Scala game math

How to add in sbt:

resolvers += "jitpack" at "https://jitpack.io"
...
libraryDependencies += "com.github.Kright" % "ScalaGameMath" % "0.5.0"

Or for separate modules

libraryDependencies += Seq(
  "com.github.Kright.ScalaGameMath" %% "math" % "0.5.0",
  "com.github.Kright.ScalaGameMath" %% "physics3d" % "0.5.0",
)

for latest version:

libraryDependencies += "com.github.Kright" % "ScalaGameMath" % "master-SNAPSHOT"

For other variants see https://jitpack.io/#Kright/ScalaGameMath.

Modules

vector: Vector2d, Vector3d, Vector4d
math:
- Quaternion
- Matrix: 2x2, 3x3, 4x4
- Euler angles: yaw Z, pitch Y, roll X
physics3d: Rigid body physics
- Transform3d (position and orientation)
- Inertia3d (mass and tensor of angular mass)
- Force3d, Impulse3d, Velocity3d, Acceleration3d (combined linear and angular)
- Joint3d with Spring3d, AngularSpring3d, Friction, AngularFriction3d, OrientationSpring3d
- BodySystem for handling system of bodies with joints between them
swizzle: swizzle operators for vectors
solvers: helper for solving differential equations with Euler or Runge-Kutta methods
symbolic: simple implementation for AST like (1.0 + ("y" * "x"))
ga: experimental support for geometric algebra (GA) and plane-based geometric algebra (PGA). See https://bivector.net for more details. Suitable for any dimensions
pga3d: experimental library for 3d PGA with generated code and some common cases (Pga3dPlane, Pga3dPoint, Pga3dBivector, etc). There is a huge amount of similars methods (for each pair of classes for each type of multiplication). Because of generated methods for each case it's possible to know at compile time that, for example, dot product of two bivectors is a scalar.
pga3dCodeGen: hand-made code generator for library above. It does operations in symbolic form, and searches the most narrow subclass of multivector for result.

Vectors treated as columns. For quaternions and matrices, multiplication order is math-like, for example:

(matrixA * matrixB) * vec === matrixA * (matrixB * vec)
(quaternionA * quaternionB) * vec === quaternionA * (quaternionB * vec)

Support conversions between rotation matrix, quaternions and Euler angles.

Unfortunately JVM doesn't support lightweight structs, so there are a bunch of helper operators:

import com.github.kright.math.Quaternion

val q = Quaternion() // assign reference
q := Quaternion()    // assign by value (w, x, y, z)
val q2 = q * q       // new object created, reference assigned to q2
q *= q2              // q := q * q2, inplace, no objects created
q *> q2              // q2 := q * q2, inplace, no objects created

Library had module with swizzle operators:

import com.github.kright.math.{Vector3d, Vector4d}

val v = Vector4d(1, 2, 3, 4)
v.yx = v.xy
// v == (2, 1, 3, 4)
v.xy = v.yx
// v == (1, 2, 3, 4)
v = Vector3d(1, 2, 3).xyzz
// v == (1, 2, 3, 3)

Library doesn't have any external dependencies.

Physics

This part is still under development.

I prefer code correctness and simplicity over computational efficiency.

For example, BodySystem allocates a lot of temporary objects. So this class could be used as example or as reference implementation for bug-fixing. Maybe for some specific case with a lot of objects you will need your own implementation.

PGA

I'm inspired by https://bivector.net/PGADYN.html I want to rewrite physics equations in PGA. Work in progress.

Tests

sbt test

I use scalaCheck and property based approach. It goes well with checking math properties such as addition or multiplication associativity, zero and id elements, morphisms between quaternions and corresponding matrices or euler angles. For physics, it's ok to check that total energy and impulse are constant in body systems without friction.

How to change this library and try changes locally in other project

Change lib code, publish to local ivy repo:

sbt publishLocal

In my case "~/.ivy2/local/scalagamemath/scalagamemath_3/0.3.0-SNAPSHOT"

After that in other project add local library. In my case it was:

libraryDependencies += "scalagamemath" %% "scalagamemath" % "0.3.0-SNAPSHOT"

May be you will need to remove cached lib of jitpack, it will be placed in path like "~ /.cache/coursier/v1/https/jitpack.io/com/github/Kright/ScalaGameMath/master-SNAPSHOT".