102 lines
3.8 KiB
Markdown
102 lines
3.8 KiB
Markdown
<img src="docs/banner.png">
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# VMath - 2d and 3d vector math.
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`nimble install vmath`
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[API reference](https://nimdocs.com/treeform/vmath)
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This library has no dependencies other than the Nim standard library.
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## About
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Your one stop shop for vector math routines for 2d and 3d graphics.
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* Pure Nim with no dependencies.
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* Very similar to GLSL Shader Language with extra stuff.
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* Extensively [benchmarked](tests/bench_raytracer.nim).
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## Has vector functions for GLSL types:
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Type | Constructor | Description
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------|-------------| ---------------------------------------------------
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BVec# | bvec# | a vector of booleans
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IVec# | ivec# | a vector of signed integers
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UVec# | uvec# | a vector of unsigned integers
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Vec# | vec# | a vector of single-precision floating-point numbers
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DVec# | dvec# | a vector of double-precision floating-point numbers
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You can use these constructors to make them:
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NIM | GLSL | 2 | 3 | 4 | 9 | 16 | 4 |
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--------|--------|-------|-------|-------|-------|-------|-------|
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bool | bool | BVec2 | BVec3 | BVec4 | | | |
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int32 | int | IVec2 | IVec3 | IVec4 | | | |
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uint32 | uint | UVec2 | UVec3 | UVec4 | | | |
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float32 | float | Vec2 | Vec3 | Vec4 | Mat3 | Mat4 | Quat |
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float64 | double | DVec2 | DVec3 | DVec4 | DMat3 | DMat4 | DQuat |
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## 2D & 3D matrix math
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You can combine and create 2d and 3d matrices by passing 2d or 3d vectors to matrix functions:
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```nim
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let mat2d = translate(vec2(10, 20)) * rotate(45.toRadians) * scale(vec2(2))
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let mat3d = translate(vec3(10, 20, 0)) * rotateZ(45.toRadians) * scale(vec3(2))
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```
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## Almost equal operator
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Easily check if floating point numbers are close, very useful for tests:
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```nim
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1.0 ~= 1.0
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vec2(1.0, 2.0) ~= vec2(1.0, 2.0)
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dvec2(1) ~= dvec2(1)
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quat(1.0, 2.0, 3.0, 4.0) ~= quat(1.0, 2.0, 3.0, 4.0)
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```
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## Number functions
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* `between` - Returns true if value is between min and max or equal to them.
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* `sign` - Returns the sign of a number, -1 or 1.
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* `quantize` - Makes v be a multiple of n. Rounding to integer quantize by 1.0.
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* `fractional` - Returns fractional part of a number. 3.14 -> 0.14
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* `lerp` - Interpolates value between a and b.
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## Angle functions
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* `fixAngle` - Make angle be from -PI to PI radians.
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* `angleBetween` - Find the angle between angle a and angle b.
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* `turnAngle` - Move from angle a to angle b with step of v.
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## Vector and matrix representation and benchmarks.
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C compilers seem to optimize different representations differently. This is very surprising for us and vmath has 3 different implementations:
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* `-d:vmathObjBased` - A vector is an object of 3 floats.
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* `-d:vmathArrayBased` - A vector is an array of 3 floats.
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* `-d:vmathObjArrayBased` (default) - A vector is an object that has an array of 3 floats.
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```
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name ............................... min time avg time std dv runs
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vmathObjBased ..................... 74.061 ms 74.297 ms ±0.347 x100
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vmathArrayBased ................... 89.498 ms 89.911 ms ±1.019 x100
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vmathObjArrayBased ................ 73.968 ms 74.292 ms ±0.631 x100
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```
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* [3d Ray Trace Benchmark](tests/bench_raytracer.nim)
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* [2d SVG Render Benchmark](https://github.com/treeform/pixie/blob/master/tests/bench_svg.nim)
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# 0.x.x to 1.0.0 vmath breaking changes:
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* `vec3(v)` no longer works please use `vec3(v.x, v.y, 0)` instead.
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* `vec3(v, 0)` no longer works please use `vec3(v.x, v.y, 0)` instead.
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* `2 * v` no longer works due to more vec types please use `v * 2` instead.
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* `m[15]` no longer works because matrices are now m[x, y].
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* Concept of 3x3 rotation 3d matrix was removed.
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* `angleBetween` got renamed to `angle(a, b)`
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* `scaleMat` got renamed to `scale(v)`
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* `rotationMat3` got renamed to `rotate(x)`
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