# 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)

## Building the project

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

\$ ./gradlew assemble

## Types

Vector types:

• Float2, vector of 2 floats
• Float3, vector of 3 floats
• Float4, vector of 4 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

## 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
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

• == 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
forward = myMat4[MatrixColumns.Z]

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

v = myMat4.z
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]

## 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.