# VMath - 2D and 3D vector math. `nimble install vmath`  [API reference](https://treeform.github.io/vmath) This library has no dependencies other than the Nim standard library. Supports c, cpp and js backend. ## About Your one stop shop for vector math routines for 2d and 3d graphics. * Pure Nim with no dependencies. * Very similar to GLSL Shader Language with extra stuff. * Extensively [benchmarked](tests/bench_raytracer.nim). ## Has vector functions for GLSL types: Type | Constructor | Description ------|-------------| --------------------------------------------------- BVec# | bvec# | a vector of booleans IVec# | ivec# | a vector of signed integers UVec# | uvec# | a vector of unsigned integers Vec# | vec# | a vector of single-precision floating-point numbers DVec# | dvec# | a vector of double-precision floating-point numbers You can use these constructors to make them: NIM | GLSL | 2 | 3 | 4 | 9 | 16 | 4 | --------|--------|-------|-------|-------|-------|-------|-------| bool | bool | BVec2 | BVec3 | BVec4 | | | | int32 | int | IVec2 | IVec3 | IVec4 | | | | uint32 | uint | UVec2 | UVec3 | UVec4 | | | | float32 | float | Vec2 | Vec3 | Vec4 | Mat3 | Mat4 | Quat | float64 | double | DVec2 | DVec3 | DVec4 | DMat3 | DMat4 | DQuat | ## 2D & 3D matrix math You can combine and create 2d and 3d matrices by passing 2d or 3d vectors to matrix functions: ```nim let mat2d = translate(vec2(10, 20)) * rotate(45.toRadians) * scale(vec2(2)) let mat3d = translate(vec3(10, 20, 0)) * rotateZ(45.toRadians) * scale(vec3(2)) ``` ## Almost equal operator Easily check if floating point numbers are close, very useful for tests: ```nim 1.0 ~= 1.0 vec2(1.0, 2.0) ~= vec2(1.0, 2.0) dvec2(1) ~= dvec2(1) quat(1.0, 2.0, 3.0, 4.0) ~= quat(1.0, 2.0, 3.0, 4.0) ``` ## Number functions * `between` - Returns true if value is between min and max or equal to them. * `sign` - Returns the sign of a number, -1 or 1. * `quantize` - Makes v be a multiple of n. Rounding to integer quantize by 1.0. * `fractional` - Returns fractional part of a number. 3.14 -> 0.14 * `lerp` - Interpolates value between a and b. ## Angle functions * `fixAngle` - Make angle be from -PI to PI radians. * `angleBetween` - Find the angle between angle a and angle b. * `turnAngle` - Move from angle a to angle b with step of v. ## Vector and matrix representation and benchmarks. C compilers seem to optimize different representations differently. This is very surprising for us and vmath has 3 different implementations: * `-d:vmathObjBased` - A vector is an object of 3 floats. * `-d:vmathArrayBased` - A vector is an array of 3 floats. * `-d:vmathObjArrayBased` (default) - A vector is an object that has an array of 3 floats. ``` name ............................... min time avg time std dv runs vmathObjBased ..................... 74.061 ms 74.297 ms ±0.347 x100 vmathArrayBased ................... 89.498 ms 89.911 ms ±1.019 x100 vmathObjArrayBased ................ 73.968 ms 74.292 ms ±0.631 x100 ``` * [3d Ray Trace Benchmark](tests/bench_raytracer.nim) * [2d SVG Render Benchmark](https://github.com/treeform/pixie/blob/master/tests/bench_svg.nim) ## Zmod - GLSL mod GLSL uses a different type of float point mod. Because mod is a Nim keyword please use `zmod` when you need GLSL `mod` behavior. ## Coordinate System Right-hand z-forward coordinate system This is the same system used in the GLTF file format. > glTF uses a right-handed coordinate system. > glTF defines +Y as up, +Z as forward, and -X as right; > the front of a glTF asset faces +Z. [glTF Spec 2.0](https://registry.khronos.org/glTF/specs/2.0/glTF-2.0.html#coordinate-system-and-units) ## OpenGL matrix column-major notation. > [9.005](https://www.opengl.org/archives/resources/faq/technical/transformations.htm) For programming purposes, OpenGL matrices are 16-value arrays with base vectors laid out contiguously in memory. The translation components occupy the 13th, 14th, and 15th elements of the 16-element matrix, where indices are numbered from 1 to 16 as described in section 2.11.2 of the [OpenGL 2.1 Specification](https://registry.khronos.org/OpenGL/specs/gl/glspec21.pdf). > > Sadly, the use of column-major format in the spec and blue book has resulted in endless confusion in the OpenGL programming community. Column-major notation suggests that matrices are not laid out in memory as a programmer would expect. OpenGL/GLSL/vmath vs Math/Specification notation: ``` mat4([ a, b, c, 0, | a d g x | d, e, f, 0, | b e h y | g, h, i, 0, | c f i z | x, y, z, 1 | 0 0 0 1 | ]) ``` # 1.x.x to 2.0.0 vmath breaking changes: * New right-hand-z-forward cordate system and functions that care about coordinate system where moved there. * deprecated `lookAt()` please use `toAngles()`/`fromAngles()` instead. * deprecated `fractional()` use `frac()` instead. # 0.x.x to 1.0.0 vmath breaking changes: * `vec3(v)` no longer works please use `vec3(v.x, v.y, 0)` instead. * `vec3(v, 0)` no longer works please use `vec3(v.x, v.y, 0)` instead. * `2 * v` no longer works due to more vec types please use `v * 2` instead. * `m[15]` no longer works because matrices are now m[x, y]. * Concept of 3x3 rotation 3d matrix was removed. * `angleBetween` got renamed to `angle(a, b)` * `scaleMat` got renamed to `scale(v)` * `rotationMat3` got renamed to `rotate(x)`