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shapes.go
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shapes.go
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package fauxgl
import "math"
func NewPlane() *Mesh {
v1 := Vector{-0.5, -0.5, 0}
v2 := Vector{0.5, -0.5, 0}
v3 := Vector{0.5, 0.5, 0}
v4 := Vector{-0.5, 0.5, 0}
return NewTriangleMesh([]*Triangle{
NewTriangleForPoints(v1, v2, v3),
NewTriangleForPoints(v1, v3, v4),
})
}
func NewCube() *Mesh {
v := []Vector{
{-1, -1, -1}, {-1, -1, 1}, {-1, 1, -1}, {-1, 1, 1},
{1, -1, -1}, {1, -1, 1}, {1, 1, -1}, {1, 1, 1},
}
mesh := NewTriangleMesh([]*Triangle{
NewTriangleForPoints(v[3], v[5], v[7]),
NewTriangleForPoints(v[5], v[3], v[1]),
NewTriangleForPoints(v[0], v[6], v[4]),
NewTriangleForPoints(v[6], v[0], v[2]),
NewTriangleForPoints(v[0], v[5], v[1]),
NewTriangleForPoints(v[5], v[0], v[4]),
NewTriangleForPoints(v[5], v[6], v[7]),
NewTriangleForPoints(v[6], v[5], v[4]),
NewTriangleForPoints(v[6], v[3], v[7]),
NewTriangleForPoints(v[3], v[6], v[2]),
NewTriangleForPoints(v[0], v[3], v[2]),
NewTriangleForPoints(v[3], v[0], v[1]),
})
mesh.Transform(Scale(Vector{0.5, 0.5, 0.5}))
return mesh
}
func NewCubeForBox(box Box) *Mesh {
m := Translate(Vector{0.5, 0.5, 0.5})
m = m.Scale(box.Size())
m = m.Translate(box.Min)
cube := NewCube()
cube.Transform(m)
return cube
}
func NewCubeOutlineForBox(box Box) *Mesh {
x0 := box.Min.X
y0 := box.Min.Y
z0 := box.Min.Z
x1 := box.Max.X
y1 := box.Max.Y
z1 := box.Max.Z
return NewLineMesh([]*Line{
NewLineForPoints(Vector{x0, y0, z0}, Vector{x0, y0, z1}),
NewLineForPoints(Vector{x0, y1, z0}, Vector{x0, y1, z1}),
NewLineForPoints(Vector{x1, y0, z0}, Vector{x1, y0, z1}),
NewLineForPoints(Vector{x1, y1, z0}, Vector{x1, y1, z1}),
NewLineForPoints(Vector{x0, y0, z0}, Vector{x0, y1, z0}),
NewLineForPoints(Vector{x0, y0, z1}, Vector{x0, y1, z1}),
NewLineForPoints(Vector{x1, y0, z0}, Vector{x1, y1, z0}),
NewLineForPoints(Vector{x1, y0, z1}, Vector{x1, y1, z1}),
NewLineForPoints(Vector{x0, y0, z0}, Vector{x1, y0, z0}),
NewLineForPoints(Vector{x0, y1, z0}, Vector{x1, y1, z0}),
NewLineForPoints(Vector{x0, y0, z1}, Vector{x1, y0, z1}),
NewLineForPoints(Vector{x0, y1, z1}, Vector{x1, y1, z1}),
})
}
func NewLatLngSphere(latStep, lngStep int) *Mesh {
var triangles []*Triangle
for lat0 := -90; lat0 < 90; lat0 += latStep {
lat1 := lat0 + latStep
v0 := float64(lat0+90) / 180
v1 := float64(lat1+90) / 180
for lng0 := -180; lng0 < 180; lng0 += lngStep {
lng1 := lng0 + lngStep
u0 := float64(lng0+180) / 360
u1 := float64(lng1+180) / 360
if lng1 >= 180 {
lng1 -= 360
}
p00 := LatLngToXYZ(float64(lat0), float64(lng0))
p01 := LatLngToXYZ(float64(lat0), float64(lng1))
p10 := LatLngToXYZ(float64(lat1), float64(lng0))
p11 := LatLngToXYZ(float64(lat1), float64(lng1))
t1 := NewTriangleForPoints(p00, p01, p11)
t2 := NewTriangleForPoints(p00, p11, p10)
if lat0 != -90 {
t1.V1.Texture = Vector{u0, v0, 0}
t1.V2.Texture = Vector{u1, v0, 0}
t1.V3.Texture = Vector{u1, v1, 0}
triangles = append(triangles, t1)
}
if lat1 != 90 {
t2.V1.Texture = Vector{u0, v0, 0}
t2.V2.Texture = Vector{u1, v1, 0}
t2.V3.Texture = Vector{u0, v1, 0}
triangles = append(triangles, t2)
}
}
}
return NewTriangleMesh(triangles)
}
func NewSphere(detail int) *Mesh {
var triangles []*Triangle
ico := NewIcosahedron()
for _, t := range ico.Triangles {
v1 := t.V1.Position
v2 := t.V2.Position
v3 := t.V3.Position
triangles = append(triangles, newSphereHelper(detail, v1, v2, v3)...)
}
return NewTriangleMesh(triangles)
}
func newSphereHelper(detail int, v1, v2, v3 Vector) []*Triangle {
if detail == 0 {
t := NewTriangleForPoints(v1, v2, v3)
return []*Triangle{t}
}
var triangles []*Triangle
v12 := v1.Add(v2).DivScalar(2).Normalize()
v13 := v1.Add(v3).DivScalar(2).Normalize()
v23 := v2.Add(v3).DivScalar(2).Normalize()
triangles = append(triangles, newSphereHelper(detail-1, v1, v12, v13)...)
triangles = append(triangles, newSphereHelper(detail-1, v2, v23, v12)...)
triangles = append(triangles, newSphereHelper(detail-1, v3, v13, v23)...)
triangles = append(triangles, newSphereHelper(detail-1, v12, v23, v13)...)
return triangles
}
func NewCylinder(step int, capped bool) *Mesh {
var triangles []*Triangle
for a0 := 0; a0 < 360; a0 += step {
a1 := (a0 + step) % 360
r0 := Radians(float64(a0))
r1 := Radians(float64(a1))
x0 := math.Cos(r0)
y0 := math.Sin(r0)
x1 := math.Cos(r1)
y1 := math.Sin(r1)
p00 := Vector{x0, y0, -0.5}
p10 := Vector{x1, y1, -0.5}
p11 := Vector{x1, y1, 0.5}
p01 := Vector{x0, y0, 0.5}
t1 := NewTriangleForPoints(p00, p10, p11)
t2 := NewTriangleForPoints(p00, p11, p01)
triangles = append(triangles, t1)
triangles = append(triangles, t2)
if capped {
p0 := Vector{0, 0, -0.5}
p1 := Vector{0, 0, 0.5}
t3 := NewTriangleForPoints(p0, p10, p00)
t4 := NewTriangleForPoints(p1, p01, p11)
triangles = append(triangles, t3)
triangles = append(triangles, t4)
}
}
return NewTriangleMesh(triangles)
}
func NewCone(step int, capped bool) *Mesh {
var triangles []*Triangle
for a0 := 0; a0 < 360; a0 += step {
a1 := (a0 + step) % 360
r0 := Radians(float64(a0))
r1 := Radians(float64(a1))
x0 := math.Cos(r0)
y0 := math.Sin(r0)
x1 := math.Cos(r1)
y1 := math.Sin(r1)
p00 := Vector{x0, y0, -0.5}
p10 := Vector{x1, y1, -0.5}
p1 := Vector{0, 0, 0.5}
t1 := NewTriangleForPoints(p00, p10, p1)
triangles = append(triangles, t1)
if capped {
p0 := Vector{0, 0, -0.5}
t2 := NewTriangleForPoints(p0, p10, p00)
triangles = append(triangles, t2)
}
}
return NewTriangleMesh(triangles)
}
func NewIcosahedron() *Mesh {
const a = 0.8506507174597755
const b = 0.5257312591858783
vertices := []Vector{
{-a, -b, 0},
{-a, b, 0},
{-b, 0, -a},
{-b, 0, a},
{0, -a, -b},
{0, -a, b},
{0, a, -b},
{0, a, b},
{b, 0, -a},
{b, 0, a},
{a, -b, 0},
{a, b, 0},
}
indices := [][3]int{
{0, 3, 1},
{1, 3, 7},
{2, 0, 1},
{2, 1, 6},
{4, 0, 2},
{4, 5, 0},
{5, 3, 0},
{6, 1, 7},
{6, 7, 11},
{7, 3, 9},
{8, 2, 6},
{8, 4, 2},
{8, 6, 11},
{8, 10, 4},
{8, 11, 10},
{9, 3, 5},
{10, 5, 4},
{10, 9, 5},
{11, 7, 9},
{11, 9, 10},
}
triangles := make([]*Triangle, len(indices))
for i, idx := range indices {
p1 := vertices[idx[0]]
p2 := vertices[idx[1]]
p3 := vertices[idx[2]]
triangles[i] = NewTriangleForPoints(p1, p2, p3)
}
return NewTriangleMesh(triangles)
}