musileko/src/math/zalgebra

zalgebra

Linear algebra library for games and computer graphics.

The goal is to become as complete and useful as the Unity one. I'm currently using it for my projects and will continue to update it as new needs are coming.

If you would like to contribute, don't hesitate! ;)

Examples

const za = @import("zalgebra");
const Vec3 = za.Vec3;
const Mat4 = za.Mat4;

pub fn main () void {
  var projection = za.perspective(45.0, 800.0 / 600.0, 0.1, 100.0);
  var view = za.lookAt(Vec3.new(0., 0., -3.), Vec3.zero(), Vec3.up());
  var model = Mat4.fromTranslate(Vec3.new(0.2, 0.5, 0.0));
  
  var mvp = Mat4.mult(projection, view.mult(model));
}

Quick reference

Aliases

Type	Description
Vec2	Two dimensional vector for f32
Vec2_f64	Two dimensional vector for f64
Vec2_i32	Two dimensional vector for i32
Vec3	Three dimensional vector for f32
Vec3_f64	Three dimensional vector for f64
Vec3_i32	Three dimensional vector for i32
Vec4	Four dimensional vector for f32
Vec4_f64	Four dimensional vector for f64
Vec4_i32	Four dimensional vector for i32
Mat4	4x4 matrix for f32
Mat4_f64	4x4 matrix for f64
Quat	Quaternion for f32
Quat_f64	Quaternion for f64
perspective	Perspective function for f32 4x4 mat4
orthographic	Orthographic function for f32 4x4 mat4
lookAt	LookAt function for f32 4x4 mat4

Vectors

Methods	Description
new	Construct a vector from 2 to 4 components
at	Return component from given index
set	Set all components to the same given value
negate	Scale all components by -1
cast	Cast a type to another type
fromSlice	Construct new vectors from slice
zero	Shorthand for (0, 0, 0)
one	Shorthand for (1, 1, 1)
up	Shorthand for (0, 1, 0) (only for vec3)
down	Shorthand for (0, -1, 0) (only for vec3)
right	Shorthand for (1, 0, 0) (only for vec3)
left	Shorthand for (-1, 0, 0) (only for vec3)
forward	Shorthand for (0, 0, 1) (only for vec3)
back	Shorthand for (0, 0, -1) (only for vec3)
toArray	Return an array of same size.
getAngle	Return angle in degrees between two vectors (only for vec2 and vec3)
length	Return the magnitude of the current vector
distance	Return the distance between two points
norm	Construct a new normalized vector based on the given one
eql	Return true if two vectors are equals
sub	Construct new vector resulting from the substraction between two vectors
add	Construct new vector resulting from the addition between two vectors
scale	Construct new vector after multiplying each components by the given scalar
cross	Construct the cross product (as vector) from two vectors (only for vec3)
dot	Return the dot product between two vectors
lerp	Linear interpolation between two vectors
min	Construct vector from the min components between two vectors
max	Construct vector from the min components between two vectors

Matrices

Note: All matrices are column-major.

Methods	Description
identity	Construct an identity matrix
fromSlice	Construct new matrix from given slice of data
getData	Return a pointer to the inner data
transpose	Return the transpose matrix
negate	Scale all components by -1
eql	Return true if two matrices are equals
multByVec4	Multiply a given vec4 by matrix (only for mat4)
fromTranslate	Construct a translation matrix
translate	Construct a translation from the given matrix according to given axis (vec3)
fromRotation	Construct a rotation matrix
fromEulerAngle	Construct a rotation matrix from pitch/yaw/roll in degrees (X * Y * Z)
rotate	Construct a rotation from the given matrix according to given axis (vec3)
fromScale	Construct a scale matrix
scale	Construct a scale from the given matrix according to given axis (vec3)
extractTranslation	Return a vector with proper translation
orthoNormalize	Ortho normalize the given matrix.
extractRotation	Return a vector with proper pitch/yaw/roll
extractScale	Return a vector with proper scale
perspective	Construct a perspective matrix from given fovy, aspect ratio, near/far inputs
orthographic	Construct an orthographic matrix from given left, right, bottom, top, near/far inputs
lookAt	Construct a right-handed lookAt matrix from given position (eye) and target
mult	Multiply two matrices
inv	Inverse the given matrix
recompose	Return matrix from given translation, rotation and scale components
decompose	Return components translation, rotation and scale from given matrix.
debugPrint	Print the matrix data for debug purpose

Quaternions

Methods	Description
new	Construct new quat from given floats
zero	Construct quat as (1, 0, 0, 0)
fromSlice	Construct new quaternion from slice
fromVec3	Construct quaternion from vec3
eql	Return true if two quaternions are equal
norm	Normalize given quaternion
length	Return the magniture of the given quaternion
sub	Construct quaternion resulting from the subtraction of two given ones
add	Construct quaternion resulting from the addition of two given ones
mult	Construct quaternion resulting from the multiplication of two given ones
scale	Construct quaternion resulting from the multiplication of all components of the given quat
dot	Return the dot product between two quaternions
toMat4	Convert given quat to rotation 4x4 matrix
fromEulerAngle	Construct quaternion from Euler angle
fromAxis	Construct quat from angle around specified axis
extractRotation	Get euler angles from given quaternion
rotateVec	Rotate given vector

Utilities

Methods	Description
toRadians	Convert degrees to radians
toDegrees	Convert radians to degrees
lerp	Linear interpolation between two floats

Contributing to the project

Don’t be shy about shooting any questions you may have. If you are a beginner/junior, don’t hesitate, I will always encourage you. It’s a safe place here. Also, I would be very happy to receive any kind of pull requests, you will have (at least) some feedback/guidance rapidly.

Behind screens, there are human beings, living any sort of story. So be always kind and respectful, because we all sheer to learn new things.

Thanks

This project is inspired by Handmade Math, nalgebra and Unity.