vmath/README.md

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# VMath - 2D and 3D vector math.

`nimble install vmath`

![Github Actions](https://github.com/treeform/vmath/workflows/Github%20Actions/badge.svg)

[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)`