eseed math

namespace esd::math OR namespace esdm

Goal

This library aims to provide fast, flexible, and modern vector, matrix, and quaternion functions. constexpr is used everywhere possible, including constructors and operators, to maximize compile-time optimizations. As this is intended to be a modern library, and will likely be under active development for some time, C++20 has been chosen as the language standard as its concepts allow for much cleaner template code. There is no intention to support obscure or old compilers, however, all code should be standard compliant.

This project began as part of a game engine, and is designed primarily with game programming in mind.

Usage

This is a header only library. Simply include the include folder in your project.

Alternatively, link eseed_math in CMake:

add_subdirectory("path/to/eseed_math/")
target_link_libraries(target eseed_math)

Quick introduction

#include <iostream>
#include <eseed/math/vecops.hpp>
#include <eseed/math/matops.hpp>

int main() {
    esdm::Vec3<float> a(1, 2, 3);
    esdm::Vec3<float> b(4, 5, 6);

    std::cout << "a: " << a << std::endl;
    std::cout << "b: " << b << std::endl;

    esdm::Vec4<float> point(5, 0, 0, 1);
    esdm::Mat4<float> rotation = esdm::matrot(esdm::Vec3<float>(0, 1, 0), esdm::pi<float>() * 0.5f);

    std::cout << "point: " << point << std::endl;
    std::cout << "rotation: " << rotation << std::endl;
    
    point *= rotation;

    std::cout << "rotated point: " << point << std::endl;
}

Full feature list

Scalar functions

Full commented header

• Special floating point values
  • Infinity
    • Constant
    • Check
  • NaN
    • Quiet constant
    • Signaling constant
    • Check
  • Constants
    • Pi
• General functions
  • Absolute value
  • Square
  • Square root
  • Power
• Rounding
  • Truncate
  • Floor
  • Ceil
  • Round
• Direct-to-integer rounding
  • Truncate to int
  • Floor to int
  • Ceil to int
  • Round to int

Vector class

Full commented header

• Templated with length and type
  • esdm::Vec<std::size_t L, typename T>
• Common-sized aliases
  • esdm::Vec1<typename T>
  • esdm::Vec2<typename T>
  • esdm::Vec3<typename T>
  • esdm::Vec4<typename T>
• Constructors
  • Default
    • esdm::Vec3<float>() = [0, 0, 0]
  • Component-wise
    • esdm::Vec3<float>(x, y) = [x, y, 0]
    • esdm::Vec3<float>(x, y, z) = [x, y, z]
  • Copy constructor
    • esdm::Vec3<float>(otherFloatVec3 /* [1.f, 2.f, 3.f] */) = [1.f, 2.f, 3.f]
    • esdm::Vec3<float>(otherIntVec3 /* [1, 2, 3] */) = [1.f, 2.f, 3.f]
    • esdm::Vec3<float>(otherDoubleVec2 /* [0.5, 1.0] */) = [0.5f, 1.f]
• Operators (where applicable)
  • Subscript
    • []
      • vec[i]
      • Value and reference
  • Comparison
    • ==
      • vec == vec
  • Component-wise post and pre increment and decrement
    • ++ --
      • vec++
      • ++vec
  • Component-wise unary
    • + - ! ~
      • -vec
  • Component-wise binary
    • + - * / % & | ^ << >> && ||
      • vec + vec
      • vec + number
      • number + vec
  • Component-wise assignment
    • += -= *= /= %= &= |= ^= <<= >>=
      • vec += vec
      • vec += number
  • ostream
    • <<
      • std::cout << aVec3 << std::endl; prints in format "[x, y, z]"
• Named component accessors
  • Spatial components
    • x, y, z, w
  • Color components
    • r, g, b, a
  • Texture coord components
    • u, v
  • get_() - retrieve component, constexpr compatible
    • vec.getX()
  • set_(n) - set a component
    • vec.setX(5)
  • _() - retrieve reference to component
    • vec.x() = 5

Vector Functions

Full commented header

• Special floating point values
  • Infinity
    • Check all components
    • Check any component
  • NaN
    • Check all components
    • Check any component
• General component-wise functions
  • Absolute value
  • Square
  • Square root
  • Power
• General vector functions
  • Dot product
  • Cross product
• Component-wise rounding
  • Truncate
  • Floor
  • Ceil
  • Round
• Component-wise direct-to-integer rounding
  • Truncate to int
  • Floor to int
  • Ceil to int
  • Round to int

Matrix Class

Full commented header

• Templated with column size, row size, and type
  • esdm::Mat<std::size_t M, std::size_t N, typename T>
• Stored column-major
  • Important! When assigning components to a matrix, make sure the components are in a column-major format
• Shorthands for common sizes
  • Any column and row size up to 4 as esdm::Mat[M]x[N]<T>
    • e.g. esdm::Mat2x4<T>, esdm::Mat3x3<T>
  • Shorter-hand for square matrix as esdm::Mat[L]<T>
    • e.g. esdm::Mat4<T>
• Constructors
  • Default
    • esdm::Mat2<float>() = [[0, 0], [0, 0]]
  • Component-wise
    • esdm::Mat2<float>(1, 2, 3, 4) = [[1, 2], [3, 4]]
• Column and row getters
• Operators
  • Subscript
    • []
      • mat[i]
      • Value and reference
      • Returns a column vector
  • Comparison
    • ==
      • mat == mat
  • Component-wise post and pre increment and decrement
    • ++ --
      • mat++
      • ++mat
  • Component-wise unary
    • + - ! ~
      • -mat
  • Component-wise binary
    • + - * / % & | ^ << >> && ||
      • mat + mat (+ - only)
      • mat + number
      • number + mat
  • Component-wise assignment
    • += -= *= /= %= &= |= ^= <<= >>=
      • mat += mat (+= -= only)
      • mat += number
  • Matrix multiplication
    • *
      • mat * mat
      • mat * vec
      • vec * mat
  • ostream
    • <<
      • std::cout << aMat2 << std::endl; prints in format "[[0, 1], [2, 3]]"

Matrix functions

Full commented header

• Builders
  • Identity
• General functions
  • Inverse
  • Matrix multiplication
    • Matrix * matrix
    • Matrix * row vector
    • Column vector * matrix
• Matrix generation
  • Translation
  • Rotation