Geometry 2D

Point and Matrix

Point and Matrix are classes holding doubles (to get consistency among targets including JavaScript) that represent a 2D Point (with x and y) and a 2D Affine Transform Matrix (with a, b, c, d, tx and ty). Point is a typealias of Vector2.

Vector2

Polar coordinates

You can construct a Vector2/Point from polar coordinates like:

Point.polar(Point(100, 100), 45.degrees, 50f, up = Vector2.UP_SCREEN) // (135.35535, 64.64466)
Point.polar(Point(100, 100), 45.degrees, 50f, up = Vector2.UP)        // (135.35535, 135.35535)
Point.polar(Point(100, 100), 45.degrees, 50f)                         // (135.35535, 135.35535)

The up vector is to determine where the up is, since by default it is going to be Y+ up, and that would be interpreted differently for drawn points in the case of KorGE since Y+ is down.

BoundsBuilder

BoundsBuilder is a class that allows to compute the bounds of a set of points without additional allocations.

class BoundsBuilder {
    fun reset()
    fun add(x: Double, y: Double): BoundsBuilder
    fun getBounds(out: Rectangle = Rectangle()): Rectangle
}

inline fun BoundsBuilder.add(x: Number, y: Number)
fun BoundsBuilder.add(p: IPoint)
fun BoundsBuilder.add(ps: Iterable<IPoint>)
fun BoundsBuilder.add(ps: IPointArrayList)
fun BoundsBuilder.add(rect: Rectangle)

PointArrayList

PointArrayList and PointIntArrayList can be used to store a list of points (pair of numbers) without allocating objects per element. You can later access x and y components with getX and getY or convert them into a list of Point for convenience that actually allocate objects.

class PointArrayList(capacity: Int = 7) {
    constructor(capacity: Int = 7, callback: PointArrayList.() -> Unit)
    constructor(points: List<IPoint>): PointArrayList
    constructor(vararg points: IPoint): PointArrayList

    val size: Int
    fun isEmpty(): Boolean
    fun isNotEmpty(): Boolean
    fun add(x: Double, y: Double)
    fun getX(index: Int)
    fun getY(index: Int)

    fun setX(index: Int, x: Double)
    fun setY(index: Int, y: Double)
    fun setXY(index: Int, x: Double, y: Double)
    fun reverse()
    fun sort()
}

fun PointArrayList.getPoint(index: Int): Point
fun PointArrayList.toPoints(): List<Point>
inline fun IPointArrayList.contains(x: Number, y: Number): Boolean

inline fun PointArrayList.add(x: Number, y: Number)
fun PointArrayList.add(p: Point)
fun PointArrayList.add(other: PointArrayList)
inline fun PointArrayList.setX(index: Int, x: Number)
inline fun PointArrayList.setY(index: Int, y: Number)
inline fun PointArrayList.setXY(index: Int, x: Number, y: Number)

Rectangle, Size, Anchor, Orientation and ScaleMode

data class Rectangle(
    var x: Double, var y: Double,
    var width: Double, var height: Double
) : MutableInterpolable<Rectangle>, Interpolable<Rectangle>, IRectangle, Sizeable

inline class Size(val p: Point) : MutableInterpolable<Size>, Interpolable<Size>, ISize, Sizeable

data class Anchor(val sx: Double, val sy: Double) : Interpolable<Anchor>

enum class Orientation(val value: Int) { CW(+1), CCW(-1), COLLINEAR(0) }

class ScaleMode {
    operator fun invoke(item: Size, container: Size, target: Size = Size()): Size

    companion object {
        val COVER: ScaleMode
        val SHOW_ALL: ScaleMode
        val EXACT: ScaleMode
        val NO_SCALE: ScaleMode
    }
}

As a sample combining most of these entities:

assertEquals(
    Rectangle(0, -150, 600, 600),
    Size(100, 100).applyScaleMode(
        Rectangle(0, 0, 600, 300),
        ScaleMode.COVER,
        Anchor.MIDDLE_CENTER
    )
)

Ray

The Ray class represents an infinite Line starting in a specific point and in a direction.

Constructing Ray

You can construct a Ray instance with:

val ray: Ray = Ray.fromTwoPoints(Point(1, 1), Point(3, 1)) // A ray starting at 1,1 and going to the right
val ray: Ray = Ray(point = Point(1, 1), direction = Vector2(1, 0)) // A ray starting at 1,1 and going to the right
val ray: Ray = Ray(point = Point(1, 1), angle = 0.degrees) // A ray starting at 1,1 and going to the right

The angle represents: 0 degrees is right, 90 degrees down, 180 degrees left, 270 degrees up.

Getting the starting point and the direction

You have point for the starting point, and direction (that is normalized) and angle representing the direction of the Ray.

val startPoint: Point = ray.point
val normalizedDirection: Vector2 = ray.direction // direction.length will be ~1
val angle: Angle = ray.angle // the angle: 0.degrees, right, 90.degrees down

Transforming and converting the Ray

You can apply an affine transformation to a Ray instance, and also we can convert it into a Line instance providing a length:

val newRay: Ray = ray.transformed(matrix) // Creates a new ray transformed
val line: Line = ray.toLine(10f) // Creates a new line going from the start point of the ray to its direction with a length of 10f

Checking for equality

Since Ray uses floating point, it provides a way to check for equality using an epsilon value as tolerance:

val isEquals: Boolean = ray1.isAlmostEquals(ray2, epsilon = 0.00001f)

BVH

N-dimensional Bounding Volume Hierarchy implementation

class BVH<T> {
	data class IntersectResult<T>(val intersect: Double, val obj: Node<T>)
}

BVH2D

A Bounding Volume Hierarchy implementation for 2D. It uses Rectangle to describe volumes and Ray for raycasting.

open class BVH2D<T>(val allowUpdateObjects: Boolean = true) {
    val bvh = BVH<T>(allowUpdateObjects = allowUpdateObjects)
    fun intersectRay(ray: Ray, rect: Rectangle? = null): BVHIntervals?
    fun envelope(): Rectangle
    fun intersect(ray: Ray, return_array = fastArrayListOf()): FastArrayList<IntersectResult<T>>
    fun search(rect: IRectangle, return_array = fastArrayListOf()): FastArrayList<BVH.Node<T>>
    fun insertOrUpdate(rect: IRectangle, obj: T)
    fun remove(rect: IRectangle, obj: T? = null)
    fun remove(obj: T)
    fun getObjectBounds(obj: T, out: Rectangle = Rectangle()): Rectangle
    fun debug()
}

fun BVHIntervals.toRectangle(out: Rectangle = Rectangle())
fun IRectangle.toBVH(out: BVHIntervals = BVHIntervals(2)): BVHIntervals
fun Ray.toBVH(out: BVHIntervals = BVHIntervals(2)): BVHIntervals