3D maths for Kotlin Multiplatform: vectors, matrices, quaternions, bounding volumes and colour, with the same API as three.js.

Documentation · a guided tour, a first program, plus the generated API reference.

29 maths types in common Kotlin: Vector2/3/4, Matrix2/3/4, Quaternion, Euler, Box2/Box3, Sphere, Plane, Ray, Line3, Triangle, Frustum, FrustumArray, Spherical, Cylindrical, SphericalHarmonics3, Color, ColorManagement, MathUtils, and Interpolant with its five keyframe subclasses.

Kite3D draws nothing. It has no Object3D, no scene graph, no BufferGeometry, no camera, material, light, shader graph or GPU backend. Use it for the maths. It is not an engine.

The library ships as one artifact of pure commonMain Kotlin. It uses no expect/actual, no cinterop and no JNI. Its only dependency is kotlin-stdlib.

import io.github.yuroyami.kite3d.math.*

// Is this box inside a camera's view? Build the projection matrix yourself.
// Kite3D has no camera type.
val projection = Matrix4().makePerspective(-1.0, 1.0, 1.0, -1.0, 1.0, 100.0)
val frustum = Frustum().setFromProjectionMatrix(projection)

val box = Box3(Vector3(0.0, 0.0, 0.0), Vector3(1.0, 1.0, 1.0))
frustum.intersectsBox(box)                          // false: the box is behind the camera

box.translate(Vector3(-1.0001, -1.0001, -1.0001))
frustum.intersectsBox(box)                          // true: the box now crosses the near plane

kotlin {
    sourceSets {
        commonMain.dependencies {
            implementation("io.github.yuroyami:kite3d:0.1.0")
        }
    }
}

Everything lives in io.github.yuroyami.kite3d.math. The five interpolants live in io.github.yuroyami.kite3d.math.interpolants. There is no facade object and no entry point. Import the types you use.

Four rules cover the whole library.

Objects are mutable, and methods return the receiver.

val v = Vector3(1.0, 2.0, 3.0)
    .multiplyScalar(2.0)
    .add(Vector3(0.0, 1.0, 0.0))
    .normalize()

a.add(b) changes a. Call clone() first when you need the original.

A query that computes a new value writes into a target you pass in.

val box = Box3(Vector3(-1.0, -1.0, -1.0), Vector3(1.0, 3.0, 1.0))

val center = Vector3()
box.getCenter(center)     // writes (0.0, 1.0, 0.0) into center, and returns it

box.getCenter() with no argument does not compile. No query method has an allocating overload. That is true of getCenter, getSize, projectPoint, intersectSphere and all the others. Pass a fresh Vector3() when you have nowhere to keep the result.

Plain properties work differently. sphere.center, box.min and ray.origin read state the object already holds, so they take no argument.

Constructors keep the object you hand them.

val center = Vector3(0.0, 0.0, 0.0)
val sphere = Sphere(center, 1.0)

center.set(5.0, 0.0, 0.0)
sphere.center                 // (5.0, 0.0, 0.0): the same Vector3

Sphere, Box3, Ray, Line3, Plane and Triangle store the vectors you pass. They do not copy them. Clone a vector first if you do not want that.

Every scalar is Double. There are no Float overloads.

val model = Matrix4().compose(
    Vector3(0.0, 2.0, 0.0),                                        // position
    Quaternion().setFromEuler(Euler(0.0, MathUtils.degToRad(90.0), 0.0)),
    Vector3(1.0, 1.0, 1.0),                                        // scale
)

Vector3(1.0, 0.0, 0.0).applyMatrix4(model)   // (2.2e-16, 2.0, -1.0); x is 0 plus rounding error

val position = Vector3()
val rotation = Quaternion()
val scale = Vector3()
model.decompose(position, rotation, scale)   // (0, 2, 0), the rotation, (1, 1, 1)

Euler holds its own rotation order. The default is EulerOrder.XYZ. Call reorder to convert between orders. Matrix4 also has lookAt, makeBasis, makeShear, makePerspective, makeOrthographic and the per-axis makeRotationX/Y/Z.

val bounds = Box3().setFromPoints(
    listOf(
        Vector3(-1.0, -1.0, -1.0),
        Vector3(2.0, 0.5, 1.0),
        Vector3(0.0, 3.0, -2.0),
    ),
)

bounds.getSize(Vector3())                                  // (3.0, 4.0, 3.0)
bounds.intersectsSphere(Sphere(Vector3(), 2.0))            // true
bounds.containsPoint(Vector3())                            // true
bounds.getBoundingSphere(Sphere()).radius                  // 2.9154759474226504

Box3 intersects boxes, spheres, planes and triangles. Sphere, Plane, Triangle and Frustum have the matching methods. A culling pass needs three of them: Frustum.containsPoint, Frustum.intersectsSphere and Frustum.intersectsBox.

val ray = Ray(Vector3(0.0, 0.0, 5.0), Vector3(0.0, 0.0, -1.0))

val hit: Vector3? = ray.intersectSphere(Sphere(Vector3(), 1.0), Vector3())
// (0.0, 0.0, 1.0), or null when the ray misses

ray.at(2.0, Vector3())                                     // (0.0, 0.0, 3.0)

ray.intersectTriangle(
    Vector3(-1.0, -1.0, 0.0),
    Vector3(1.0, -1.0, 0.0),
    Vector3(0.0, 1.0, 0.0),
    backfaceCulling = false,
    Vector3(),
)                                                          // (0.0, 0.0, 0.0)

intersectSphere, intersectBox, intersectPlane and intersectTriangle return null when the ray misses. intersectsSphere, intersectsBox and intersectsPlane answer the same question without producing a point.

val offset = Vector3(0.0, 5.0, 10.0)          // camera position, relative to its target
val s = Spherical().setFromVector3(offset)    // radius 11.180339887498949

s.theta += 0.05                               // rotate sideways
s.phi -= 0.05                                 // rotate upward
s.makeSafe()                                  // keep phi away from the poles

offset.setFromSpherical(s)

Cylindrical works the same way. It has radius, theta and y, and pairs with Vector3.setFromCylindrical.

val mixed = Color().lerpColors(Color(0xff0000), Color(0x0000ff), 0.5)
mixed.getHexString()          // "bc00bc"

Color(0xff0000) reads the hex value as sRGB. It then stores the colour in the working colour space. ColorManagement sets that space to linear sRGB by default. The blend therefore happens in linear light, and the midpoint comes back as bc00bc rather than 7f007f.

All four readers take a colour space, but their defaults differ:

Pass the colour space explicitly to getRGB and getHSL when you want sRGB numbers back. There is no string constructor. See Limits.

import io.github.yuroyami.kite3d.math.interpolants.*

val times = doubleArrayOf(0.0, 1.0, 2.0)
val values = doubleArrayOf(0.0, 10.0, 20.0)
val track = LinearInterpolant(times, values, 1, DoubleArray(1))

track.evaluate(0.5)[0]        // 5.0
track.evaluate(1.5)[0]        // 15.0

LinearInterpolant, CubicInterpolant, DiscreteInterpolant, QuaternionLinearInterpolant and BezierInterpolant all extend the abstract Interpolant. Its copySampleValue_ method is open, so a glTF cubic-spline subclass can override it.

One artifact, 22 targets.

There is no androidTarget. Declaring it would require a configured Android SDK to build the project, so Kite3D leaves it out on purpose. No -android artifact is published. An Android module that depends on io.github.yuroyami:kite3d resolves the jvm artifact instead.

That works, because the code is target-agnostic and the bytecode level is 11. There is still no declared minSdk and no Android-specific variant. The androidNative* entries above are the NDK targets. They are not a substitute.

Kite3D renders nothing. The published artifact contains one package, io.github.yuroyami.kite3d.math, and its sub-package of interpolants.

Some methods are missing, because they need types that Kite3D does not have:

The rest of the current limits:

• FrustumArray is public but does almost nothing. Only clone() and coordinateSystem are available. Every intersection method and setFromArrayCamera is missing. Use Frustum for culling.
• Color cannot read CSS strings. setStyle, setColorName, getStyle and Color.NAMES are missing, so you cannot build a colour from "#ff0000" or "red". Use the Int hex constructor, three Double values, or setHSL.
• The element constructors are missing. Matrix4(n11, n12, …) does not exist. Use Matrix4().set(…), which takes the same sixteen arguments in the same row-major order. Matrix3 and Matrix2 work the same way, with nine arguments and four.
• Results are not bit-identical across targets. sin, cos and exp differ slightly between JavaScript, the JVM and native libm. The same call can return a slightly different Double on another target. Compare results with a tolerance.
• No instance is thread-safe. ColorManagement is not thread-safe either, because it holds the global enabled and workingColorSpace values. Separate instances are safe to use at the same time on different threads. A JVM concurrency test checks that.
• Explicit API mode and a committed ABI dump under kite3d/api/ lock the public API, so a signature change fails the build. That guard starts at 0.1.0. It does not make 0.1.0 a stable API.

452 tests cover the maths in common code. One more test runs on the JVM only. It puts 32 threads through the shared types and compares the results against a single-threaded baseline. CI runs the common suite on ten hosts: JVM, JS (Node), Wasm (Node), Wasm (WASI), linuxX64, macosArm64, iosSimulatorArm64, tvosSimulatorArm64, watchosSimulatorArm64 and mingwX64. The remaining targets are compile-checked by assemble, because no GitHub-hosted runner can execute them.

Matrix2, BezierInterpolant and FrustumArray have no tests.

See CONTRIBUTING.md. Every change lands with its tests. Regenerate the ABI dump with ./gradlew :kite3d:updateKotlinAbi when you change the public surface.

MIT. Kotlin port © 2026 yuroyami; original three.js © 2010-2026 three.js authors. See LICENSE and CHANGELOG.md.

Part of the Kite family: KiteCore, KitePDF, KiteQR.