# kotlin-math

Set of Kotlin APIs to make graphics math easier to write. These APIs are mostly modeled after GLSL (OpenGL Shading Language) to make porting code to and from shaders easier.

The various types offered by this library are only meant to be *value types*. Most APIs are therefore exposed as top-level functions and not as methods. For instance:

```
val v = Float3(1.0f, 3.0f, 4.0f)
val n = normalize(v)
```

This project supports multi-platform thanks to ekgame.

## Maven

```
repositories {
// ...
mavenCentral()
}
dependencies {
implementation 'dev.romainguy:kotlin-math:1.5.3'
}
```

## Building the project

Simply run the following command to generate `build/libs/kotlin-math.jar`

:

`$ ./gradlew assemble`

## Types

Scalar types:

`Half`

, half-precision floating point values (also called fp16)`Rational`

, number expressed as the ratio of two integer

Vector types:

`Float2`

, vector of 2 floats`Float3`

, vector of 3 floats`Float4`

, vector of 4 floats`Half2`

, vector of 2 half-precision floats`Half3`

, vector of 3 half-precision floats`Half4`

, vector of 4 half-precision floats`Bool2`

, vector of 2 booleans`Bool3`

, vector of 3 booleans`Bool4`

, vector of 4 booleans

Matrix types:

`Mat3`

, 3x3 float matrix`Mat4`

, 4x4 float matrix

Other types:

`Quaternion`

, unit quaternions to represent orientation`Ray`

, simple representation of a 3D ray (origin plus direction)

## Vector types

### Accessing components

Each vector type exposes its component as properties:

```
val x = myVector.x
val (x, y, z) = myVector
```

A vector can also be treated as an array:

```
val x = myVector[0]
val x = myVector[VectorComponents.X]
```

The traditional mathematical form with 1-based indexing can be used:

`val x = myVector(1)`

### Property aliases

To improve code readability, the vector types provide aliases for each property, allowing you to choose the most appropriate names:

```
val (x, y, z) = myPosition.xyz
val (r, g, b) = myColor.rgb
val (s, t) = myTextureCoordinates.st
```

### Swizzling

Vector types also provide different ways to swizzle their components, although in a more limited way than in GLSL. The most obvious use for swizzling is to extract sub-vectors:

```
val position = Float3(…)
val position2d = position.xy // extract a Float2
val colorWithAlpha = Float4(…)
val rgbColor = colorWithAlpha.rgb // extract a Float3
```

The get operators allows for more complex swizzling by enabling re-ordering and duplication of the components:

```
val colorWithAlpha = Float4(…)
val bgrColor = colorWithAlpha[
VectorComponents.B,
VectorComponents.G,
VectorComponents.R
] // re-ordered 3 components sub-vector
```

### Comparing vector types

Vector comparisons follow GLSL rules:

`==`

returns true if all components are equal`!=`

returns true if not all components are equal

In addition you can use component-wise relational operators that return a vector of boolean with the result of each component-wise comparison:

`lessThan`

`lessThanEqual`

`greaterThan`

`greaterThanEqual`

`equal`

`notEqual`

Example:

```
if (all(lessThan(v1, v2))) {
// …
}
```

You can also use the following infix operators if you prefer the operator syntax:

`lt`

`lte`

`gt`

`gte`

`eq`

`neq`

Example:

```
if (any(v1 lte v2)) {
// …
}
```

## Matrix types

Matrices are represented as a set of column vectors. For instance, a `Mat4`

can be destructured into the right, up, forward and translation vectors:

`val (right, up, forward, translation) = myMat4`

Each vector can be accessed as a property or by its index:

```
forward = myMat4.forward
forward = myMat4.z
forward = myMat4[2]
forward = myMat4[MatrixColumns.Z]
```

Matrix types also offer APIs to access each element individually by specifying the column then row:

```
v = myMat4.z[1]
v = myMat4[2, 1]
v = myMat4[MatrixColumns.Z, 1]
```

You can also use the invoke operator to access elements in row-major mode with 1-based indices to follow the traditional mathematical notation:

`v = myMat4(2, 3) // equivalent to myMat4[2, 1]`

## Quaternions and rotations

Construct a Euler angles rotation matrix using per-axis angles in degrees:

`rotationMatrix = rotation(d = Float3(y = 90.0f)) // rotation of 90° around y axis`

Construct a Euler angles rotation matrix using an axis direction and an angle in degrees:

`rotationMatrix = rotation(axis = Float3(y = 1.0f), angle = 90.0f) // rotation of 90° around y axis`

Construct a quaternion rotation matrix following the Hamilton convention (assumes the destination and local coordinate spaces are initially aligned, and the local coordinate space is then rotated counter-clockwise about a unit-length axis, k, by an angle, theta):

`rotationMatrix = rotation(quaternion = Quaternion(y = 1.0f, w = 1.0f)) // rotation of 90° around y axis`

## Scalar APIs

The file `Scalar.kt`

contains various helper methods to use common math operations with floats. It is intended to be used in combination with Kotlin 1.2's new float math methods.

## Rational numbers

This library provides simple support for rational numbers to avoid numerical imprecision. The current implementation is limited to 32 bits of storage for the numerator and the denominator. The current implementation is also not written for speed.

```
val a = Rational(2, 5) // Represents 2/5
val b = Rational(127) // Integers can be represented exactly
val c = Rational(0.25f) // Floats and doubles will be converted to a rational representation
// The following operators are supported:
println(+a)
println(-a)
println(a + b)
println(a - b)
println(c * d)
println(c / d)
// And you can convert back to other types:
println(a.toFloat())
println(a.toLong())
```