNew = libtess.mesh.makeEdgePair_(eOrg);
  var eNewSym = eNew.sym;

  if (eDst.lFace !== eOrg.lFace) {
    // We are connecting two disjoint loops -- destroy eDst.lFace
    joiningLoops = true;
    libtess.mesh.killFace_(eDst.lFace, eOrg.lFace);
  }

  // Connect the new edge appropriately
  libtess.mesh.splice_(eNew, eOrg.lNext);
  libtess.mesh.splice_(eNewSym, eDst);

  // Set the vertex and face information
  eNew.org = eOrg.dst();
  eNewSym.org = eDst.org;
  eNew.lFace = eNewSym.lFace = eOrg.lFace;

  // Make sure the old face points to a valid half-edge
  eOrg.lFace.anEdge = eNewSym;

  if (!joiningLoops) {
    // We split one loop into two -- the new loop is eNew.lFace
    libtess.mesh.makeFace_(eNew, eOrg.lFace);
  }
  return eNew;
};

/******************** Other Operations **********************/


/**
 * zapFace(fZap) destroys a face and removes it from the
 * global face list. All edges of fZap will have a null pointer as their
 * left face. Any edges which also have a null pointer as their right face
 * are deleted entirely (along with any isolated vertices this produces).
 * An entire mesh can be deleted by zapping its faces, one at a time,
 * in any order. Zapped faces cannot be used in further mesh operations!
 *
 * @param {libtess.GluFace} fZap [description].
 */
libtess.mesh.zapFace = function(fZap) {
  var eStart = fZap.anEdge;

  // walk around face, deleting edges whose right face is also NULL
  var eNext = eStart.lNext;
  var e;
  do {
    e = eNext;
    eNext = e.lNext;

    e.lFace = null;
    if (e.rFace() === null) {
      // delete the edge -- see mesh.deleteEdge above
      if (e.oNext === e) {
        libtess.mesh.killVertex_(e.org, null);

      } else {
        // Make sure that e.org points to a valid half-edge
        e.org.anEdge = e.oNext;
        libtess.mesh.splice_(e, e.oPrev());
      }

      var eSym = e.sym;

      if (eSym.oNext === eSym) {
        libtess.mesh.killVertex_(eSym.org, null);

      } else {
        // Make sure that eSym.org points to a valid half-edge
        eSym.org.anEdge = eSym.oNext;
        libtess.mesh.splice_(eSym, eSym.oPrev());
      }
      libtess.mesh.killEdge_(e);
    }
  } while (e !== eStart);

  // delete from circular doubly-linked list
  var fPrev = fZap.prev;
  var fNext = fZap.next;
  fNext.prev = fPrev;
  fPrev.next = fNext;

  // TODO(bckenny): memFree( fZap );
  // TODO(bckenny): probably null at callsite
};

// TODO(bckenny): meshUnion isn't called within libtess and isn't part of the
// public API. Could be useful if more mesh manipulation functions are exposed.
/* istanbul ignore next */
/**
 * meshUnion() forms the union of all structures in
 * both meshes, and returns the new mesh (the old meshes are destroyed).
 *
 * @param {!libtess.GluMesh} mesh1
 * @param {!libtess.GluMesh} mesh2
 * @return {!libtess.GluMesh}
 */
libtess.mesh.meshUnion = function(mesh1, mesh2) {
  // TODO(bceknny): probably move to GluMesh method
  var f1 = mesh1.fHead;
  var v1 = mesh1.vHead;
  var e1 = mesh1.eHead;

  var f2 = mesh2.fHead;
  var v2 = mesh2.vHead;
  var e2 = mesh2.eHead;

  // Add the faces, vertices, and edges of mesh2 to those of mesh1
  if (f2.next !== f2) {
    f1.prev.next = f2.next;
    f2.next.prev = f1.prev;
    f2.prev.next = f1;
    f1.prev = f2.prev;
  }

  if (v2.next !== v2) {
    v1.prev.next = v2.next;
    v2.next.prev = v1.prev;
    v2.prev.next = v1;
    v1.prev = v2.prev;
  }

  if (e2.next !== e2) {
    e1.sym.next.sym.next = e2.next;
    e2.next.sym.next = e1.sym.next;
    e2.sym.next.sym.next = e1;
    e1.sym.next = e2.sym.next;
  }

  // TODO(bckenny): memFree(mesh2);
  // TODO(bckenny): If function is kept, remove mesh2's data to enforce.
  return mesh1;
};


/**
 * deleteMesh(mesh) will free all storage for any valid mesh.
 * @param {libtess.GluMesh} mesh [description].
 */
libtess.mesh.deleteMesh = function(mesh) {
  // TODO(bckenny): unnecessary, I think.
  // TODO(bckenny): might want to explicitly null at callsite
  // lots of memFrees. see also DELETE_BY_ZAPPING
};

/************************ Utility Routines ************************/


/**
 * Creates a new pair of half-edges which form their own loop.
 * No vertex or face structures are allocated, but these must be assigned
 * before the current edge operation is completed.
 *
 * TODO(bckenny): warning about eNext strictly being first of pair? (see code)
 *
 * @private
 * @param {libtess.GluHalfEdge} eNext [description].
 * @return {libtess.GluHalfEdge} [description].
 */
libtess.mesh.makeEdgePair_ = function(eNext) {
  var e = new libtess.GluHalfEdge();
  var eSym = new libtess.GluHalfEdge();

  // TODO(bckenny): how do we ensure this? see above comment in jsdoc
  // Make sure eNext points to the first edge of the edge pair
  // if (eNext->Sym < eNext ) { eNext = eNext->Sym; }

  // NOTE(bckenny): check this for bugs in current implementation!

  // Insert in circular doubly-linked list before eNext.
  // Note that the prev pointer is stored in sym.next.
  var ePrev = eNext.sym.next;
  eSym.next = ePrev;
  ePrev.sym.next = e;
  e.next = eNext;
  eNext.sym.next = eSym;

  e.sym = eSym;
  e.oNext = e;
  e.lNext = eSym;

  eSym.sym = e;
  eSym.oNext = eSym;
  eSym.lNext = e;

  return e;
};


/**
 * splice_ is best described by the Guibas/Stolfi paper or the
 * CS348a notes. Basically, it modifies the mesh so that
 * a.oNext and b.oNext are exchanged. This can have various effects
 * depending on whether a and b belong to different face or vertex rings.
 * For more explanation see mesh.meshSplice below.
 *
 * @private
 * @param {libtess.GluHalfEdge} a [description].
 * @param {libtess.GluHalfEdge} b [description].
 */
libtess.mesh.splice_ = function(a, b) {
  var aONext = a.oNext;
  var bONext = b.oNext;

  aONext.sym.lNext = b;
  bONext.sym.lNext = a;
  a.oNext = bONext;
  b.oNext = aONext;
};


/**
 * makeVertex_(eOrig, vNext) attaches a new vertex and makes it the
 * origin of all edges in the vertex loop to which eOrig belongs. "vNext" gives
 * a place to insert the new vertex in the global vertex list.  We insert
 * the new vertex *before* vNext so that algorithms which walk the vertex
 * list will not see the newly created vertices.
 *
 * NOTE: unlike original, acutally allocates new vertex.
 *
 * @private
 * @param {libtess.GluHalfEdge} eOrig [description].
 * @param {libtess.GluVertex} vNext [description].
 */
libtess.mesh.makeVertex_ = function(eOrig, vNext) {
  // insert in circular doubly-linked list before vNext
  var vPrev = vNext.prev;
  var vNew = new libtess.GluVertex(vNext, vPrev);
  vPrev.next = vNew;
  vNext.prev = vNew;

  vNew.anEdge = eOrig;
  // leave coords, s, t undefined
  // TODO(bckenny): does above line mean 0 specifically, or does it matter?

  // fix other edges on this vertex loop
  var e = eOrig;
  do {
    e.org = vNew;
    e = e.oNext;
  } while (e !== eOrig);
};


/**
 * makeFace_(eOrig, fNext) attaches a new face and makes it the left
 * face of all edges in the face loop to which eOrig belongs. "fNext" gives
 * a place to insert the new face in the global face list.  We insert
 * the new face *before* fNext so that algorithms which walk the face
 * list will not see the newly created faces.
 *
 * NOTE: unlike original, acutally allocates new face.
 *
 * @private
 * @param {libtess.GluHalfEdge} eOrig [description].
 * @param {libtess.GluFace} fNext [description].
 */
libtess.mesh.makeFace_ = function(eOrig, fNext) {
  // insert in circular doubly-linked list before fNext
  var fPrev = fNext.prev;
  var fNew = new libtess.GluFace(fNext, fPrev);
  fPrev.next = fNew;
  fNext.prev = fNew;

  fNew.anEdge = eOrig;

  // The new face is marked "inside" if the old one was.  This is a
  // convenience for the common case where a face has been split in two.
  fNew.inside = fNext.inside;

  // fix other edges on this face loop
  var e = eOrig;
  do {
    e.lFace = fNew;
    e = e.lNext;
  } while (e !== eOrig);
};


/**
 * killEdge_ destroys an edge (the half-edges eDel and eDel.sym),
 * and removes from the global edge list.
 *
 * @private
 * @param {libtess.GluHalfEdge} eDel [description].
 */
libtess.mesh.killEdge_ = function(eDel) {
  // TODO(bckenny): in this case, no need to worry(?), but check when checking mesh.makeEdgePair_
  // Half-edges are allocated in pairs, see EdgePair above
  // if (eDel->Sym < eDel ) { eDel = eDel->Sym; }

  // delete from circular doubly-linked list
  var eNext = eDel.next;
  var ePrev = eDel.sym.next;
  eNext.sym.next = ePrev;
  ePrev.sym.next = eNext;

  // TODO(bckenny): memFree( eDel ); (which also frees eDel.sym)
  // TODO(bckenny): need to null at callsites?
};


/**
 * killVertex_ destroys a vertex and removes it from the global
 * vertex list. It updates the vertex loop to point to a given new vertex.
 *
 * @private
 * @param {libtess.GluVertex} vDel [description].
 * @param {libtess.GluVertex} newOrg [description].
 */
libtess.mesh.killVertex_ = function(vDel, newOrg) {
  var eStart = vDel.anEdge;

  // change the origin of all affected edges
  var e = eStart;
  do {
    e.org = newOrg;
    e = e.oNext;
  } while (e !== eStart);

  // delete from circular doubly-linked list
  var vPrev = vDel.prev;
  var vNext = vDel.next;
  vNext.prev = vPrev;
  vPrev.next = vNext;

  // TODO(bckenny): memFree( vDel );
  // TODO(bckenny): need to null at callsites?
};


/**
 * killFace_ destroys a face and removes it from the global face
 * list. It updates the face loop to point to a given new face.
 *
 * @private
 * @param {libtess.GluFace} fDel [description].
 * @param {libtess.GluFace} newLFace [description].
 */
libtess.mesh.killFace_ = function(fDel, newLFace) {
  var eStart = fDel.anEdge;

  // change the left face of all affected edges
  var e = eStart;
  do {
    e.lFace = newLFace;
    e = e.lNext;
  } while (e !== eStart);

  // delete from circular doubly-linked list
  var fPrev = fDel.prev;
  var fNext = fDel.next;
  fNext.prev = fPrev;
  fPrev.next = fNext;

  // TODO(bckenny): memFree( fDel );
  // TODO(bckenny): need to null at callsites?
};

/* global libtess */

/** @const */
libtess.normal = {};

// TODO(bckenny): Integrate SLANTED_SWEEP somehow?
/* The "feature merging" is not intended to be complete. There are
 * special cases where edges are nearly parallel to the sweep line
 * which are not implemented. The algorithm should still behave
 * robustly (ie. produce a reasonable tesselation) in the presence
 * of such edges, however it may miss features which could have been
 * merged. We could minimize this effect by choosing the sweep line
 * direction to be something unusual (ie. not parallel to one of the
 * coordinate axes).
 * #if defined(SLANTED_SWEEP)
 * #define S_UNIT_X  0.50941539564955385 // Pre-normalized
 * #define S_UNIT_Y  0.86052074622010633
 * #endif
 */

/**
 * X coordinate of local basis for polygon projection.
 * @private {number}
 * @const
 */
libtess.normal.S_UNIT_X_ = 1.0;

/**
 * Y coordinate of local basis for polygon projection.
 * @private {number}
 * @const
 */
libtess.normal.S_UNIT_Y_ = 0.0;

/**
 * Determines a polygon normal and projects vertices onto the plane of the
 * polygon. A pre-computed normal for the data may be provided, or set to the
 * zero vector if one should be computed from it.
 * @param {!libtess.GluTesselator} tess
 * @param {number} normalX
 * @param {number} normalY
 * @param {number} normalZ
 */
libtess.normal.projectPolygon = function(tess, normalX, normalY, normalZ) {
  var computedNormal = false;

  var norm = [
    normalX,
    normalY,
    normalZ
  ];
  if (normalX === 0 && normalY === 0 && normalZ === 0) {
    libtess.normal.computeNormal_(tess, norm);
    computedNormal = true;
  }

  var i = libtess.normal.longAxis_(norm);
  var vHead = tess.mesh.vHead;
  var v;

  // NOTE(bckenny): This branch is never taken. See comment on
  // libtess.TRUE_PROJECT.
  /* istanbul ignore if */
  if (libtess.TRUE_PROJECT) {
    // Choose the initial sUnit vector to be approximately perpendicular
    // to the normal.
    libtess.normal.normalize_(norm);

    var sUnit = [0, 0, 0];
    var tUnit = [0, 0, 0];

    sUnit[i] = 0;
    sUnit[(i + 1) % 3] = libtess.normal.S_UNIT_X_;
    sUnit[(i + 2) % 3] = libtess.normal.S_UNIT_Y_;

    // Now make it exactly perpendicular
    var w = libtess.normal.dot_(sUnit, norm);
    sUnit[0] -= w * norm[0];
    sUnit[1] -= w * norm[1];
    sUnit[2] -= w * norm[2];
    libtess.normal.normalize_(sUnit);

    // Choose tUnit so that (sUnit,tUnit,norm) form a right-handed frame
    tUnit[0] = norm[1] * sUnit[2] - norm[2] * sUnit[1];
    tUnit[1] = norm[2] * sUnit[0] - norm[0] * sUnit[2];
    tUnit[2] = norm[0] * sUnit[1] - norm[1] * sUnit[0];
    libtess.normal.normalize_(tUnit);

    // Project the vertices onto the sweep plane
    for (v = vHead.next; v !== vHead; v = v.next) {
      v.s = libtess.normal.dot_(v.coords, sUnit);
      v.t = libtess.normal.dot_(v.coords, tUnit);
    }

  } else {
    // Project perpendicular to a coordinate axis -- better numerically
    var sAxis = (i + 1) % 3;
    var tAxis = (i + 2) % 3;
    var tNegate = norm[i] > 0 ? 1 : -1;

    // Project the vertices onto the sweep plane
    for (v = vHead.next; v !== vHead; v = v.next) {
      v.s = v.coords[sAxis];
      v.t = tNegate * v.coords[tAxis];
    }
  }

  if (computedNormal) {
    libtess.normal.checkOrientation_(tess);
  }
};

// NOTE(bckenny): libtess.normal.dot_ is no longer called in code without
// libtess.TRUE_PROJECT defined.
/* istanbul ignore next */
/**
 * Computes the dot product of vectors u and v.
 * @private
 * @param {!Array<number>} u
 * @param {!Array<number>} v
 * @return {number}
 */
libtess.normal.dot_ = function(u, v) {
  return u[0] * v[0] + u[1] * v[1] + u[2] * v[2];
};

// NOTE(bckenny): only called from within libtess.normal.projectPolygon's
// TRUE_PROJECT branch, so ignoring for code coverage.
/* istanbul ignore next */
/**
 * Normalize vector v.
 * @private
 * @param {!Array<number>} v
 */
libtess.normal.normalize_ = function(v) {
  var len = v[0] * v[0] + v[1] * v[1] + v[2] * v[2];

  libtess.assert(len > 0);
  len = Math.sqrt(len);
  v[0] /= len;
  v[1] /= len;
  v[2] /= len;
};

/**
 * Returns the index of the longest component of vector v.
 * @private
 * @param {!Array<number>} v
 * @return {number}
 */
libtess.normal.longAxis_ = function(v) {
  var i = 0;

  if (Math.abs(v[1]) > Math.abs(v[0])) {
    i = 1;
  }
  if (Math.abs(v[2]) > Math.abs(v[i])) {
    i = 2;
  }

  return i;
};

/**
 * Compute an approximate normal of the polygon from the vertices themselves.
 * Result returned in norm.
 * @private
 * @param {!libtess.GluTesselator} tess
 * @param {!Array<number>} norm
 */
libtess.normal.computeNormal_ = function(tess, norm) {
  var maxVal = [
    -2 * libtess.GLU_TESS_MAX_COORD,
    -2 * libtess.GLU_TESS_MAX_COORD,
    -2 * libtess.GLU_TESS_MAX_COORD
  ];
  var minVal = [
    2 * libtess.GLU_TESS_MAX_COORD,
    2 * libtess.GLU_TESS_MAX_COORD,
    2 * libtess.GLU_TESS_MAX_COORD
  ];
  var maxVert = [];
  var minVert = [];

  var v;
  var vHead = tess.mesh.vHead;
  for (v = vHead.next; v !== vHead; v = v.next) {
    for (var i = 0; i < 3; ++i) {
      var c = v.coords[i];
      if (c < minVal[i]) { minVal[i] = c; minVert[i] = v; }
      if (c > maxVal[i]) { maxVal[i] = c; maxVert[i] = v; }
    }
  }

  // Find two vertices separated by at least 1/sqrt(3) of the maximum
  // distance between any two vertices
  var index = 0;
  if (maxVal[1] - minVal[1] > maxVal[0] - minVal[0]) { index = 1; }
  if (maxVal[2] - minVal[2] > maxVal[index] - minVal[index]) { index = 2; }
  if (minVal[index] >= maxVal[index]) {
    // All vertices are the same -- normal doesn't matter
    norm[0] = 0; norm[1] = 0; norm[2] = 1;
    return;
  }

  // Look for a third vertex which forms the triangle with maximum area
  // (Length of normal == twice the triangle area)
  var maxLen2 = 0;
  var v1 = minVert[index];
  var v2 = maxVert[index];
  var tNorm = [0, 0, 0];
  var d1 = [
    v1.coords[0] - v2.coords[0],
    v1.coords[1] - v2.coords[1],
    v1.coords[2] - v2.coords[2]
  ];
  var d2 = [0, 0, 0];
  for (v = vHead.next; v !== vHead; v = v.next) {
    d2[0] = v.coords[0] - v2.coords[0];
    d2[1] = v.coords[1] - v2.coords[1];
    d2[2] = v.coords[2] - v2.coords[2];
    tNorm[0] = d1[1] * d2[2] - d1[2] * d2[1];
    tNorm[1] = d1[2] * d2[0] - d1[0] * d2[2];
    tNorm[2] = d1[0] * d2[1] - d1[1] * d2[0];
    var tLen2 = tNorm[0] * tNorm[0] + tNorm[1] * tNorm[1] + tNorm[2] * tNorm[2];
    if (tLen2 > maxLen2) {
      maxLen2 = tLen2;
      norm[0] = tNorm[0];
      norm[1] = tNorm[1];
      norm[2] = tNorm[2];
    }
  }

  if (maxLen2 <= 0) {
    // All points lie on a single line -- any decent normal will do
    norm[0] = norm[1] = norm[2] = 0;
    norm[libtess.normal.longAxis_(d1)] = 1;
  }
};

/**
 * Check that the sum of the signed area of all projected contours is
 * non-negative. If not, negate the t-coordinates to reverse the orientation and
 * make it so.
 * @private
 * @param {!libtess.GluTesselator} tess
 */
libtess.normal.checkOrientation_ = function(tess) {
  var area = 0;
  var fHead = tess.mesh.fHead;
  for (var f = fHead.next; f !== fHead; f = f.next) {
    var e = f.anEdge;
    if (e.winding <= 0) { continue; }
    do {
      area += (e.org.s - e.dst().s) * (e.org.t + e.dst().t);
      e = e.lNext;
    } while (e !== f.anEdge);
  }

  if (area < 0) {
    // Reverse the orientation by flipping all the t-coordinates
    var vHead = tess.mesh.vHead;
    for (var v = vHead.next; v !== vHead; v = v.next) {
      v.t = -v.t;
    }
  }
};

/* global libtess */

/** @const */
libtess.render = {};

/**
 * Takes a mesh, breaks it into separate triangles, and renders them. The
 * rendering output is provided as callbacks (see the API). Set flagEdges to
 * true to get edgeFlag callbacks (tess.flagBoundary in original libtess).
 * @param {!libtess.GluTesselator} tess
 * @param {!libtess.GluMesh} mesh
 * @param {boolean} flagEdges
 */
libtess.render.renderMesh = function(tess, mesh, flagEdges) {
  var beginCallbackCalled = false;

  // TODO(bckenny): edgeState needs to be boolean, but !== on first call
  // force edge state output for first vertex
  var edgeState = -1;

  // We examine all faces in an arbitrary order. Whenever we find
  // an inside triangle f, we render f.
  // NOTE(bckenny): go backwards through face list to match original libtess
  // triangle order
  for (var f = mesh.fHead.prev; f !== mesh.fHead; f = f.prev) {
    if (f.inside) {
      // We're going to emit a triangle, so call begin callback once
      if (!beginCallbackCalled) {
        tess.callBeginCallback(libtess.primitiveType.GL_TRIANGLES);
        beginCallbackCalled = true;
      }

      // check that face has only three edges
      var e = f.anEdge;
      libtess.assert(e.lNext.lNext.lNext === e,
          'renderMesh called with non-triangulated mesh');
      // Loop once for each edge (there will always be 3 edges)
      do {
        if (flagEdges) {
          // Set the "edge state" to true just before we output the
          // first vertex of each edge on the polygon boundary.
          var newState = !e.rFace().inside ? 1 : 0; // TODO(bckenny): total hack to get edgeState working. fix me.
          if (edgeState !== newState) {
            edgeState = newState;
            // TODO(bckenny): edgeState should be boolean now
            tess.callEdgeFlagCallback(!!edgeState);
          }
        }

        // emit vertex
        tess.callVertexCallback(e.org.data);

        e = e.lNext;
      } while (e !== f.anEdge);
    }
  }

  // only call end callback if begin was called
  if (beginCallbackCalled) {
    tess.callEndCallback();
  }
};

/**
 * Takes a mesh, and outputs one contour for each face marked "inside". The
 * rendering output is provided as callbacks (see the API).
 * @param {!libtess.GluTesselator} tess
 * @param {!libtess.GluMesh} mesh
 */
libtess.render.renderBoundary = function(tess, mesh) {
  for (var f = mesh.fHead.next; f !== mesh.fHead; f = f.next) {
    if (f.inside) {
      tess.callBeginCallback(libtess.primitiveType.GL_LINE_LOOP);

      var e = f.anEdge;
      do {
        tess.callVertexCallback(e.org.data);
        e = e.lNext;
      } while (e !== f.anEdge);

      tess.callEndCallback();
    }
  }
};

/* global libtess */

// TODO(bckenny): a number of these never return null (as opposed to original) and should be typed appropriately

/*
 * Invariants for the Edge Dictionary.
 * - each pair of adjacent edges e2=succ(e1) satisfies edgeLeq_(e1,e2)
 *   at any valid location of the sweep event
 * - if edgeLeq_(e2,e1) as well (at any valid sweep event), then e1 and e2
 *   share a common endpoint
 * - for each e, e.dst() has been processed, but not e.org
 * - each edge e satisfies vertLeq(e.dst(),event) && vertLeq(event,e.org)
 *   where "event" is the current sweep line event.
 * - no edge e has zero length
 *
 * Invariants for the Mesh (the processed portion).
 * - the portion of the mesh left of the sweep line is a planar graph,
 *   ie. there is *some* way to embed it in the plane
 * - no processed edge has zero length
 * - no two processed vertices have identical coordinates
 * - each "inside" region is monotone, ie. can be broken into two chains
 *   of monotonically increasing vertices according to VertLeq(v1,v2)
 *   - a non-invariant: these chains may intersect (very slightly)
 *
 * Invariants for the Sweep.
 * - if none of the edges incident to the event vertex have an activeRegion
 *   (ie. none of these edges are in the edge dictionary), then the vertex
 *   has only right-going edges.
 * - if an edge is marked "fixUpperEdge" (it is a temporary edge introduced
 *   by ConnectRightVertex), then it is the only right-going edge from
 *   its associated vertex.  (This says that these edges exist only
 *   when it is necessary.)
 */

/** @const */
libtess.sweep = {};


/**
 * Make the sentinel coordinates big enough that they will never be
 * merged with real input features.  (Even with the largest possible
 * input contour and the maximum tolerance of 1.0, no merging will be
 * done with coordinates larger than 3 * libtess.GLU_TESS_MAX_COORD).
 * @private
 * @const
 * @type {number}
 */
libtess.sweep.SENTINEL_COORD_ = 4 * libtess.GLU_TESS_MAX_COORD;


/**
 * Because vertices at exactly the same location are merged together
 * before we process the sweep event, some degenerate cases can't occur.
 * However if someone eventually makes the modifications required to
 * merge features which are close together, the cases below marked
 * TOLERANCE_NONZERO will be useful.  They were debugged before the
 * code to merge identical vertices in the main loop was added.
 * @private
 * @const
 * @type {boolean}
 */
libtess.sweep.TOLERANCE_NONZERO_ = false;


/**
 * computeInterior(tess) computes the planar arrangement specified
 * by the given contours, and further subdivides this arrangement
 * into regions. Each region is marked "inside" if it belongs
 * to the polygon, according to the rule given by tess.windingRule.
 * Each interior region is guaranteed be monotone.
 *
 * @param {libtess.GluTesselator} tess [description].
 */
libtess.sweep.computeInterior = function(tess) {
  tess.fatalError = false;

  // Each vertex defines an event for our sweep line. Start by inserting
  // all the vertices in a priority queue. Events are processed in
  // lexicographic order, ie.
  // e1 < e2  iff  e1.x < e2.x || (e1.x == e2.x && e1.y < e2.y)
  libtess.sweep.removeDegenerateEdges_(tess);
  libtess.sweep.initPriorityQ_(tess);
  libtess.sweep.initEdgeDict_(tess);

  var v;
  while ((v = tess.pq.extractMin()) !== null) {
    for (;;) {
      var vNext = tess.pq.minimum();
      if (vNext === null || !libtess.geom.vertEq(vNext, v)) {
        break;
      }

      /* Merge together all vertices at exactly the same location.
       * This is more efficient than processing them one at a time,
       * simplifies the code (see connectLeftDegenerate), and is also
       * important for correct handling of certain degenerate cases.
       * For example, suppose there are two identical edges A and B
       * that belong to different contours (so without this code they would
       * be processed by separate sweep events).  Suppose another edge C
       * crosses A and B from above.  When A is processed, we split it
       * at its intersection point with C.  However this also splits C,
       * so when we insert B we may compute a slightly different
       * intersection point.  This might leave two edges with a small
       * gap between them.  This kind of error is especially obvious
       * when using boundary extraction (GLU_TESS_BOUNDARY_ONLY).
       */
      vNext = tess.pq.extractMin();
      libtess.sweep.spliceMergeVertices_(tess, v.anEdge, vNext.anEdge);
    }
    libtess.sweep.sweepEvent_(tess, v);
  }

  // TODO(bckenny): what does the next comment mean? can we eliminate event except when debugging?
  // Set tess.event for debugging purposes
  var minRegion = tess.dict.getMin().getKey();
  tess.event = minRegion.eUp.org;
  libtess.sweep.doneEdgeDict_(tess);
  libtess.sweep.donePriorityQ_(tess);

  libtess.sweep.removeDegenerateFaces_(tess.mesh);
  tess.mesh.checkMesh();
};


/**
 * When we merge two edges into one, we need to compute the combined
 * winding of the new edge.
 * @private
 * @param {libtess.GluHalfEdge} eDst [description].
 * @param {libtess.GluHalfEdge} eSrc [description].
 */
libtess.sweep.addWinding_ = function(eDst, eSrc) {
  // NOTE(bckenny): from AddWinding macro
  eDst.winding += eSrc.winding;
  eDst.sym.winding += eSrc.sym.winding;
};


/**
 * Both edges must be directed from right to left (this is the canonical
 * direction for the upper edge of each region).
 *
 * The strategy is to evaluate a "t" value for each edge at the
 * current sweep line position, given by tess.event.  The calculations
 * are designed to be very stable, but of course they are not perfect.
 *
 * Special case: if both edge destinations are at the sweep event,
 * we sort the edges by slope (they would otherwise compare equally).
 *
 * @private
 * @param {!libtess.GluTesselator} tess
 * @param {!libtess.ActiveRegion} reg1
 * @param {!libtess.ActiveRegion} reg2
 * @return {boolean}
 */
libtess.sweep.edgeLeq_ = function(tess, reg1, reg2) {
  var event = tess.event;
  var e1 = reg1.eUp;
  var e2 = reg2.eUp;

  if (e1.dst() === event) {
    if (e2.dst() === event) {
      // Two edges right of the sweep line which meet at the sweep event.
      // Sort them by slope.
      if (libtess.geom.vertLeq(e1.org, e2.org)) {
        return libtess.geom.edgeSign(e2.dst(), e1.org, e2.org) <= 0;
      }

      return libtess.geom.edgeSign(e1.dst(), e2.org, e1.org) >= 0;
    }

    return libtess.geom.edgeSign(e2.dst(), event, e2.org) <= 0;
  }

  if (e2.dst() === event) {
    return libtess.geom.edgeSign(e1.dst(), event, e1.org) >= 0;
  }

  // General case - compute signed distance *from* e1, e2 to event
  var t1 = libtess.geom.edgeEval(e1.dst(), event, e1.org);
  var t2 = libtess.geom.edgeEval(e2.dst(), event, e2.org);
  return (t1 >= t2);
};


/**
 * [deleteRegion_ description]
 * @private
 * @param {libtess.GluTesselator} tess [description].
 * @param {libtess.ActiveRegion} reg [description].
 */
libtess.sweep.deleteRegion_ = function(tess, reg) {
  if (reg.fixUpperEdge) {
    // It was created with zero winding number, so it better be
    // deleted with zero winding number (ie. it better not get merged
    // with a real edge).
    libtess.assert(reg.eUp.winding === 0);
  }

  reg.eUp.activeRegion = null;

  tess.dict.deleteNode(reg.nodeUp);
  reg.nodeUp = null;

  // memFree( reg ); TODO(bckenny)
  // TODO(bckenny): may need to null at callsite
};


/**
 * Replace an upper edge which needs fixing (see connectRightVertex).
 * @private
 * @param {libtess.ActiveRegion} reg [description].
 * @param {libtess.GluHalfEdge} newEdge [description].
 */
libtess.sweep.fixUpperEdge_ = function(reg, newEdge) {
  libtess.assert(reg.fixUpperEdge);
  libtess.mesh.deleteEdge(reg.eUp);

  reg.fixUpperEdge = false;
  reg.eUp = newEdge;
  newEdge.activeRegion = reg;
};


/**
 * Find the region above the uppermost edge with the same origin.
 * @private
 * @param {libtess.ActiveRegion} reg [description].
 * @return {libtess.ActiveRegion} [description].
 */
libtess.sweep.topLeftRegion_ = function(reg) {
  var org = reg.eUp.org;

  // Find the region above the uppermost edge with the same origin
  do {
    reg = reg.regionAbove();
  } while (reg.eUp.org === org);

  // If the edge above was a temporary edge introduced by connectRightVertex,
  // now is the time to fix it.
  if (reg.fixUpperEdge) {
    var e = libtess.mesh.connect(reg.regionBelow().eUp.sym, reg.eUp.lNext);
    libtess.sweep.fixUpperEdge_(reg, e);
    reg = reg.regionAbove();
  }

  return reg;
};


/**
 * Find the region above the uppermost edge with the same destination.
 * @private
 * @param {libtess.ActiveRegion} reg [description].
 * @return {libtess.ActiveRegion} [description].
 */
libtess.sweep.topRightRegion_ = function(reg) {
  var dst = reg.eUp.dst();

  do {
    reg = reg.regionAbove();
  } while (reg.eUp.dst() === dst);

  return reg;
};


/**
 * Add a new active region to the sweep line, *somewhere* below "regAbove"
 * (according to where the new edge belongs in the sweep-line dictionary).
 * The upper edge of the new region will be "eNewUp".
 * Winding number and "inside" flag are not updated.
 *
 * @private
 * @param {libtess.GluTesselator} tess [description].
 * @param {libtess.ActiveRegion} regAbove [description].
 * @param {libtess.GluHalfEdge} eNewUp [description].
 * @return {libtess.ActiveRegion} regNew.
 */
libtess.sweep.addRegionBelow_ = function(tess, regAbove, eNewUp) {
  var regNew = new libtess.ActiveRegion();

  regNew.eUp = eNewUp;
  regNew.nodeUp = tess.dict.insertBefore(regAbove.nodeUp, regNew);
  eNewUp.activeRegion = regNew;

  return regNew;
};


/**
 * [isWindingInside_ description]
 * @private
 * @param {libtess.GluTesselator} tess [description].
 * @param {number} n int.
 * @return {boolean} [description].
 */
libtess.sweep.isWindingInside_ = function(tess, n) {
  switch (tess.windingRule) {
    case libtess.windingRule.GLU_TESS_WINDING_ODD:
      return ((n & 1) !== 0);
    case libtess.windingRule.GLU_TESS_WINDING_NONZERO:
      return (n !== 0);
    case libtess.windingRule.GLU_TESS_WINDING_POSITIVE:
      return (n > 0);
    case libtess.windingRule.GLU_TESS_WINDING_NEGATIVE:
      return (n < 0);
    case libtess.windingRule.GLU_TESS_WINDING_ABS_GEQ_TWO:
      return (n >= 2) || (n <= -2);
  }

  // TODO(bckenny): not reached
  libtess.assert(false);
  return false;
};


/**
 * [computeWinding_ description]
 * @private
 * @param {libtess.GluTesselator} tess [description].
 * @param {libtess.ActiveRegion} reg [description].
 */
libtess.sweep.computeWinding_ = function(tess, reg) {
  reg.windingNumber = reg.regionAbove().windingNumber + reg.eUp.winding;
  reg.inside = libtess.sweep.isWindingInside_(tess, reg.windingNumber);
};


/**
 * Delete a region from the sweep line. This happens when the upper
 * and lower chains of a region meet (at a vertex on the sweep line).
 * The "inside" flag is copied to the appropriate mesh face (we could
 * not do this before -- since the structure of the mesh is always
 * changing, this face may not have even existed until now).
 *
 * @private
 * @param {libtess.GluTesselator} tess [description].
 * @param {libtess.ActiveRegion} reg [description].
 */
libtess.sweep.finishRegion_ = function(tess, reg) {
  // TODO(bckenny): may need to null reg at callsite

  var e = reg.eUp;
  var f = e.lFace;

  f.inside = reg.inside;
  f.anEdge = e;   // optimization for tessmono.tessellateMonoRegion() // TODO(bckenny): how so?
  libtess.sweep.deleteRegion_(tess, reg);
};


/**
 * We are given a vertex with one or more left-going edges. All affected
 * edges should be in the edge dictionary. Starting at regFirst.eUp,
 * we walk down deleting all regions where both edges have the same
 * origin vOrg. At the same time we copy the "inside" flag from the
 * active region to the face, since at this point each face will belong
 * to at most one region (this was not necessarily true until this point
 * in the sweep). The walk stops at the region above regLast; if regLast
 * is null we walk as far as possible. At the same time we relink the
 * mesh if necessary, so that the ordering of edges around vOrg is the
 * same as in the dictionary.
 *
 * @private
 * @param {libtess.GluTesselator} tess [description].
 * @param {libtess.ActiveRegion} regFirst [description].
 * @param {libtess.ActiveRegion} regLast [description].
 * @return {libtess.GluHalfEdge} [description].
 */
libtess.sweep.finishLeftRegions_ = function(tess, regFirst, regLast) {
  var regPrev = regFirst;
  var ePrev = regFirst.eUp;
  while (regPrev !== regLast) {
    // placement was OK
    regPrev.fixUpperEdge = false;
    var reg = regPrev.regionBelow();
    var e = reg.eUp;
    if (e.org !== ePrev.org) {
      if (!reg.fixUpperEdge) {
        /* Remove the last left-going edge. Even though there are no further
         * edges in the dictionary with this origin, there may be further
         * such edges in the mesh (if we are adding left edges to a vertex
         * that has already been processed). Thus it is important to call
         * finishRegion rather than just deleteRegion.
         */
        libtess.sweep.finishRegion_(tess, regPrev);
        break;
      }

      // If the edge below was a temporary edge introduced by
      // connectRightVertex, now is the time to fix it.
      e = libtess.mesh.connect(ePrev.lPrev(), e.sym);
      libtess.sweep.fixUpperEdge_(reg, e);
    }

    // Relink edges so that ePrev.oNext === e
    if (ePrev.oNext !== e) {
      libtess.mesh.meshSplice(e.oPrev(), e);
      libtess.mesh.meshSplice(ePrev, e);
    }

    // may change reg.eUp
    libtess.sweep.finishRegion_(tess, regPrev);
    ePrev = reg.eUp;
    regPrev = reg;
  }

  return ePrev;
};


/**
 * Purpose: insert right-going edges into the edge dictionary, and update
 * winding numbers and mesh connectivity appropriately. All right-going
 * edges share a common origin vOrg. Edges are inserted CCW starting at
 * eFirst; the last edge inserted is eLast.oPrev. If vOrg has any
 * left-going edges already processed, then eTopLeft must be the edge
 * such that an imaginary upward vertical segment from vOrg would be
 * contained between eTopLeft.oPrev and eTopLeft; otherwise eTopLeft
 * should be null.
 *
 * @private
 * @param {libtess.GluTesselator} tess [description].
 * @param {libtess.ActiveRegion} regUp [description].
 * @param {libtess.GluHalfEdge} eFirst [description].
 * @param {libtess.GluHalfEdge} eLast [description].
 * @param {libtess.GluHalfEdge} eTopLeft [description].
 * @param {boolean} cleanUp [description].
 */
libtess.sweep.addRightEdges_ = function(tess, regUp, eFirst, eLast, eTopLeft,
    cleanUp) {

  var firstTime = true;

  // Insert the new right-going edges in the dictionary
  var e = eFirst;
  do {
    libtess.assert(libtess.geom.vertLeq(e.org, e.dst()));
    libtess.sweep.addRegionBelow_(tess, regUp, e.sym);
    e = e.oNext;
  } while (e !== eLast);

  // Walk *all* right-going edges from e.org, in the dictionary order,
  // updating the winding numbers of each region, and re-linking the mesh
  // edges to match the dictionary ordering (if necessary).
  if (eTopLeft === null) {
    eTopLeft = regUp.regionBelow().eUp.rPrev();
  }
  var regPrev = regUp;
  var ePrev = eTopLeft;
  var reg;
  for (;;) {
    reg = regPrev.regionBelow();
    e = reg.eUp.sym;
    if (e.org !== ePrev.org) {
      break;
    }

    if (e.oNext !== ePrev) {
      // Unlink e from its current position, and relink below ePrev
      libtess.mesh.meshSplice(e.oPrev(), e);
      libtess.mesh.meshSplice(ePrev.oPrev(), e);
    }
    // Compute the winding number and "inside" flag for the new regions
    reg.windingNumber = regPrev.windingNumber - e.winding;
    reg.inside = libtess.sweep.isWindingInside_(tess, reg.windingNumber);

    // Check for two outgoing edges with same slope -- process these
    // before any intersection tests (see example in libtess.sweep.computeInterior).
    regPrev.dirty = true;
    if (!firstTime && libtess.sweep.checkForRightSplice_(tess, regPrev)) {
      libtess.sweep.addWinding_(e, ePrev);
      libtess.sweep.deleteRegion_(tess, regPrev); // TODO(bckenny): need to null regPrev anywhere else?
      libtess.mesh.deleteEdge(ePrev);
    }
    firstTime = false;
    regPrev = reg;
    ePrev = e;
  }

  regPrev.dirty = true;
  libtess.assert(regPrev.windingNumber - e.winding === reg.windingNumber);

  if (cleanUp) {
    // Check for intersections between newly adjacent edges.
    libtess.sweep.walkDirtyRegions_(tess, regPrev);
  }
};


/**
 * Set up data for and call GLU_TESS_COMBINE callback on GluTesselator.
 * @private
 * @param {!libtess.GluTesselator} tess
 * @param {!libtess.GluVertex} isect A raw vertex at the intersection.
 * @param {!Array<Object>} data The vertices of the intersecting edges.
 * @param {!Array<number>} weights The linear combination coefficients for this intersection.
 * @param {boolean} needed Whether a returned vertex is necessary in this case.
 */
libtess.sweep.callCombine_ = function(tess, isect, data, weights, needed) {
  // Copy coord data in case the callback changes it.
  var coords = [
    isect.coords[0],
    isect.coords[1],
    isect.coords[2]
  ];

  isect.data = null;
  isect.data = tess.callCombineCallback(coords, data, weights);
  if (isect.data === null) {
    if (!needed) {
      // not needed, so just use data from first vertex
      isect.data = data[0];

    } else if (!tess.fatalError) {
      // The only way fatal error is when two edges are found to intersect,
      // but the user has not provided the callback necessary to handle
      // generated intersection points.
      tess.callErrorCallback(libtess.errorType.GLU_TESS_NEED_COMBINE_CALLBACK);
      tess.fatalError = true;
    }
  }
};


/**
 * Two vertices with idential coordinates are combined into one.
 * e1.org is kept, while e2.org is discarded.
 * @private
 * @param {!libtess.GluTesselator} tess
 * @param {libtess.GluHalfEdge} e1 [description].
 * @param {libtess.GluHalfEdge} e2 [description].
 */
libtess.sweep.spliceMergeVertices_ = function(tess, e1, e2) {
  // TODO(bckenny): better way to init these? save them?
  var data = [null, null, null, null];
  var weights = [0.5, 0.5, 0, 0];

  data[0] = e1.org.data;
  data[1] = e2.org.data;
  libtess.sweep.callCombine_(tess, e1.org, data, weights, false);
  libtess.mesh.meshSplice(e1, e2);
};


/**
 * Find some weights which describe how the intersection vertex is
 * a linear combination of org and dst. Each of the two edges
 * which generated "isect" is allocated 50% of the weight; each edge
 * splits the weight between its org and dst according to the
 * relative distance to "isect".
 *
 * @private
 * @param {libtess.GluVertex} isect [description].
 * @param {libtess.GluVertex} org [description].
 * @param {libtess.GluVertex} dst [description].
 * @param {Array.<number>} weights [description].
 * @param {number} weightIndex Index into weights for first weight to supply.
 */
libtess.sweep.vertexWeights_ = function(isect, org, dst, weights, weightIndex) {
  // TODO(bckenny): think through how we can use L1dist here and be correct for coords
  var t1 = libtess.geom.vertL1dist(org, isect);
  var t2 = libtess.geom.vertL1dist(dst, isect);

  // TODO(bckenny): introduced weightIndex to mimic addressing in original
  // 1) document (though it is private and only used from getIntersectData)
  // 2) better way? manually inline into getIntersectData? supply two two-length tmp arrays?
  var i0 = weightIndex;
  var i1 = weightIndex + 1;
  weights[i0] = 0.5 * t2 / (t1 + t2);
  weights[i1] = 0.5 * t1 / (t1 + t2);
  isect.coords[0] += weights[i0] * org.coords[0] + weights[i1] * dst.coords[0];
  isect.coords[1] += weights[i0] * org.coords[1] + weights[i1] * dst.coords[1];
  isect.coords[2] += weights[i0] * org.coords[2] + weights[i1] * dst.coords[2];
};


/**
 * We've computed a new intersection point, now we need a "data" pointer
 * from the user so that we can refer to this new vertex in the
 * rendering callbacks.
 * @private
 * @param {!libtess.GluTesselator} tess
 * @param {libtess.GluVertex} isect [description].
 * @param {libtess.GluVertex} orgUp [description].
 * @param {libtess.GluVertex} dstUp [description].
 * @param {libtess.GluVertex} orgLo [description].
 * @param {libtess.GluVertex} dstLo [description].
 */
libtess.sweep.getIntersectData_ = function(tess, isect, orgUp, dstUp, orgLo,
    dstLo) {

  // TODO(bckenny): called for every intersection event, should these be from a pool?
  // TODO(bckenny): better way to init these?
  var weights = [0, 0, 0, 0];
  var data = [
    orgUp.data,
    dstUp.data,
    orgLo.data,
    dstLo.data
  ];

  // TODO(bckenny): it appears isect is a reappropriated vertex, so does need to be zeroed.
  // double check this.
  isect.coords[0] = isect.coords[1] = isect.coords[2] = 0;

  // TODO(bckenny): see note in libtess.sweep.vertexWeights_ for explanation of weightIndex. fix?
  libtess.sweep.vertexWeights_(isect, orgUp, dstUp, weights, 0);
  libtess.sweep.vertexWeights_(isect, orgLo, dstLo, weights, 2);

  libtess.sweep.callCombine_(tess, isect, data, weights, true);
};


/**
 * Check the upper and lower edge of regUp, to make sure that the
 * eUp.org is above eLo, or eLo.org is below eUp (depending on which
 * origin is leftmost).
 *
 * The main purpose is to splice right-going edges with the same
 * dest vertex and nearly identical slopes (ie. we can't distinguish
 * the slopes numerically). However the splicing can also help us
 * to recover from numerical errors. For example, suppose at one
 * point we checked eUp and eLo, and decided that eUp.org is barely
 * above eLo. Then later, we split eLo into two edges (eg. from
 * a splice operation like this one). This can change the result of
 * our test so that now eUp.org is incident to eLo, or barely below it.
 * We must correct this condition to maintain the dictionary invariants.
 *
 * One possibility is to check these edges for intersection again
 * (i.e. checkForIntersect). This is what we do if possible. However
 * checkForIntersect requires that tess.event lies between eUp and eLo,
 * so that it has something to fall back on when the intersection
 * calculation gives us an unusable answer. So, for those cases where
 * we can't check for intersection, this routine fixes the problem
 * by just splicing the offending vertex into the other edge.
 * This is a guaranteed solution, no matter how degenerate things get.
 * Basically this is a combinatorial solution to a numerical problem.
 *
 * @private
 * @param {libtess.GluTesselator} tess [description].
 * @param {libtess.ActiveRegion} regUp [description].
 * @return {boolean} [description].
 */
libtess.sweep.checkForRightSplice_ = function(tess, regUp) {
  // TODO(bckenny): fully learn how these two checks work

  var regLo = regUp.regionBelow();
  var eUp = regUp.eUp;
  var eLo = regLo.eUp;

  if (libtess.geom.vertLeq(eUp.org, eLo.org)) {
    if (libtess.geom.edgeSign(eLo.dst(), eUp.org, eLo.org) > 0) {
      return false;
    }

    // eUp.org appears to be below eLo
    if (!libtess.geom.vertEq(eUp.org, eLo.org)) {
      // Splice eUp.org into eLo
      libtess.mesh.splitEdge(eLo.sym);
      libtess.mesh.meshSplice(eUp, eLo.oPrev());
      regUp.dirty = regLo.dirty = true;

    } else if (eUp.org !== eLo.org) {
      // merge the two vertices, discarding eUp.org
      tess.pq.remove(eUp.org.pqHandle);
      libtess.sweep.spliceMergeVertices_(tess, eLo.oPrev(), eUp);
    }

  } else {
    if (libtess.geom.edgeSign(eUp.dst(), eLo.org, eUp.org) < 0) {
      return false;
    }

    // eLo.org appears to be above eUp, so splice eLo.org into eUp
    regUp.regionAbove().dirty = regUp.dirty = true;
    libtess.mesh.splitEdge(eUp.sym);
    libtess.mesh.meshSplice(eLo.oPrev(), eUp);
  }

  return true;
};


/**
 * Check the upper and lower edge of regUp to make sure that the
 * eUp.dst() is above eLo, or eLo.dst() is below eUp (depending on which
 * destination is rightmost).
 *
 * Theoretically, this should always be true. However, splitting an edge
 * into two pieces can change the results of previous tests. For example,
 * suppose at one point we checked eUp and eLo, and decided that eUp.dst()
 * is barely above eLo. Then later, we split eLo into two edges (eg. from
 * a splice operation like this one). This can change the result of
 * the test so that now eUp.dst() is incident to eLo, or barely below it.
 * We must correct this condition to maintain the dictionary invariants
 * (otherwise new edges might get inserted in the wrong place in the
 * dictionary, and bad stuff will happen).
 *
 * We fix the problem by just splicing the offending vertex into the
 * other edge.
 *
 * @private
 * @param {libtess.GluTesselator} tess description].
 * @param {libtess.ActiveRegion} regUp [description].
 * @return {boolean} [description].
 */
libtess.sweep.checkForLeftSplice_ = function(tess, regUp) {
  var regLo = regUp.regionBelow();
  var eUp = regUp.eUp;
  var eLo = regLo.eUp;
  var e;

  libtess.assert(!libtess.geom.vertEq(eUp.dst(), eLo.dst()));

  if (libtess.geom.vertLeq(eUp.dst(), eLo.dst())) {
    if (libtess.geom.edgeSign(eUp.dst(), eLo.dst(), eUp.org) < 0) {
      return false;
    }

    // eLo.dst() is above eUp, so splice eLo.dst() into eUp
    regUp.regionAbove().dirty = regUp.dirty = true;
    e = libtess.mesh.splitEdge(eUp);
    libtess.mesh.meshSplice(eLo.sym, e);
    e.lFace.inside = regUp.inside;

  } else {
    if (libtess.geom.edgeSign(eLo.dst(), eUp.dst(), eLo.org) > 0) {
      return false;
    }

    // eUp.dst() is below eLo, so splice eUp.dst() into eLo
    regUp.dirty = regLo.dirty = true;
    e = libtess.mesh.splitEdge(eLo);
    libtess.mesh.meshSplice(eUp.lNext, eLo.sym);
    e.rFace().inside = regUp.inside;
  }

  return true;
};


/**
 * Check the upper and lower edges of the given region to see if
 * they intersect. If so, create the intersection and add it
 * to the data structures.
 *
 * Returns true if adding the new intersection resulted in a recursive
 * call to addRightEdges_(); in this case all "dirty" regions have been
 * checked for intersections, and possibly regUp has been deleted.
 *
 * @private
 * @param {libtess.GluTesselator} tess [description].
 * @param {libtess.ActiveRegion} regUp [description].
 * @return {boolean} [description].
 */
libtess.sweep.checkForIntersect_ = function(tess, regUp) {
  var regLo = regUp.regionBelow();
  var eUp = regUp.eUp;
  var eLo = regLo.eUp;
  var orgUp = eUp.org;
  var orgLo = eLo.org;
  var dstUp = eUp.dst();
  var dstLo = eLo.dst();

  var isect = new libtess.GluVertex();

  libtess.assert(!libtess.geom.vertEq(dstLo, dstUp));
  libtess.assert(libtess.geom.edgeSign(dstUp, tess.event, orgUp) <= 0);
  libtess.assert(libtess.geom.edgeSign(dstLo, tess.event, orgLo) >= 0);
  libtess.assert(orgUp !== tess.event && orgLo !== tess.event);
  libtess.assert(!regUp.fixUpperEdge && !regLo.fixUpperEdge);

  if (orgUp === orgLo) {
    // right endpoints are the same
    return false;
  }

  var tMinUp = Math.min(orgUp.t, dstUp.t);
  var tMaxLo = Math.max(orgLo.t, dstLo.t);
  if (tMinUp > tMaxLo) {
    // t ranges do not overlap
    return false;
  }

  if (libtess.geom.vertLeq(orgUp, orgLo)) {
    if (libtess.geom.edgeSign(dstLo, orgUp, orgLo) > 0) {
      return false;
    }
  } else {
    if (libtess.geom.edgeSign(dstUp, orgLo, orgUp) < 0) {
      return false;
    }
  }

  // At this point the edges intersect, at least marginally
  libtess.geom.edgeIntersect(dstUp, orgUp, dstLo, orgLo, isect);

  // The following properties are guaranteed:
  libtess.assert(Math.min(orgUp.t, dstUp.t) <= isect.t);
  libtess.assert(isect.t <= Math.max(orgLo.t, dstLo.t));
  libtess.assert(Math.min(dstLo.s, dstUp.s) <= isect.s);
  libtess.assert(isect.s <= Math.max(orgLo.s, orgUp.s));

  if (libtess.geom.vertLeq(isect, tess.event)) {
    /* The intersection point lies slightly to the left of the sweep line,
     * so move it until it's slightly to the right of the sweep line.
     * (If we had perfect numerical precision, this would never happen
     * in the first place). The easiest and safest thing to do is
     * replace the intersection by tess.event.
     */
    isect.s = tess.event.s;
    isect.t = tess.event.t;
  }

  // TODO(bckenny): try to find test54.d
  /* Similarly, if the computed intersection lies to the right of the
   * rightmost origin (which should rarely happen), it can cause
   * unbelievable inefficiency on sufficiently degenerate inputs.
   * (If you have the test program, try running test54.d with the
   * "X zoom" option turned on).
   */
  var orgMin = libtess.geom.vertLeq(orgUp, orgLo) ? orgUp : orgLo;
  if (libtess.geom.vertLeq(orgMin, isect)) {
    isect.s = orgMin.s;
    isect.t = orgMin.t;
  }

  if (libtess.geom.vertEq(isect, orgUp) || libtess.geom.vertEq(isect, orgLo)) {
    // Easy case -- intersection at one of the right endpoints
    libtess.sweep.checkForRightSplice_(tess, regUp);
    return false;
  }

  // TODO(bckenny): clean this up; length is distracting
  if ((!libtess.geom.vertEq(dstUp, tess.event) &&
      libtess.geom.edgeSign(dstUp, tess.event, isect) >= 0) ||
      (!libtess.geom.vertEq(dstLo, tess.event) &&
      libtess.geom.edgeSign(dstLo, tess.event, isect) <= 0)) {

    /* Very unusual -- the new upper or lower edge would pass on the
     * wrong side of the sweep event, or through it. This can happen
     * due to very small numerical errors in the intersection calculation.
     */
    if (dstLo === tess.event) {
      // Splice dstLo into eUp, and process the new region(s)
      libtess.mesh.splitEdge(eUp.sym);
      libtess.mesh.meshSplice(eLo.sym, eUp);
      regUp = libtess.sweep.topLeftRegion_(regUp);
      eUp = regUp.regionBelow().eUp;
      libtess.sweep.finishLeftRegions_(tess, regUp.regionBelow(), regLo);
      libtess.sweep.addRightEdges_(tess, regUp, eUp.oPrev(), eUp, eUp, true);
      return true;
    }

    if (dstUp === tess.event) {
      // Splice dstUp into eLo, and process the new region(s)
      libtess.mesh.splitEdge(eLo.sym);
      libtess.mesh.meshSplice(eUp.lNext, eLo.oPrev());
      regLo = regUp;
      regUp = libtess.sweep.topRightRegion_(regUp);
      var e = regUp.regionBelow().eUp.rPrev();
      regLo.eUp = eLo.oPrev();
      eLo = libtess.sweep.finishLeftRegions_(tess, regLo, null);
      libtess.sweep.addRightEdges_(tess, regUp, eLo.oNext, eUp.rPrev(), e,
          true);
      return true;
    }

    /* Special case: called from connectRightVertex. If either
     * edge passes on the wrong side of tess.event, split it
     * (and wait for connectRightVertex to splice it appropriately).
     */
    if (libtess.geom.edgeSign(dstUp, tess.event, isect) >= 0) {
      regUp.regionAbove().dirty = regUp.dirty = true;
      libtess.mesh.splitEdge(eUp.sym);
      eUp.org.s = tess.event.s;
      eUp.org.t = tess.event.t;
    }

    if (libtess.geom.edgeSign(dstLo, tess.event, isect) <= 0) {
      regUp.dirty = regLo.dirty = true;
      libtess.mesh.splitEdge(eLo.sym);
      eLo.org.s = tess.event.s;
      eLo.org.t = tess.event.t;
    }

    // leave the rest for connectRightVertex
    return false;
  }

  /* General case -- split both edges, splice into new vertex.
   * When we do the splice operation, the order of the arguments is
   * arbitrary as far as correctness goes. However, when the operation
   * creates a new face, the work done is proportional to the size of
   * the new face. We expect the faces in the processed part of
   * the mesh (ie. eUp.lFace) to be smaller than the faces in the
   * unprocessed original contours (which will be eLo.oPrev.lFace).
   */
  libtess.mesh.splitEdge(eUp.sym);
  libtess.mesh.splitEdge(eLo.sym);
  libtess.mesh.meshSplice(eLo.oPrev(), eUp);
  eUp.org.s = isect.s;
  eUp.org.t = isect.t;
  eUp.org.pqHandle = tess.pq.insert(eUp.org);
  libtess.sweep.getIntersectData_(tess, eUp.org, orgUp, dstUp, orgLo, dstLo);
  regUp.regionAbove().dirty = regUp.dirty = regLo.dirty = true;

  return false;
};


/**
 * When the upper or lower edge of any region changes, the region is
 * marked "dirty". This routine walks through all the dirty regions
 * and makes sure that the dictionary invariants are satisfied
 * (see the comments at the beginning of this file). Of course,
 * new dirty regions can be created as we make changes to restore
 * the invariants.
 * @private
 * @param {libtess.GluTesselator} tess [description].
 * @param {libtess.ActiveRegion} regUp [description].
 */
libtess.sweep.walkDirtyRegions_ = function(tess, regUp) {
  var regLo = regUp.regionBelow();

  for (;;) {
    // Find the lowest dirty region (we walk from the bottom up).
    while (regLo.dirty) {
      regUp = regLo;
      regLo = regLo.regionBelow();
    }
    if (!regUp.dirty) {
      regLo = regUp;
      regUp = regUp.regionAbove();
      if (regUp === null || !regUp.dirty) {
        // We've walked all the dirty regions
        return;
      }
    }

    regUp.dirty = false;
    var eUp = regUp.eUp;
    var eLo = regLo.eUp;

    if (eUp.dst() !== eLo.dst()) {
      // Check that the edge ordering is obeyed at the dst vertices.
      if (libtess.sweep.checkForLeftSplice_(tess, regUp)) {
        // If the upper or lower edge was marked fixUpperEdge, then
        // we no longer need it (since these edges are needed only for
        // vertices which otherwise have no right-going edges).
        if (regLo.fixUpperEdge) {
          libtess.sweep.deleteRegion_(tess, regLo);
          libtess.mesh.deleteEdge(eLo);
          regLo = regUp.regionBelow();
          eLo = regLo.eUp;

        } else if (regUp.fixUpperEdge) {
          libtess.sweep.deleteRegion_(tess, regUp);
          libtess.mesh.deleteEdge(eUp);
          regUp = regLo.regionAbove();
          eUp = regUp.eUp;
        }
      }
    }

    if (eUp.org !== eLo.org) {
      if (eUp.dst() !== eLo.dst() && !regUp.fixUpperEdge &&
          !regLo.fixUpperEdge &&
          (eUp.dst() === tess.event || eLo.dst() === tess.event)) {
        /* When all else fails in checkForIntersect(), it uses tess.event
         * as the intersection location. To make this possible, it requires
         * that tess.event lie between the upper and lower edges, and also
         * that neither of these is marked fixUpperEdge (since in the worst
         * case it might splice one of these edges into tess.event, and
         * violate the invariant that fixable edges are the only right-going
         * edge from their associated vertex).
         */
        if (libtess.sweep.checkForIntersect_(tess, regUp)) {
          // walkDirtyRegions() was called recursively; we're done
          return;
        }

      } else {
        // Even though we can't use checkForIntersect(), the org vertices
        // may violate the dictionary edge ordering. Check and correct this.
        libtess.sweep.checkForRightSplice_(tess, regUp);
      }
    }

    if (eUp.org === eLo.org && eUp.dst() === eLo.dst()) {
      // A degenerate loop consisting of only two edges -- delete it.
      libtess.sweep.addWinding_(eLo, eUp);
      libtess.sweep.deleteRegion_(tess, regUp);
      libtess.mesh.deleteEdge(eUp);
      regUp = regLo.regionAbove();
    }
  }
};


/**
 * Purpose: connect a "right" vertex vEvent (one where all edges go left)
 * to the unprocessed portion of the mesh. Since there are no right-going
 * edges, two regions (one above vEvent and one below) are being merged
 * into one. regUp is the upper of these two regions.
 *
 * There are two reasons for doing this (adding a right-going edge):
 *  - if the two regions being merged are "inside", we must add an edge
 *    to keep them separated (the combined region would not be monotone).
 *  - in any case, we must leave some record of vEvent in the dictionary,
 *    so that we can merge vEvent with features that we have not seen yet.
 *    For example, maybe there is a vertical edge which passes just to
 *    the right of vEvent; we would like to splice vEvent into this edge.
 *
 * However, we don't want to connect vEvent to just any vertex. We don't
 * want the new edge to cross any other edges; otherwise we will create
 * intersection vertices even when the input data had no self-intersections.
 * (This is a bad thing; if the user's input data has no intersections,
 * we don't want to generate any false intersections ourselves.)
 *
 * Our eventual goal is to connect vEvent to the leftmost unprocessed
 * vertex of the combined region (the union of regUp and regLo).
 * But because of unseen vertices with all right-going edges, and also
 * new vertices which may be created by edge intersections, we don't
 * know where that leftmost unprocessed vertex is. In the meantime, we
 * connect vEvent to the closest vertex of either chain, and mark the region
 * as "fixUpperEdge". This flag says to delete and reconnect this edge
 * to the next processed vertex on the boundary of the combined region.
 * Quite possibly the vertex we connected to will turn out to be the
 * closest one, in which case we won't need to make any changes.
 *
 * @private
 * @param {libtess.GluTesselator} tess [description].
 * @param {libtess.ActiveRegion} regUp [description].
 * @param {libtess.GluHalfEdge} eBottomLeft [description].
 */
libtess.sweep.connectRightVertex_ = function(tess, regUp, eBottomLeft) {
  var eTopLeft = eBottomLeft.oNext;
  var regLo = regUp.regionBelow();
  var eUp = regUp.eUp;
  var eLo = regLo.eUp;
  var degenerate = false;

  if (eUp.dst() !== eLo.dst()) {
    libtess.sweep.checkForIntersect_(tess, regUp);
  }

  // Possible new degeneracies: upper or lower edge of regUp may pass
  // through vEvent, or may coincide with new intersection vertex
  if (libtess.geom.vertEq(eUp.org, tess.event)) {
    libtess.mesh.meshSplice(eTopLeft.oPrev(), eUp);
    regUp = libtess.sweep.topLeftRegion_(regUp);
    eTopLeft = regUp.regionBelow().eUp;
    libtess.sweep.finishLeftRegions_(tess, regUp.regionBelow(), regLo);
    degenerate = true;
  }
  if (libtess.geom.vertEq(eLo.org, tess.event)) {
    libtess.mesh.meshSplice(eBottomLeft, eLo.oPrev());
    eBottomLeft = libtess.sweep.finishLeftRegions_(tess, regLo, null);
    degenerate = true;
  }
  if (degenerate) {
    libtess.sweep.addRightEdges_(tess, regUp, eBottomLeft.oNext, eTopLeft,
        eTopLeft, true);
    return;
  }

  // Non-degenerate situation -- need to add a temporary, fixable edge.
  // Connect to the closer of eLo.org, eUp.org.
  var eNew;
  if (libtess.geom.vertLeq(eLo.org, eUp.org)) {
    eNew = eLo.oPrev();
  } else {
    eNew = eUp;
  }
  eNew = libtess.mesh.connect(eBottomLeft.lPrev(), eNew);

  // Prevent cleanup, otherwise eNew might disappear before we've even
  // had a chance to mark it as a temporary edge.
  libtess.sweep.addRightEdges_(tess, regUp, eNew, eNew.oNext, eNew.oNext,
      false);
  eNew.sym.activeRegion.fixUpperEdge = true;
  libtess.sweep.walkDirtyRegions_(tess, regUp);
};


/**
 * The event vertex lies exacty on an already-processed edge or vertex.
 * Adding the new vertex involves splicing it into the already-processed
 * part of the mesh.
 * @private
 * @param {!libtess.GluTesselator} tess
 * @param {libtess.ActiveRegion} regUp [description].
 * @param {libtess.GluVertex} vEvent [description].
 */
libtess.sweep.connectLeftDegenerate_ = function(tess, regUp, vEvent) {
  var e = regUp.eUp;
  /* istanbul ignore if */
  if (libtess.geom.vertEq(e.org, vEvent)) {
    // NOTE(bckenny): this code is unreachable but remains for a hypothetical
    // future extension of libtess. See docs on libtess.sweep.TOLERANCE_NONZERO_
    // for more information. Conditional on TOLERANCE_NONZERO_ to help Closure
    // Compiler eliminate dead code.
    // e.org is an unprocessed vertex - just combine them, and wait
    // for e.org to be pulled from the queue
    libtess.assert(libtess.sweep.TOLERANCE_NONZERO_);
    if (libtess.sweep.TOLERANCE_NONZERO_) {
      libtess.sweep.spliceMergeVertices_(tess, e, vEvent.anEdge);
    }
    return;
  }

  if (!libtess.geom.vertEq(e.dst(), vEvent)) {
    // General case -- splice vEvent into edge e which passes through it
    libtess.mesh.splitEdge(e.sym);

    if (regUp.fixUpperEdge) {
      // This edge was fixable -- delete unused portion of original edge
      libtess.mesh.deleteEdge(e.oNext);
      regUp.fixUpperEdge = false;
    }

    libtess.mesh.meshSplice(vEvent.anEdge, e);

    // recurse
    libtess.sweep.sweepEvent_(tess, vEvent);
    return;
  }

  // NOTE(bckenny): this code is unreachable but remains for a hypothetical
  // future extension of libtess. See docs on libtess.sweep.TOLERANCE_NONZERO_
  // for more information. Conditional on TOLERANCE_NONZERO_ to help Closure
  // Compiler eliminate dead code.
  // vEvent coincides with e.dst(), which has already been processed.
  // Splice in the additional right-going edges.
  /* istanbul ignore next */
  libtess.assert(libtess.sweep.TOLERANCE_NONZERO_);

  /* istanbul ignore next */
  if (libtess.sweep.TOLERANCE_NONZERO_) {
    regUp = libtess.sweep.topRightRegion_(regUp);
    var reg = regUp.regionBelow();
    var eTopRight = reg.eUp.sym;
    var eTopLeft = eTopRight.oNext;
    var eLast = eTopLeft;

    if (reg.fixUpperEdge) {
      // Here e.dst() has only a single fixable edge going right.
      // We can delete it since now we have some real right-going edges.

      // there are some left edges too
      libtess.assert(eTopLeft !== eTopRight);
      libtess.sweep.deleteRegion_(tess, reg); // TODO(bckenny): something to null?
      libtess.mesh.deleteEdge(eTopRight);
      eTopRight = eTopLeft.oPrev();
    }

    libtess.mesh.meshSplice(vEvent.anEdge, eTopRight);
    if (!libtess.geom.edgeGoesLeft(eTopLeft)) {
      // e.dst() had no left-going edges -- indicate this to addRightEdges()
      eTopLeft = null;
    }

    libtess.sweep.addRightEdges_(tess, regUp, eTopRight.oNext, eLast, eTopLeft,
        true);
  }
};


/**
 * Connect a "left" vertex (one where both edges go right)
 * to the processed portion of the mesh. Let R be the active region
 * containing vEvent, and let U and L be the upper and lower edge
 * chains of R. There are two possibilities:
 *
 * - the normal case: split R into two regions, by connecting vEvent to
 *   the rightmost vertex of U or L lying to the left of the sweep line
 *
 * - the degenerate case: if vEvent is close enough to U or L, we
 *   merge vEvent into that edge chain. The subcases are:
 *  - merging with the rightmost vertex of U or L
 *  - merging with the active edge of U or L
 *  - merging with an already-processed portion of U or L
 *
 * @private
 * @param {libtess.GluTesselator} tess   [description].
 * @param {libtess.GluVertex} vEvent [description].
 */
libtess.sweep.connectLeftVertex_ = function(tess, vEvent) {
  // TODO(bckenny): tmp only used for sweep. better to keep tmp across calls?
  var tmp = new libtess.ActiveRegion();

  // NOTE(bckenny): this was commented out in the original
  // libtess.assert(vEvent.anEdge.oNext.oNext === vEvent.anEdge);

  // Get a pointer to the active region containing vEvent
  tmp.eUp = vEvent.anEdge.sym;
  var regUp = tess.dict.search(tmp).getKey();
  var regLo = regUp.regionBelow();
  var eUp = regUp.eUp;
  var eLo = regLo.eUp;

  // try merging with U or L first
  if (libtess.geom.edgeSign(eUp.dst(), vEvent, eUp.org) === 0) {
    libtess.sweep.connectLeftDegenerate_(tess, regUp, vEvent);
    return;
  }

  // Connect vEvent to rightmost processed vertex of either chain.
  // e.dst() is the vertex that we will connect to vEvent.
  var reg = libtess.geom.vertLeq(eLo.dst(), eUp.dst()) ? regUp : regLo;
  var eNew;
  if (regUp.inside || reg.fixUpperEdge) {
    if (reg === regUp) {
      eNew = libtess.mesh.connect(vEvent.anEdge.sym, eUp.lNext);

    } else {
      var tempHalfEdge = libtess.mesh.connect(eLo.dNext(), vEvent.anEdge);
      eNew = tempHalfEdge.sym;
    }

    if (reg.fixUpperEdge) {
      libtess.sweep.fixUpperEdge_(reg, eNew);

    } else {
      libtess.sweep.computeWinding_(tess,
          libtess.sweep.addRegionBelow_(tess, regUp, eNew));
    }
    libtess.sweep.sweepEvent_(tess, vEvent);

  } else {
    // The new vertex is in a region which does not belong to the polygon.
    // We don''t need to connect this vertex to the rest of the mesh.
    libtess.sweep.addRightEdges_(tess, regUp, vEvent.anEdge, vEvent.anEdge,
        null, true);
  }
};


/**
 * Does everything necessary when the sweep line crosses a vertex.
 * Updates the mesh and the edge dictionary.
 * @private
 * @param {libtess.GluTesselator} tess [description].
 * @param {libtess.GluVertex} vEvent [description].
 */
libtess.sweep.sweepEvent_ = function(tess, vEvent) {
  tess.event = vEvent; // for access in edgeLeq_ // TODO(bckenny): wuh?

  /* Check if this vertex is the right endpoint of an edge that is
   * already in the dictionary.  In this case we don't need to waste
   * time searching for the location to insert new edges.
   */
  var e = vEvent.anEdge;
  while (e.activeRegion === null) {
    e = e.oNext;
    if (e === vEvent.anEdge) {
      // All edges go right -- not incident to any processed edges
      libtess.sweep.connectLeftVertex_(tess, vEvent);
      return;
    }
  }

  /* Processing consists of two phases: first we "finish" all the
   * active regions where both the upper and lower edges terminate
   * at vEvent (ie. vEvent is closing off these regions).
   * We mark these faces "inside" or "outside" the polygon according
   * to their winding number, and delete the edges from the dictionary.
   * This takes care of all the left-going edges from vEvent.
   */
  var regUp = libtess.sweep.topLeftRegion_(e.activeRegion);
  var reg = regUp.regionBelow();
  var eTopLeft = reg.eUp;
  var eBottomLeft = libtess.sweep.finishLeftRegions_(tess, reg, null);

  /* Next we process all the right-going edges from vEvent. This
   * involves adding the edges to the dictionary, and creating the
   * associated "active regions" which record information about the
   * regions between adjacent dictionary edges.
   */
  if (eBottomLeft.oNext === eTopLeft) {
    // No right-going edges -- add a temporary "fixable" edge
    libtess.sweep.connectRightVertex_(tess, regUp, eBottomLeft);

  } else {
    libtess.sweep.addRightEdges_(tess, regUp, eBottomLeft.oNext, eTopLeft,
        eTopLeft, true);
  }
};


/**
 * We add two sentinel edges above and below all other edges,
 * to avoid special cases at the top and bottom.
 * @private
 * @param {libtess.GluTesselator} tess [description].
 * @param {number} t [description].
 */
libtess.sweep.addSentinel_ = function(tess, t) {
  var reg = new libtess.ActiveRegion();

  var e = libtess.mesh.makeEdge(tess.mesh);

  e.org.s = libtess.sweep.SENTINEL_COORD_;
  e.org.t = t;
  e.dst().s = -libtess.sweep.SENTINEL_COORD_;
  e.dst().t = t;
  tess.event = e.dst(); //initialize it

  reg.eUp = e;
  reg.windingNumber = 0;
  reg.inside = false;
  reg.fixUpperEdge = false;
  reg.sentinel = true;
  reg.dirty = false;
  reg.nodeUp = tess.dict.insert(reg);
};


/**
 * We maintain an ordering of edge intersections with the sweep line.
 * This order is maintained in a dynamic dictionary.
 * @private
 * @param {libtess.GluTesselator} tess [description].
 */
libtess.sweep.initEdgeDict_ = function(tess) {
  tess.dict = new libtess.Dict(tess, libtess.sweep.edgeLeq_);

  libtess.sweep.addSentinel_(tess, -libtess.sweep.SENTINEL_COORD_);
  libtess.sweep.addSentinel_(tess, libtess.sweep.SENTINEL_COORD_);
};


/**
 * [doneEdgeDict_ description]
 * @private
 * @param {libtess.GluTesselator} tess [description].
 */
libtess.sweep.doneEdgeDict_ = function(tess) {
  // NOTE(bckenny): fixedEdges is only used in the assert below, so ignore so
  // when asserts are removed jshint won't error.
  /* jshint unused:false */
  var fixedEdges = 0;

  var reg;
  while ((reg = tess.dict.getMin().getKey()) !== null) {
    // At the end of all processing, the dictionary should contain
    // only the two sentinel edges, plus at most one "fixable" edge
    // created by connectRightVertex().
    if (!reg.sentinel) {
      libtess.assert(reg.fixUpperEdge);
      libtess.assert(++fixedEdges === 1);
    }
    libtess.assert(reg.windingNumber === 0);
    libtess.sweep.deleteRegion_(tess, reg);
  }

  // NOTE(bckenny): see tess.dict.deleteDict_() for old delete dict function
  tess.dict = null;
};


/**
 * Remove zero-length edges, and contours with fewer than 3 vertices.
 * @private
 * @param {libtess.GluTesselator} tess [description].
 */
libtess.sweep.removeDegenerateEdges_ = function(tess) {
  var eHead = tess.mesh.eHead;

  var eNext;
  for (var e = eHead.next; e !== eHead; e = eNext) {
    eNext = e.next;
    var eLNext = e.lNext;

    if (libtess.geom.vertEq(e.org, e.dst()) && e.lNext.lNext !== e) {
      // Zero-length edge, contour has at least 3 edges
      libtess.sweep.spliceMergeVertices_(tess, eLNext, e); // deletes e.org
      libtess.mesh.deleteEdge(e); // e is a self-loop TODO(bckenny): does this comment really apply here?
      e = eLNext;
      eLNext = e.lNext;
    }

    if (eLNext.lNext === e) {
      // Degenerate contour (one or two edges)
      if (eLNext !== e) {
        if (eLNext === eNext || eLNext === eNext.sym) {
          eNext = eNext.next;
        }
        libtess.mesh.deleteEdge(eLNext);
      }

      if (e === eNext || e === eNext.sym) {
        eNext = eNext.next;
      }
      libtess.mesh.deleteEdge(e);
    }
  }
};


/**
 * Construct priority queue and insert all vertices into it, which determines
 * the order in which vertices cross the sweep line.
 * @private
 * @param {libtess.GluTesselator} tess [description].
 */
libtess.sweep.initPriorityQ_ = function(tess) {
  var pq = new libtess.PriorityQ();
  tess.pq = pq;

  var vHead = tess.mesh.vHead;
  var v;
  for (v = vHead.next; v !== vHead; v = v.next) {
    v.pqHandle = pq.insert(v);
  }

  pq.init();
};


/**
 * [donePriorityQ_ description]
 * @private
 * @param {libtess.GluTesselator} tess [description].
 */
libtess.sweep.donePriorityQ_ = function(tess) {
  // TODO(bckenny): probably don't need deleteQ. check that function for comment
  tess.pq.deleteQ();
  tess.pq = null;
};


/**
 * Delete any degenerate faces with only two edges. walkDirtyRegions()
 * will catch almost all of these, but it won't catch degenerate faces
 * produced by splice operations on already-processed edges.
 * The two places this can happen are in finishLeftRegions(), when
 * we splice in a "temporary" edge produced by connectRightVertex(),
 * and in checkForLeftSplice(), where we splice already-processed
 * edges to ensure that our dictionary invariants are not violated
 * by numerical errors.
 *
 * In both these cases it is *very* dangerous to delete the offending
 * edge at the time, since one of the routines further up the stack
 * will sometimes be keeping a pointer to that edge.
 *
 * @private
 * @param {libtess.GluMesh} mesh [description].
 */
libtess.sweep.removeDegenerateFaces_ = function(mesh) {
  var fNext;
  for (var f = mesh.fHead.next; f !== mesh.fHead; f = fNext) {
    fNext = f.next;
    var e = f.anEdge;
    libtess.assert(e.lNext !== e);

    if (e.lNext.lNext === e) {
      // A face with only two edges
      libtess.sweep.addWinding_(e.oNext, e);
      libtess.mesh.deleteEdge(e);
    }
  }
};

/* global libtess */

/** @const */
libtess.tessmono = {};

/**
 * Tessellates a monotone region (what else would it do??). The region must
 * consist of a single loop of half-edges (see mesh.js) oriented CCW. "Monotone"
 * in this case means that any vertical line intersects the interior of the
 * region in a single interval.
 *
 * Tessellation consists of adding interior edges (actually pairs of
 * half-edges), to split the region into non-overlapping triangles.
 * @private
 * @param {!libtess.GluFace} face
 */
libtess.tessmono.tessellateMonoRegion_ = function(face) {
  /* The basic idea is explained in Preparata and Shamos (which I don't
   * have handy right now), although their implementation is more
   * complicated than this one. The are two edge chains, an upper chain
   * and a lower chain. We process all vertices from both chains in order,
   * from right to left.
   *
   * The algorithm ensures that the following invariant holds after each
   * vertex is processed: the untessellated region consists of two
   * chains, where one chain (say the upper) is a single edge, and
   * the other chain is concave. The left vertex of the single edge
   * is always to the left of all vertices in the concave chain.
   *
   * Each step consists of adding the rightmost unprocessed vertex to one
   * of the two chains, and forming a fan of triangles from the rightmost
   * of two chain endpoints. Determining whether we can add each triangle
   * to the fan is a simple orientation test. By making the fan as large
   * as possible, we restore the invariant (check it yourself).
   *
   * All edges are oriented CCW around the boundary of the region.
   * First, find the half-edge whose origin vertex is rightmost.
   * Since the sweep goes from left to right, face.anEdge should
   * be close to the edge we want.
   */
  var up = face.anEdge;
  libtess.assert(up.lNext !== up && up.lNext.lNext !== up);

  for (; libtess.geom.vertLeq(up.dst(), up.org); up = up.lPrev()) { }
  for (; libtess.geom.vertLeq(up.org, up.dst()); up = up.lNext) { }

  var lo = up.lPrev();

  var tempHalfEdge;
  while (up.lNext !== lo) {
    if (libtess.geom.vertLeq(up.dst(), lo.org)) {
      // up.dst() is on the left. It is safe to form triangles from lo.org.
      // The edgeGoesLeft test guarantees progress even when some triangles
      // are CW, given that the upper and lower chains are truly monotone.
      while (lo.lNext !== up && (libtess.geom.edgeGoesLeft(lo.lNext) ||
          libtess.geom.edgeSign(lo.org, lo.dst(), lo.lNext.dst()) <= 0)) {

        tempHalfEdge = libtess.mesh.connect(lo.lNext, lo);
        lo = tempHalfEdge.sym;
      }
      lo = lo.lPrev();

    } else {
      // lo.org is on the left. We can make CCW triangles from up.dst().
      while (lo.lNext !== up && (libtess.geom.edgeGoesRight(up.lPrev()) ||
          libtess.geom.edgeSign(up.dst(), up.org, up.lPrev().org) >= 0)) {

        tempHalfEdge = libtess.mesh.connect(up, up.lPrev());
        up = tempHalfEdge.sym;
      }
      up = up.lNext;
    }
  }

  // Now lo.org == up.dst() == the leftmost vertex. The remaining region
  // can be tessellated in a fan from this leftmost vertex.
  libtess.assert(lo.lNext !== up);
  while (lo.lNext.lNext !== up) {
    tempHalfEdge = libtess.mesh.connect(lo.lNext, lo);
    lo = tempHalfEdge.sym;
  }
};

/**
 * Tessellates each region of the mesh which is marked "inside" the polygon.
 * Each such region must be monotone.
 * @param {!libtess.GluMesh} mesh
 */
libtess.tessmono.tessellateInterior = function(mesh) {
  var next;
  for (var f = mesh.fHead.next; f !== mesh.fHead; f = next) {
    // Make sure we don't try to tessellate the new triangles.
    next = f.next;
    if (f.inside) {
      libtess.tessmono.tessellateMonoRegion_(f);
    }
  }
};

/**
 * Zaps (i.e. sets to null) all faces which are not marked "inside" the polygon.
 * Since further mesh operations on null faces are not allowed, the main purpose
 * is to clean up the mesh so that exterior loops are not represented in the
 * data structure.
 * @param {!libtess.GluMesh} mesh
 */
libtess.tessmono.discardExterior = function(mesh) {
  var next;
  for (var f = mesh.fHead.next; f !== mesh.fHead; f = next) {
    // Since f will be destroyed, save its next pointer.
    next = f.next;
    if (!f.inside) {
      libtess.mesh.zapFace(f);
    }
  }
};

/**
 * Resets the winding numbers on all edges so that regions marked "inside" the
 * polygon have a winding number of "value", and regions outside have a winding
 * number of 0.
 *
 * If keepOnlyBoundary is true, it also deletes all edges which do not separate
 * an interior region from an exterior one.
 *
 * @param {!libtess.GluMesh} mesh
 * @param {number} value
 * @param {boolean} keepOnlyBoundary
 */
libtess.tessmono.setWindingNumber = function(mesh, value, keepOnlyBoundary) {
  var eNext;
  for (var e = mesh.eHead.next; e !== mesh.eHead; e = eNext) {
    eNext = e.next;

    if (e.rFace().inside !== e.lFace.inside) {
      // This is a boundary edge (one side is interior, one is exterior).
      e.winding = (e.lFace.inside) ? value : -value;

    } else {
      // Both regions are interior, or both are exterior.
      if (!keepOnlyBoundary) {
        e.winding = 0;

      } else {
        libtess.mesh.deleteEdge(e);
      }
    }
  }
};

/* global libtess */

/**
 * A list of edges crossing the sweep line, sorted from top to bottom.
 * Implementation is a doubly-linked list, sorted by the injected edgeLeq
 * comparator function. Here it is a simple ordering, but see libtess.sweep for
 * the list of invariants on the edge dictionary this ordering creates.
 * @constructor
 * @struct
 * @param {!libtess.GluTesselator} frame
 * @param {function(!libtess.GluTesselator, !libtess.ActiveRegion, !libtess.ActiveRegion): boolean} leq
 */
libtess.Dict = function(frame, leq) {

  /**
   * The head of the doubly-linked DictNode list. At creation time, links back
   * and forward only to itself.
   * @private {!libtess.DictNode}
   */
  this.head_ = new libtess.DictNode();

  /**
   * The GluTesselator used as the frame for edge/event comparisons.
   * @private {!libtess.GluTesselator}
   */
  this.frame_ = frame;

  /**
   * Comparison function to maintain the invariants of the Dict. See
   * libtess.sweep.edgeLeq_ for source.
   * @private
   * @type {function(!libtess.GluTesselator, !libtess.ActiveRegion, !libtess.ActiveRegion): boolean}
   */
  this.leq_ = leq;
};

/* istanbul ignore next */
/**
 * Formerly used to delete the dict.
 * NOTE(bckenny): No longer called but left for memFree documentation. Nulled at
 * former callsite instead (sweep.doneEdgeDict_)
 * @private
 */
libtess.Dict.prototype.deleteDict_ = function() {
  // for (var node = this.head_.next; node !== this.head_; node = node.next) {
  //   memFree(node);
  // }
  // memFree(dict);
};

/**
 * Insert the supplied key into the edge list and return its new node.
 * @param {libtess.DictNode} node
 * @param {!libtess.ActiveRegion} key
 * @return {!libtess.DictNode}
 */
libtess.Dict.prototype.insertBefore = function(node, key) {
  do {
    node = node.prev;
  } while (node.key !== null && !this.leq_(this.frame_, node.key, key));

  // insert the new node and update the surrounding nodes to point to it
  var newNode = new libtess.DictNode(key, node.next, node);
  node.next.prev = newNode;
  node.next = newNode;

  return newNode;
};

/**
 * Insert key into the dict and return the new node that contains it.
 * @param {!libtess.ActiveRegion} key
 * @return {!libtess.DictNode}
 */
libtess.Dict.prototype.insert = function(key) {
  // NOTE(bckenny): from a macro in dict.h/dict-list.h
  return this.insertBefore(this.head_, key);
};

/**
 * Remove node from the list.
 * @param {libtess.DictNode} node
 */
libtess.Dict.prototype.deleteNode = function(node) {
  node.next.prev = node.prev;
  node.prev.next = node.next;

  // NOTE(bckenny): nulled at callsite (sweep.deleteRegion_)
  // memFree( node );
};

/**
 * Search returns the node with the smallest key greater than or equal
 * to the given key. If there is no such key, returns a node whose
 * key is null. Similarly, max(d).getSuccessor() has a null key, etc.
 * @param {!libtess.ActiveRegion} key
 * @return {!libtess.DictNode}
 */
libtess.Dict.prototype.search = function(key) {
  var node = this.head_;

  do {
    node = node.next;
  } while (node.key !== null && !this.leq_(this.frame_, key, node.key));

  return node;
};

/**
 * Return the node with the smallest key.
 * @return {!libtess.DictNode}
 */
libtess.Dict.prototype.getMin = function() {
  // NOTE(bckenny): from a macro in dict.h/dict-list.h
  return this.head_.next;
};

// NOTE(bckenny): libtess.Dict.getMax isn't called within libtess and isn't part
// of the public API. For now, leaving in but ignoring for coverage.
/* istanbul ignore next */
/**
 * Returns the node with the greatest key.
 * @return {!libtess.DictNode}
 */
libtess.Dict.prototype.getMax = function() {
  // NOTE(bckenny): from a macro in dict.h/dict-list.h
  return this.head_.prev;
};

/* global libtess */

/**
 * A doubly-linked-list node with a libtess.ActiveRegion payload.
 * The key for this node and the next and previous nodes in the parent Dict list
 * can be provided to insert it into an existing list (or all can be omitted if
 * this is to be the founding node of the list).
 * @param {!libtess.ActiveRegion=} opt_key
 * @param {!libtess.DictNode=} opt_nextNode
 * @param {!libtess.DictNode=} opt_prevNode
 * @constructor
 * @struct
 */
libtess.DictNode = function(opt_key, opt_nextNode, opt_prevNode) {
  /**
   * The ActiveRegion key for this node, or null if the head of the list.
   * @type {libtess.ActiveRegion}
   */
  this.key = opt_key || null;

  /**
   * Link to next DictNode in parent list or to self if this is the first node.
   * @type {!libtess.DictNode}
   */
  this.next = opt_nextNode || this;

  /**
   * Link to previous DictNode in parent list or to self if this is the first
   * node.
   * @type {!libtess.DictNode}
   */
  this.prev = opt_prevNode || this;
};

/**
 * Get the key from this node.
 * @return {libtess.ActiveRegion}
 */
libtess.DictNode.prototype.getKey = function() {
  return this.key;
};

/**
 * Get the successor node to this one.
 * @return {!libtess.DictNode}
 */
libtess.DictNode.prototype.getSuccessor = function() {
  return this.next;
};

/**
 * Get the predecessor node to this one.
 * @return {!libtess.DictNode}
 */
libtess.DictNode.prototype.getPredecessor = function() {
  return this.prev;
};

/* global libtess */

// TODO(bckenny): create more javascript-y API, e.g. make gluTessEndPolygon
// async, don't require so many temp objects created

/**
 * The tesselator main class, providing the public API.
 * @constructor
 * @struct
 */
libtess.GluTesselator = function() {
  // Only initialize fields which can be changed by the api. Other fields
  // are initialized where they are used.

  /*** state needed for collecting the input data ***/

  /**
   * Tesselator state, tracking what begin/end calls have been seen.
   * @private {libtess.GluTesselator.tessState_}
   */
  this.state_ = libtess.GluTesselator.tessState_.T_DORMANT;

  /**
   * lastEdge_.org is the most recent vertex
   * @private {libtess.GluHalfEdge}
   */
  this.lastEdge_ = null;

  /**
   * stores the input contours, and eventually the tessellation itself
   * @type {libtess.GluMesh}
   */
  this.mesh = null;

  /**
   * Error callback.
   * @private {?function((libtess.errorType|libtess.gluEnum), Object=)}
   */
  this.errorCallback_ = null;

  /*** state needed for projecting onto the sweep plane ***/

  /**
   * user-specified normal (if provided)
   * @private {!Array<number>}
   */
  this.normal_ = [0, 0, 0];

  /*** state needed for the line sweep ***/

  /**
   * rule for determining polygon interior
   * @type {libtess.windingRule}
   */
  this.windingRule = libtess.windingRule.GLU_TESS_WINDING_ODD;

  /**
   * fatal error: needed combine callback
   * @type {boolean}
   */
  this.fatalError = false;

  /**
   * edge dictionary for sweep line
   * @type {libtess.Dict}
   */
  this.dict = null;
  // NOTE(bckenny): dict initialized in sweep.initEdgeDict_, removed in sweep.doneEdgeDict_

  /**
   * priority queue of vertex events
   * @type {libtess.PriorityQ}
   */
  this.pq = null;
  // NOTE(bckenny): pq initialized in sweep.initPriorityQ

  /**
   * current sweep event being processed
   * @type {libtess.GluVertex}
   */
  this.event = null;

  /**
   * Combine callback.
   * @private {?function(Array<number>, Array<Object>, Array<number>, Object=): Object}
   */
  this.combineCallback_ = null;

  /*** state needed for rendering callbacks (see render.js) ***/

  /**
   * Extract contours, not triangles
   * @private {boolean}
   */
  this.boundaryOnly_ = false;

  /**
   * Begin callback.
   * @private {?function(libtess.primitiveType, Object=)}
   */
  this.beginCallback_ = null;

  /**
   * Edge flag callback.
   * @private {?function(boolean, Object=)}
   */
  this.edgeFlagCallback_ = null;

  /**
   * Vertex callback.
   * @private {?function(Object, Object=)}
   */
  this.vertexCallback_ = null;

  /**
   * End callback.
   * @private {?function(Object=)}
   */
  this.endCallback_ = null;

  /**
   * Mesh callback.
   * @private {?function(libtess.GluMesh)}
   */
  this.meshCallback_ = null;

  /**
   * client data for current polygon
   * @private {Object}
   */
  this.polygonData_ = null;
};

/**
 * The begin/end calls must be properly nested. We keep track of the current
 * state to enforce the ordering.
 * @enum {number}
 * @private
 */
libtess.GluTesselator.tessState_ = {
  T_DORMANT: 0,
  T_IN_POLYGON: 1,
  T_IN_CONTOUR: 2
};

/**
 * Destory the tesselator object. See README.
 */
libtess.GluTesselator.prototype.gluDeleteTess = function() {
  // TODO(bckenny): This does nothing but assert that it isn't called while
  // building the polygon since we rely on GC to handle memory. *If* the public
  // API changes, this should go.
  this.requireState_(libtess.GluTesselator.tessState_.T_DORMANT);
  // memFree(tess); TODO(bckenny)
};

/**
 * Set properties for control over tesselation. See README.
 * @param {libtess.gluEnum} which [description].
 * @param {number|boolean} value [description].
 */
libtess.GluTesselator.prototype.gluTessProperty = function(which, value) {
  // TODO(bckenny): split into more setters?
  // TODO(bckenny): in any case, we can do better than this switch statement

  switch (which) {
    case libtess.gluEnum.GLU_TESS_TOLERANCE:
      // NOTE(bckenny): libtess has never supported any tolerance but 0.
      return;

    case libtess.gluEnum.GLU_TESS_WINDING_RULE:
      var windingRule = /** @type {libtess.windingRule} */(value);

      switch (windingRule) {
        case libtess.windingRule.GLU_TESS_WINDING_ODD:
        case libtess.windingRule.GLU_TESS_WINDING_NONZERO:
        case libtess.windingRule.GLU_TESS_WINDING_POSITIVE:
        case libtess.windingRule.GLU_TESS_WINDING_NEGATIVE:
        case libtess.windingRule.GLU_TESS_WINDING_ABS_GEQ_TWO:
          this.windingRule = windingRule;
          return;
        default:
      }
      break;

    case libtess.gluEnum.GLU_TESS_BOUNDARY_ONLY:
      this.boundaryOnly_ = !!value;
      return;

    default:
      this.callErrorCallback(libtess.gluEnum.GLU_INVALID_ENUM);
      return;
  }
  this.callErrorCallback(libtess.gluEnum.GLU_INVALID_VALUE);
};

/**
 * Returns tessellator property
 * @param {libtess.gluEnum} which [description].
 * @return {number|boolean} [description].
 */
libtess.GluTesselator.prototype.gluGetTessProperty = function(which) {
  // TODO(bckenny): as above, split into more getters? and improve on switch statement
  // why are these being asserted in getter but not setter?

  switch (which) {
    case libtess.gluEnum.GLU_TESS_TOLERANCE:
      return 0;

    case libtess.gluEnum.GLU_TESS_WINDING_RULE:
      var rule = this.windingRule;
      libtess.assert(rule === libtess.windingRule.GLU_TESS_WINDING_ODD ||
          rule === libtess.windingRule.GLU_TESS_WINDING_NONZERO ||
          rule === libtess.windingRule.GLU_TESS_WINDING_POSITIVE ||
          rule === libtess.windingRule.GLU_TESS_WINDING_NEGATIVE ||
          rule === libtess.windingRule.GLU_TESS_WINDING_ABS_GEQ_TWO);
      return rule;

    case libtess.gluEnum.GLU_TESS_BOUNDARY_ONLY:
      libtess.assert(this.boundaryOnly_ === true ||
          this.boundaryOnly_ === false);
      return this.boundaryOnly_;

    default:
      this.callErrorCallback(libtess.gluEnum.GLU_INVALID_ENUM);
      break;
  }
  return false;
};

/**
 * Lets the user supply the polygon normal, if known. All input data is
 * projected into a plane perpendicular to the normal before tesselation. All
 * output triangles are oriented CCW with respect to the normal (CW orientation
 * can be obtained by reversing the sign of the supplied normal). For example,
 * if you know that all polygons lie in the x-y plane, call
 * `tess.gluTessNormal(0.0, 0.0, 1.0)` before rendering any polygons.
 * @param {number} x
 * @param {number} y
 * @param {number} z
 */
libtess.GluTesselator.prototype.gluTessNormal = function(x, y, z) {
  this.normal_[0] = x;
  this.normal_[1] = y;
  this.normal_[2] = z;
};

/**
 * Specify callbacks. See README for callback descriptions. A null or undefined
 * opt_fn removes current callback.
 * @param {libtess.gluEnum} which The callback-type gluEnum value.
 * @param {?Function=} opt_fn
 */
libtess.GluTesselator.prototype.gluTessCallback = function(which, opt_fn) {
  var fn = !opt_fn ? null : opt_fn;
  // TODO(bckenny): better opt_fn typing?
  // TODO(bckenny): should add documentation that references in callback are volatile (or make a copy)

  switch (which) {
    case libtess.gluEnum.GLU_TESS_BEGIN:
    case libtess.gluEnum.GLU_TESS_BEGIN_DATA:
      this.beginCallback_ = /** @type {?function(libtess.primitiveType, Object=)} */ (fn);
      return;

    case libtess.gluEnum.GLU_TESS_EDGE_FLAG:
    case libtess.gluEnum.GLU_TESS_EDGE_FLAG_DATA:
      this.edgeFlagCallback_ = /** @type {?function(boolean, Object=)} */ (fn);
      return;

    case libtess.gluEnum.GLU_TESS_VERTEX:
    case libtess.gluEnum.GLU_TESS_VERTEX_DATA:
      this.vertexCallback_ = /** @type {?function(Object, Object=)} */ (fn);
      return;

    case libtess.gluEnum.GLU_TESS_END:
    case libtess.gluEnum.GLU_TESS_END_DATA:
      this.endCallback_ = /** @type {?function(Object=)} */ (fn);
      return;

    case libtess.gluEnum.GLU_TESS_ERROR:
    case libtess.gluEnum.GLU_TESS_ERROR_DATA:
      this.errorCallback_ = /** @type {?function((libtess.errorType|libtess.gluEnum), Object=)} */ (fn);
      return;

    case libtess.gluEnum.GLU_TESS_COMBINE:
    case libtess.gluEnum.GLU_TESS_COMBINE_DATA:
      this.combineCallback_ = /** @type {?function(Array<number>, Array<Object>, Array<number>, Object=): Object} */ (fn);
      return;

    case libtess.gluEnum.GLU_TESS_MESH:
      this.meshCallback_ = /** @type {?function(libtess.GluMesh)} */ (fn);
      return;

    default:
      this.callErrorCallback(libtess.gluEnum.GLU_INVALID_ENUM);
      return;
  }
};

/**
 * Specify a vertex and associated data. Must be within calls to
 * beginContour/endContour. See README.
 * @param {!Array<number>} coords
 * @param {Object} data
 */
libtess.GluTesselator.prototype.gluTessVertex = function(coords, data) {
  var tooLarge = false;

  // TODO(bckenny): pool allocation?
  var clamped = [0, 0, 0];

  this.requireState_(libtess.GluTesselator.tessState_.T_IN_CONTOUR);

  for (var i = 0; i < 3; ++i) {
    var x = coords[i];
    if (x < -libtess.GLU_TESS_MAX_COORD) {
      x = -libtess.GLU_TESS_MAX_COORD;
      tooLarge = true;
    }
    if (x > libtess.GLU_TESS_MAX_COORD) {
      x = libtess.GLU_TESS_MAX_COORD;
      tooLarge = true;
    }
    clamped[i] = x;
  }

  if (tooLarge) {
    this.callErrorCallback(libtess.errorType.GLU_TESS_COORD_TOO_LARGE);
  }

  this.addVertex_(clamped, data);
};

/**
 * [gluTessBeginPolygon description]
 * @param {Object} data Client data for current polygon.
 */
libtess.GluTesselator.prototype.gluTessBeginPolygon = function(data) {
  this.requireState_(libtess.GluTesselator.tessState_.T_DORMANT);

  this.state_ = libtess.GluTesselator.tessState_.T_IN_POLYGON;

  this.mesh = new libtess.GluMesh();

  this.polygonData_ = data;
};

/**
 * [gluTessBeginContour description]
 */
libtess.GluTesselator.prototype.gluTessBeginContour = function() {
  this.requireState_(libtess.GluTesselator.tessState_.T_IN_POLYGON);

  this.state_ = libtess.GluTesselator.tessState_.T_IN_CONTOUR;
  this.lastEdge_ = null;
};

/**
 * [gluTessEndContour description]
 */
libtess.GluTesselator.prototype.gluTessEndContour = function() {
  this.requireState_(libtess.GluTesselator.tessState_.T_IN_CONTOUR);
  this.state_ = libtess.GluTesselator.tessState_.T_IN_POLYGON;
};

/**
 * [gluTessEndPolygon description]
 */
libtess.GluTesselator.prototype.gluTessEndPolygon = function() {
  this.requireState_(libtess.GluTesselator.tessState_.T_IN_POLYGON);
  this.state_ = libtess.GluTesselator.tessState_.T_DORMANT;

  // Determine the polygon normal and project vertices onto the plane
  // of the polygon.
  libtess.normal.projectPolygon(this, this.normal_[0], this.normal_[1],
      this.normal_[2]);

  // computeInterior(tess) computes the planar arrangement specified
  // by the given contours, and further subdivides this arrangement
  // into regions. Each region is marked "inside" if it belongs
  // to the polygon, according to the rule given by this.windingRule.
  // Each interior region is guaranteed be monotone.
  libtess.sweep.computeInterior(this);

  if (!this.fatalError) {
    // If the user wants only the boundary contours, we throw away all edges
    // except those which separate the interior from the exterior.
    // Otherwise we tessellate all the regions marked "inside".
    // NOTE(bckenny): we know this.mesh has been initialized, so help closure out.
    var mesh = /** @type {!libtess.GluMesh} */(this.mesh);
    if (this.boundaryOnly_) {
      libtess.tessmono.setWindingNumber(mesh, 1, true);
    } else {
      libtess.tessmono.tessellateInterior(mesh);
    }

    this.mesh.checkMesh();

    if (this.beginCallback_ || this.endCallback_ || this.vertexCallback_ ||
        this.edgeFlagCallback_) {

      if (this.boundaryOnly_) {
        // output boundary contours
        libtess.render.renderBoundary(this, this.mesh);

      } else {
        // output triangles (with edge callback if one is set)
        var flagEdges = !!this.edgeFlagCallback_;
        libtess.render.renderMesh(this, this.mesh, flagEdges);
      }
    }

    if (this.meshCallback_) {
      // Throw away the exterior faces, so that all faces are interior.
      // This way the user doesn't have to check the "inside" flag,
      // and we don't need to even reveal its existence. It also leaves
      // the freedom for an implementation to not generate the exterior
      // faces in the first place.
      libtess.tessmono.discardExterior(this.mesh);
      // user wants the mesh itself
      this.meshCallback_(this.mesh);

      this.mesh = null;
      this.polygonData_ = null;
      return;
    }
  }

  libtess.mesh.deleteMesh(this.mesh);
  this.polygonData_ = null;
  this.mesh = null;
};

/**
 * Change the tesselator state.
 * @private
 * @param {libtess.GluTesselator.tessState_} state
 */
libtess.GluTesselator.prototype.requireState_ = function(state) {
  if (this.state_ !== state) {
    this.gotoState_(state);
  }
};

/**
 * Change the current tesselator state one level at a time to get to the
 * desired state. Only triggered when the API is not called in the correct order
 * so an error callback is made, however the tesselator will always attempt to
 * recover afterwards (see README).
 * @private
 * @param {libtess.GluTesselator.tessState_} newState
 */
libtess.GluTesselator.prototype.gotoState_ = function(newState) {
  while (this.state_ !== newState) {
    if (this.state_ < newState) {
      switch (this.state_) {
        case libtess.GluTesselator.tessState_.T_DORMANT:
          this.callErrorCallback(
              libtess.errorType.GLU_TESS_MISSING_BEGIN_POLYGON);
          this.gluTessBeginPolygon(null);
          break;

        case libtess.GluTesselator.tessState_.T_IN_POLYGON:
          this.callErrorCallback(
              libtess.errorType.GLU_TESS_MISSING_BEGIN_CONTOUR);
          this.gluTessBeginContour();
          break;
      }

    } else {
      switch (this.state_) {
        case libtess.GluTesselator.tessState_.T_IN_CONTOUR:
          this.callErrorCallback(
              libtess.errorType.GLU_TESS_MISSING_END_CONTOUR);
          this.gluTessEndContour();
          break;

        case libtess.GluTesselator.tessState_.T_IN_POLYGON:
          this.callErrorCallback(
              libtess.errorType.GLU_TESS_MISSING_END_POLYGON);
          // NOTE(bckenny): libtess originally reset the tesselator, even though
          // the README claims it should spit out the tessellated results at
          // this point.
          // (see http://cgit.freedesktop.org/mesa/glu/tree/src/libtess/tess.c#n180)
          this.gluTessEndPolygon();
          break;
      }
    }
  }
};

/**
 * [addVertex_ description]
 * @private
 * @param {!Array<number>} coords [description].
 * @param {Object} data [description].
 */
libtess.GluTesselator.prototype.addVertex_ = function(coords, data) {
  var e = this.lastEdge_;
  if (e === null) {
    // Make a self-loop (one vertex, one edge).
    e = libtess.mesh.makeEdge(this.mesh);
    libtess.mesh.meshSplice(e, e.sym);

  } else {
    // Create a new vertex and edge which immediately follow e
    // in the ordering around the left face.
    libtess.mesh.splitEdge(e);
    e = e.lNext;
  }

  // The new vertex is now e.org.
  e.org.data = data;
  e.org.coords[0] = coords[0];
  e.org.coords[1] = coords[1];
  e.org.coords[2] = coords[2];

  // The winding of an edge says how the winding number changes as we
  // cross from the edge''s right face to its left face.  We add the
  // vertices in such an order that a CCW contour will add +1 to
  // the winding number of the region inside the contour.
  e.winding = 1;
  e.sym.winding = -1;

  this.lastEdge_ = e;
};

/**
 * Call callback to indicate the start of a primitive, to be followed by emitted
 * vertices, if any. In libtess.js, `type` will always be `GL_TRIANGLES`.
 * @param {libtess.primitiveType} type
 */
libtess.GluTesselator.prototype.callBeginCallback = function(type) {
  if (this.beginCallback_) {
    this.beginCallback_(type, this.polygonData_);
  }
};

/**
 * Call callback to emit a vertex of the tessellated polygon.
 * @param {Object} data
 */
libtess.GluTesselator.prototype.callVertexCallback = function(data) {
  if (this.vertexCallback_) {
    this.vertexCallback_(data, this.polygonData_);
  }
};

/**
 * Call callback to indicate whether the vertices to follow begin edges which
 * lie on a polygon boundary.
 * @param {boolean} flag
 */
libtess.GluTesselator.prototype.callEdgeFlagCallback = function(flag) {
  if (this.edgeFlagCallback_) {
    this.edgeFlagCallback_(flag, this.polygonData_);
  }
};

/**
 * Call callback to indicate the end of tessellation.
 */
libtess.GluTesselator.prototype.callEndCallback = function() {
  if (this.endCallback_) {
    this.endCallback_(this.polygonData_);
  }
};

/* jscs:disable maximumLineLength */
/**
 * Call callback for combining vertices at edge intersection requiring the
 * creation of a new vertex.
 * @param {!Array<number>} coords Intersection coordinates.
 * @param {!Array<Object>} data Array of vertex data, one per edge vertices.
 * @param {!Array<number>} weight Coefficients used for the linear combination of vertex coordinates that gives coords.
 * @return {?Object} Interpolated vertex.
 */
libtess.GluTesselator.prototype.callCombineCallback = function(coords, data, weight) {
  if (this.combineCallback_) {
    return this.combineCallback_(coords, data, weight, this.polygonData_) ||
        null;
  }

  return null;
};
/* jscs:enable maximumLineLength */

/**
 * Call error callback, if specified, with errno.
 * @param {(libtess.errorType|libtess.gluEnum)} errno
 */
libtess.GluTesselator.prototype.callErrorCallback = function(errno) {
  if (this.errorCallback_) {
    this.errorCallback_(errno, this.polygonData_);
  }
};

/* global libtess */

/**
 * Each face has a pointer to the next and previous faces in the
 * circular list, and a pointer to a half-edge with this face as
 * the left face (null if this is the dummy header). There is also
 * a field "data" for client data.
 *
 * @param {libtess.GluFace=} opt_nextFace
 * @param {libtess.GluFace=} opt_prevFace
 * @constructor
 * @struct
 */
libtess.GluFace = function(opt_nextFace, opt_prevFace) {
  // TODO(bckenny): reverse order of params?

  /**
   * next face (never null)
   * @type {!libtess.GluFace}
   */
  this.next = opt_nextFace || this;

  /**
   * previous face (never NULL)
   * @type {!libtess.GluFace}
   */
  this.prev = opt_prevFace || this;

  /**
   * A half edge with this left face.
   * @type {libtess.GluHalfEdge}
   */
  this.anEdge = null;

  /**
   * This face is in the polygon interior.
   * @type {boolean}
   */
  this.inside = false;
};

/* global libtess */

/**
 * The fundamental data structure is the "half-edge". Two half-edges
 * go together to make an edge, but they point in opposite directions.
 * Each half-edge has a pointer to its mate (the "symmetric" half-edge sym),
 * its origin vertex (org), the face on its left side (lFace), and the
 * adjacent half-edges in the CCW direction around the origin vertex
 * (oNext) and around the left face (lNext). There is also a "next"
 * pointer for the global edge list (see below).
 *
 * The notation used for mesh navigation:
 *  sym   = the mate of a half-edge (same edge, but opposite direction)
 *  oNext = edge CCW around origin vertex (keep same origin)
 *  dNext = edge CCW around destination vertex (keep same dest)
 *  lNext = edge CCW around left face (dest becomes new origin)
 *  rNext = edge CCW around right face (origin becomes new dest)
 *
 * "prev" means to substitute CW for CCW in the definitions above.
 *
 * The circular edge list is special; since half-edges always occur
 * in pairs (e and e.sym), each half-edge stores a pointer in only
 * one direction. Starting at eHead and following the e.next pointers
 * will visit each *edge* once (ie. e or e.sym, but not both).
 * e.sym stores a pointer in the opposite direction, thus it is
 * always true that e.sym.next.sym.next === e.
 *
 * @param {libtess.GluHalfEdge=} opt_nextEdge
 * @constructor
 * @struct
 */
libtess.GluHalfEdge = function(opt_nextEdge) {
  // TODO(bckenny): are these the right defaults? (from gl_meshNewMesh requirements)

  /**
   * doubly-linked list (prev==sym->next)
   * @type {!libtess.GluHalfEdge}
   */
  this.next = opt_nextEdge || this;

  // TODO(bckenny): how can this be required if created in pairs? move to factory creation only?
  /**
   * same edge, opposite direction
   * @type {libtess.GluHalfEdge}
   */
  this.sym = null;

  /**
   * next edge CCW around origin
   * @type {libtess.GluHalfEdge}
   */
  this.oNext = null;

  /**
   * next edge CCW around left face
   * @type {libtess.GluHalfEdge}
   */
  this.lNext = null;

  /**
   * origin vertex (oVertex too long)
   * @type {libtess.GluVertex}
   */
  this.org = null;

  /**
   * left face
   * @type {libtess.GluFace}
   */
  this.lFace = null;

  // Internal data (keep hidden)
  // NOTE(bckenny): can't be private, though...

  /**
   * a region with this upper edge (see sweep.js)
   * @type {libtess.ActiveRegion}
   */
  this.activeRegion = null;

  /**
   * change in winding number when crossing from the right face to the left face
   * @type {number}
   */
  this.winding = 0;
};

// NOTE(bckenny): the following came from macros in mesh
// TODO(bckenny): using methods as aliases for sym connections for now.
// not sure about this approach. getters? renames?


/**
 * [rFace description]
 * @return {libtess.GluFace} [description].
 */
libtess.GluHalfEdge.prototype.rFace = function() {
  return this.sym.lFace;
};


/**
 * [dst description]
 * @return {libtess.GluVertex} [description].
 */
libtess.GluHalfEdge.prototype.dst = function() {
  return this.sym.org;
};


/**
 * [oPrev description]
 * @return {libtess.GluHalfEdge} [description].
 */
libtess.GluHalfEdge.prototype.oPrev = function() {
  return this.sym.lNext;
};


/**
 * [lPrev description]
 * @return {libtess.GluHalfEdge} [description].
 */
libtess.GluHalfEdge.prototype.lPrev = function() {
  return this.oNext.sym;
};

// NOTE(bckenny): libtess.GluHalfEdge.dPrev is called nowhere in libtess and
// isn't part of the current public API. It could be useful for mesh traversal
// and manipulation if made public, however.
/* istanbul ignore next */
/**
 * The edge clockwise around destination vertex (keep same dest).
 * @return {libtess.GluHalfEdge}
 */
libtess.GluHalfEdge.prototype.dPrev = function() {
  return this.lNext.sym;
};


/**
 * [rPrev description]
 * @return {libtess.GluHalfEdge} [description].
 */
libtess.GluHalfEdge.prototype.rPrev = function() {
  return this.sym.oNext;
};


/**
 * [dNext description]
 * @return {libtess.GluHalfEdge} [description].
 */
libtess.GluHalfEdge.prototype.dNext = function() {
  return this.rPrev().sym;
};


// NOTE(bckenny): libtess.GluHalfEdge.rNext is called nowhere in libtess and
// isn't part of the current public API. It could be useful for mesh traversal
// and manipulation if made public, however.
/* istanbul ignore next */
/**
 * The edge CCW around the right face (origin of this becomes new dest).
 * @return {libtess.GluHalfEdge}
 */
libtess.GluHalfEdge.prototype.rNext = function() {
  return this.oPrev().sym;
};

/* global libtess */

/**
 * Creates a new mesh with no edges, no vertices,
 * and no loops (what we usually call a "face").
 *
 * @constructor
 * @struct
 */
libtess.GluMesh = function() {
  /**
   * dummy header for vertex list
   * @type {libtess.GluVertex}
   */
  this.vHead = new libtess.GluVertex();

  /**
   * dummy header for face list
   * @type {libtess.GluFace}
   */
  this.fHead = new libtess.GluFace();

  /**
   * dummy header for edge list
   * @type {libtess.GluHalfEdge}
   */
  this.eHead = new libtess.GluHalfEdge();

  /**
   * and its symmetric counterpart
   * @type {libtess.GluHalfEdge}
   */
  this.eHeadSym = new libtess.GluHalfEdge();

  // TODO(bckenny): better way to pair these?
  this.eHead.sym = this.eHeadSym;
  this.eHeadSym.sym = this.eHead;
};


// TODO(bckenny): #ifndef NDEBUG
/**
 * Checks mesh for self-consistency.
 */
libtess.GluMesh.prototype.checkMesh = function() {
  if (!libtess.DEBUG) {
    return;
  }

  var fHead = this.fHead;
  var vHead = this.vHead;
  var eHead = this.eHead;

  var e;

  // faces
  var f;
  var fPrev = fHead;
  for (fPrev = fHead; (f = fPrev.next) !== fHead; fPrev = f) {
    libtess.assert(f.prev === fPrev);
    e = f.anEdge;
    do {
      libtess.assert(e.sym !== e);
      libtess.assert(e.sym.sym === e);
      libtess.assert(e.lNext.oNext.sym === e);
      libtess.assert(e.oNext.sym.lNext === e);
      libtess.assert(e.lFace === f);
      e = e.lNext;
    } while (e !== f.anEdge);
  }
  libtess.assert(f.prev === fPrev && f.anEdge === null);

  // vertices
  var v;
  var vPrev = vHead;
  for (vPrev = vHead; (v = vPrev.next) !== vHead; vPrev = v) {
    libtess.assert(v.prev === vPrev);
    e = v.anEdge;
    do {
      libtess.assert(e.sym !== e);
      libtess.assert(e.sym.sym === e);
      libtess.assert(e.lNext.oNext.sym === e);
      libtess.assert(e.oNext.sym.lNext === e);
      libtess.assert(e.org === v);
      e = e.oNext;
    } while (e !== v.anEdge);
  }
  libtess.assert(v.prev === vPrev && v.anEdge === null && v.data === null);

  // edges
  var ePrev = eHead;
  for (ePrev = eHead; (e = ePrev.next) !== eHead; ePrev = e) {
    libtess.assert(e.sym.next === ePrev.sym);
    libtess.assert(e.sym !== e);
    libtess.assert(e.sym.sym === e);
    libtess.assert(e.org !== null);
    libtess.assert(e.dst() !== null);
    libtess.assert(e.lNext.oNext.sym === e);
    libtess.assert(e.oNext.sym.lNext === e);
  }
  libtess.assert(e.sym.next === ePrev.sym &&
      e.sym === this.eHeadSym &&
      e.sym.sym === e &&
      e.org === null && e.dst() === null &&
      e.lFace === null && e.rFace() === null);
};

/* global libtess */

/**
 * Each vertex has a pointer to next and previous vertices in the
 * circular list, and a pointer to a half-edge with this vertex as
 * the origin (null if this is the dummy header). There is also a
 * field "data" for client data.
 * @param {libtess.GluVertex=} opt_nextVertex Optional reference to next vertex in the vertex list.
 * @param {libtess.GluVertex=} opt_prevVertex Optional reference to previous vertex in the vertex list.
 * @constructor
 * @struct
 */
libtess.GluVertex = function(opt_nextVertex, opt_prevVertex) {
  /**
   * Next vertex (never null).
   * @type {!libtess.GluVertex}
   */
  this.next = opt_nextVertex || this;

  /**
   * Previous vertex (never null).
   * @type {!libtess.GluVertex}
   */
  this.prev = opt_prevVertex || this;

  /**
   * A half-edge with this origin.
   * @type {libtess.GluHalfEdge}
   */
  this.anEdge = null;

  /**
   * The client's data.
   * @type {Object}
   */
  this.data = null;

  /**
   * The vertex location in 3D.
   * @type {!Array.<number>}
   */
  this.coords = [0, 0, 0];
  // TODO(bckenny): we may want to rethink coords, either eliminate (using s
  // and t and user data) or index into contiguous storage?

  /**
   * Component of projection onto the sweep plane.
   * @type {number}
   */
  this.s = 0;

  /**
   * Component of projection onto the sweep plane.
   * @type {number}
   */
  this.t = 0;

  /**
   * Handle to allow deletion from priority queue, or 0 if not yet inserted into
   * queue.
   * @type {libtess.PQHandle}
   */
  this.pqHandle = 0;
};

/* global libtess */

/**
 * A priority queue of vertices, ordered by libtess.geom.vertLeq, implemented
 * with a sorted array. Used for initial insertion of vertices (see
 * libtess.sweep.initPriorityQ_), sorted once, then it uses an internal
 * libtess.PriorityQHeap for any subsequently created vertices from
 * intersections.
 * @constructor
 * @struct
 */
libtess.PriorityQ = function() {
  /**
   * An unordered list of vertices that have been inserted in the queue, with
   * null in empty slots.
   * @private {Array<libtess.GluVertex>}
   */
  this.verts_ = [];

  /**
   * Array of indices into this.verts_, sorted by vertLeq over the addressed
   * vertices.
   * @private {Array<number>}
   */
  this.order_ = null;

  /**
   * The size of this queue, not counting any vertices stored in heap_.
   * @private {number}
   */
  this.size_ = 0;

  /**
   * Indicates that the queue has been initialized via init. If false, inserts
   * are fast insertions at the end of the verts_ array. If true, the verts_
   * array is sorted and subsequent inserts are done in the heap.
   * @private {boolean}
   */
  this.initialized_ = false;

  /**
   * A priority queue heap, used for faster insertions of vertices after verts_
   * has been sorted.
   * @private {libtess.PriorityQHeap}
   */
  this.heap_ = new libtess.PriorityQHeap();
};

/**
 * Release major storage memory used by priority queue.
 */
libtess.PriorityQ.prototype.deleteQ = function() {
  // TODO(bckenny): could instead clear most of these.
  this.heap_ = null;
  this.order_ = null;
  this.verts_ = null;
  // NOTE(bckenny): nulled at callsite (sweep.donePriorityQ_)
};

/**
 * Sort vertices by libtess.geom.vertLeq. Must be called before any method other
 * than insert is called to ensure correctness when removing or querying.
 */
libtess.PriorityQ.prototype.init = function() {
  // TODO(bckenny): reuse. in theory, we don't have to empty this, as access is
  // dictated by this.size_, but array.sort doesn't know that
  this.order_ = [];

  // Create an array of indirect pointers to the verts, so that
  // the handles we have returned are still valid.
  // TODO(bckenny): valid for when? it appears we can just store indexes into
  // verts_, but what did this mean?
  for (var i = 0; i < this.size_; i++) {
    this.order_[i] = i;
  }

  // sort the indirect pointers in descending order of the verts themselves
  // TODO(bckenny): make sure it's ok that verts[a] === verts[b] returns 1
  // TODO(bckenny): unstable sort means we may get slightly different polys in
  // different browsers, but only when passing in equal points
  // TODO(bckenny): make less awkward closure?
  var comparator = (function(verts) {
    return function(a, b) {
      return libtess.geom.vertLeq(verts[a], verts[b]) ? 1 : -1;
    };
  })(this.verts_);
  this.order_.sort(comparator);

  this.initialized_ = true;
  this.heap_.init();

  // NOTE(bckenny): debug assert of ordering of the verts_ array.
  if (libtess.DEBUG) {
    var p = 0;
    var r = p + this.size_ - 1;
    for (i = p; i < r; ++i) {
      libtess.assert(libtess.geom.vertLeq(this.verts_[this.order_[i + 1]],
          this.verts_[this.order_[i]]));
    }
  }
};

/**
 * Insert a vertex into the priority queue. Returns a PQHandle to refer to it,
 * which will never be 0.
 * @param {libtess.GluVertex} vert
 * @return {libtess.PQHandle}
 */
libtess.PriorityQ.prototype.insert = function(vert) {
  // NOTE(bckenny): originally returned LONG_MAX as alloc failure signal. no
  // longer does.
  if (this.initialized_) {
    return this.heap_.insert(vert);
  }

  var curr = this.size_++;

  this.verts_[curr] = vert;

  // Negative handles index the sorted array.
  return -(curr + 1);
};

/**
 * Removes the minimum vertex from the queue and returns it. If the queue is
 * empty, null will be returned.
 * @return {libtess.GluVertex}
 */
libtess.PriorityQ.prototype.extractMin = function() {
  if (this.size_ === 0) {
    return this.heap_.extractMin();
  }

  var sortMin = this.verts_[this.order_[this.size_ - 1]];
  if (!this.heap_.isEmpty()) {
    var heapMin = this.heap_.minimum();
    if (libtess.geom.vertLeq(heapMin, sortMin)) {
      return this.heap_.extractMin();
    }
  }

  do {
    --this.size_;
  } while (this.size_ > 0 && this.verts_[this.order_[this.size_ - 1]] === null);

  return sortMin;
};

/**
 * Returns the minimum vertex in the queue. If the queue is empty, null will be
 * returned.
 * @return {libtess.GluVertex}
 */
libtess.PriorityQ.prototype.minimum = function() {
  if (this.size_ === 0) {
    return this.heap_.minimum();
  }

  var sortMin = this.verts_[this.order_[this.size_ - 1]];
  if (!this.heap_.isEmpty()) {
    var heapMin = this.heap_.minimum();
    if (libtess.geom.vertLeq(heapMin, sortMin)) {
      return heapMin;
    }
  }

  return sortMin;
};

/**
 * Remove vertex with handle removeHandle from queue.
 * @param {libtess.PQHandle} removeHandle
 */
libtess.PriorityQ.prototype.remove = function(removeHandle) {
  if (removeHandle >= 0) {
    this.heap_.remove(removeHandle);
    return;
  }
  removeHandle = -(removeHandle + 1);

  libtess.assert(removeHandle < this.verts_.length &&
      this.verts_[removeHandle] !== null);

  this.verts_[removeHandle] = null;
  while (this.size_ > 0 && this.verts_[this.order_[this.size_ - 1]] === null) {
    --this.size_;
  }
};

/* global libtess */

/**
 * A priority queue of vertices, ordered by libtess.geom.vertLeq, implemented
 * with a binary heap. Used only within libtess.PriorityQ for prioritizing
 * vertices created by intersections (see libtess.sweep.checkForIntersect_).
 * @constructor
 * @struct
 */
libtess.PriorityQHeap = function() {
  /**
   * The heap itself. Active nodes are stored in the range 1..size, with the
   * minimum at 1. Each node stores only an index into verts_ and handles_.
   * @private {!Array<number>}
   */
  this.heap_ = libtess.PriorityQHeap.reallocNumeric_([0],
      libtess.PriorityQHeap.INIT_SIZE_ + 1);

  /**
   * An unordered list of vertices in the heap, with null in empty slots.
   * @private {!Array<libtess.GluVertex>}
   */
  this.verts_ = [null, null];

  /**
   * An unordered list of indices mapping vertex handles into the heap. An entry
   * at index i will map the vertex at i in verts_ to its place in the heap
   * (i.e. heap_[handles_[i]] === i).
   * Empty slots below size_ are a free list chain starting at freeList_.
   * @private {!Array<number>}
   */
  this.handles_ = [0, 0];

  /**
   * The size of the queue.
   * @private {number}
   */
  this.size_ = 0;

  /**
   * The queue's current allocated space.
   * @private {number}
   */
  this.max_ = libtess.PriorityQHeap.INIT_SIZE_;

  /**
   * The index of the next free hole in the verts_ array. That slot in handles_
   * has the next index in the free list. If there are no holes, freeList_ === 0
   * and a new vertex must be appended to the list.
   * @private {libtess.PQHandle}
   */
  this.freeList_ = 0;

  /**
   * Indicates that the heap has been initialized via init. If false, inserts
   * are fast insertions at the end of a list. If true, all inserts will now be
   * correctly ordered in the queue before returning.
   * @private {boolean}
   */
  this.initialized_ = false;

  // Point the first index at the first (currently null) vertex.
  this.heap_[1] = 1;
};

/**
 * The initial allocated space for the queue.
 * @const
 * @private {number}
 */
libtess.PriorityQHeap.INIT_SIZE_ = 32;

/**
 * Allocate a numeric index array of size size. oldArray's contents are copied
 * to the beginning of the new array. The rest of the array is filled with
 * zeroes.
 * @private
 * @param {!Array<number>} oldArray
 * @param {number} size
 * @return {!Array<number>}
 */
libtess.PriorityQHeap.reallocNumeric_ = function(oldArray, size) {
  var newArray = new Array(size);

  // NOTE(bckenny): V8 likes this significantly more than simply growing the
  // array element-by-element or expanding the existing array all at once, so,
  // for now, emulating realloc.
  for (var index = 0; index < oldArray.length; index++) {
    newArray[index] = oldArray[index];
  }

  for (; index < size; index++) {
    newArray[index] = 0;
  }

  return newArray;
};

/**
 * Initializing ordering of the heap. Must be called before any method other
 * than insert is called to ensure correctness when removing or querying.
 */
libtess.PriorityQHeap.prototype.init = function() {
  // This method of building a heap is O(n), rather than O(n lg n).
  for (var i = this.size_; i >= 1; --i) {
    // TODO(bckenny): since init is called before anything is inserted (see
    // PriorityQ.init), this will always be empty. Better to lazily init?
    this.floatDown_(i);
  }

  this.initialized_ = true;
};

/**
 * Insert a new vertex into the heap.
 * @param {libtess.GluVertex} vert The vertex to insert.
 * @return {libtess.PQHandle} A handle that can be used to remove the vertex.
 */
libtess.PriorityQHeap.prototype.insert = function(vert) {
  var endIndex = ++this.size_;

  // If the heap overflows, double its size.
  if ((endIndex * 2) > this.max_) {
    this.max_ *= 2;

    this.handles_ = libtess.PriorityQHeap.reallocNumeric_(this.handles_,
        this.max_ + 1);
  }

  var newVertSlot;
  if (this.freeList_ === 0) {
    // No free slots, append vertex.
    newVertSlot = endIndex;
  } else {
    // Put vertex in free slot, update freeList_ to next free slot.
    newVertSlot = this.freeList_;
    this.freeList_ = this.handles_[this.freeList_];
  }

  this.verts_[newVertSlot] = vert;
  this.handles_[newVertSlot] = endIndex;
  this.heap_[endIndex] = newVertSlot;

  if (this.initialized_) {
    this.floatUp_(endIndex);
  }
  return newVertSlot;
};

/**
 * @return {boolean} Whether the heap is empty.
 */
libtess.PriorityQHeap.prototype.isEmpty = function() {
  return this.size_ === 0;
};

/**
 * Returns the minimum vertex in the heap. If the heap is empty, null will be
 * returned.
 * @return {libtess.GluVertex}
 */
libtess.PriorityQHeap.prototype.minimum = function() {
  return this.verts_[this.heap_[1]];
};

/**
 * Removes the minimum vertex from the heap and returns it. If the heap is
 * empty, null will be returned.
 * @return {libtess.GluVertex}
 */
libtess.PriorityQHeap.prototype.extractMin = function() {
  var heap = this.heap_;
  var verts = this.verts_;
  var handles = this.handles_;

  var minHandle = heap[1];
  var minVertex = verts[minHandle];

  if (this.size_ > 0) {
    // Replace min with last vertex.
    heap[1] = heap[this.size_];
    handles[heap[1]] = 1;

    // Clear min vertex and put slot at front of freeList_.
    verts[minHandle] = null;
    handles[minHandle] = this.freeList_;
    this.freeList_ = minHandle;

    // Restore heap.
    if (--this.size_ > 0) {
      this.floatDown_(1);
    }
  }

  return minVertex;
};

/**
 * Remove vertex with handle removeHandle from heap.
 * @param {libtess.PQHandle} removeHandle
 */
libtess.PriorityQHeap.prototype.remove = function(removeHandle) {
  var heap = this.heap_;
  var verts = this.verts_;
  var handles = this.handles_;

  libtess.assert(removeHandle >= 1 && removeHandle <= this.max_ &&
      verts[removeHandle] !== null);

  var heapIndex = handles[removeHandle];

  // Replace with last vertex.
  heap[heapIndex] = heap[this.size_];
  handles[heap[heapIndex]] = heapIndex;

  // Restore heap.
  if (heapIndex <= --this.size_) {
    if (heapIndex <= 1) {
      this.floatDown_(heapIndex);
    } else {
      var vert = verts[heap[heapIndex]];
      var parentVert = verts[heap[heapIndex >> 1]];
      if (libtess.geom.vertLeq(parentVert, vert)) {
        this.floatDown_(heapIndex);
      } else {
        this.floatUp_(heapIndex);
      }
    }
  }

  // Clear vertex and put slot at front of freeList_.
  verts[removeHandle] = null;
  handles[removeHandle] = this.freeList_;
  this.freeList_ = removeHandle;
};

/**
 * Restore heap by moving the vertex at index in the heap downwards to a valid
 * slot.
 * @private
 * @param {libtess.PQHandle} index
 */
libtess.PriorityQHeap.prototype.floatDown_ = function(index) {
  var heap = this.heap_;
  var verts = this.verts_;
  var handles = this.handles_;

  var currIndex = index;
  var currHandle = heap[currIndex];
  for (;;) {
    // The children of node i are nodes 2i and 2i+1.
    var childIndex = currIndex << 1;
    if (childIndex < this.size_) {
      // Set child to the index of the child with the minimum vertex.
      if (libtess.geom.vertLeq(verts[heap[childIndex + 1]],
          verts[heap[childIndex]])) {
        childIndex = childIndex + 1;
      }
    }

    libtess.assert(childIndex <= this.max_);

    var childHandle = heap[childIndex];
    if (childIndex > this.size_ ||
        libtess.geom.vertLeq(verts[currHandle], verts[childHandle])) {
      // Heap restored.
      heap[currIndex] = currHandle;
      handles[currHandle] = currIndex;
      return;
    }

    // Swap current node and child; repeat from childIndex.
    heap[currIndex] = childHandle;
    handles[childHandle] = currIndex;
    currIndex = childIndex;
  }
};

/**
 * Restore heap by moving the vertex at index in the heap upwards to a valid
 * slot.
 * @private
 * @param {libtess.PQHandle} index
 */
libtess.PriorityQHeap.prototype.floatUp_ = function(index) {
  var heap = this.heap_;
  var verts = this.verts_;
  var handles = this.handles_;

  var currIndex = index;
  var currHandle = heap[currIndex];
  for (;;) {
    // The parent of node i is node floor(i/2).
    var parentIndex = currIndex >> 1;
    var parentHandle = heap[parentIndex];

    if (parentIndex === 0 ||
        libtess.geom.vertLeq(verts[parentHandle], verts[currHandle])) {
      // Heap restored.
      heap[currIndex] = currHandle;
      handles[currHandle] = currIndex;
      return;
    }

    // Swap current node and parent; repeat from parentIndex.
    heap[currIndex] = parentHandle;
    handles[parentHandle] = currIndex;
    currIndex = parentIndex;
  }
};

/* global libtess */

// TODO(bckenny): apparently only visible outside of sweep for debugging routines.
// find out if we can hide

/**
 * For each pair of adjacent edges crossing the sweep line, there is
 * an ActiveRegion to represent the region between them. The active
 * regions are kept in sorted order in a dynamic dictionary. As the
 * sweep line crosses each vertex, we update the affected regions.
 * @constructor
 * @struct
 */
libtess.ActiveRegion = function() {
  // TODO(bckenny): I *think* eUp and nodeUp could be passed in as constructor params

  /**
   * The upper edge of the region, directed right to left
   * @type {libtess.GluHalfEdge}
   */
  this.eUp = null;

  /**
   * Dictionary node corresponding to eUp edge.
   * @type {libtess.DictNode}
   */
  this.nodeUp = null;

  /**
   * Used to determine which regions are inside the polygon.
   * @type {number}
   */
  this.windingNumber = 0;

  /**
   * Whether this region is inside the polygon.
   * @type {boolean}
   */
  this.inside = false;

  /**
   * Marks fake edges at t = +/-infinity.
   * @type {boolean}
   */
  this.sentinel = false;

  /**
   * Marks regions where the upper or lower edge has changed, but we haven't
   * checked whether they intersect yet.
   * @type {boolean}
   */
  this.dirty = false;

  /**
   * marks temporary edges introduced when we process a "right vertex" (one
   * without any edges leaving to the right)
   * @type {boolean}
   */
  this.fixUpperEdge = false;
};

/**
 * Returns the ActiveRegion below this one.
 * @return {libtess.ActiveRegion}
 */
libtess.ActiveRegion.prototype.regionBelow = function() {
  return this.nodeUp.getPredecessor().getKey();
};

/**
 * Returns the ActiveRegion above this one.
 * @return {libtess.ActiveRegion}
 */
libtess.ActiveRegion.prototype.regionAbove = function() {
  return this.nodeUp.getSuccessor().getKey();
};

/* global libtess, module */

/**
 * node.js export for non-compiled source
 */
if (typeof module !== 'undefined') {
  module.exports = libtess;
}