the intersection of two lines

TheIntersectionOfTwoLines.kt

import java.lang.AssertionError

data class Point(val x: Float, val y: Float)

fun pointAt(x: Float, y: Float) = Point(x, y)

data class Line(val p1: Point, val p2: Point)

infix fun Point.to(other: Point) = Line(this, other)

// 傾き
fun Line.slope() = (p2.y - p1.y) / (p2.x - p1.x)

// Y軸切片
fun Line.interceptYAxis() = p1.y - slope() * p1.x

// y = f(x)
fun Line.getY(x: Float): Float = slope() * x + interceptYAxis()

// 交点
fun Line.getIntercept(other: Line): Point? {
    val slopeA = this.slope()
    val slopeB = other.slope()

    return if (slopeA == slopeB) {
        // parallel
        null
    } else {
        val interceptX = (other.interceptYAxis() - this.interceptYAxis()) / (slopeA - slopeB)
        val interceptY = this.getY(interceptX)
        pointAt(interceptX, interceptY)
    }
}

// 線上に存在するかどうか
fun Line.contains(point: Point): Boolean {
    val x = point.x
    val y = point.y
    val containsX = (x in p1.x..p2.x) || (x in p2.x..p1.x)
    val containsY = (y in p1.y..p2.y) || (y in p2.y..p1.y)
    return containsX && containsY
}

// 交差しているかどうか
fun Line.isIntersect(other: Line): Boolean {
    if (this.slope() == other.slope()) return false
    val intercept = this.getIntercept(other) ?: return false
    return this.contains(intercept) && other.contains(intercept)
}

fun Point.move(point: Point) = copy(x = x + point.x, y = y + point.y)

fun Line.parallelTransport(point: Point) = copy(p1 = p1.move(point), p2 = p2.move(point))


fun main() {
    run {
        val lineA = pointAt(1f, 1f) to pointAt(-1f, -1f)
        val lineB = pointAt(-1f, 1f) to pointAt(1f, -1f)
        // 交点を持つ
        val interceptPoint = lineA.getIntercept(lineB)
        if (interceptPoint != pointAt(0f, 0f)) throw AssertionError("$interceptPoint")
        val isIntersect = lineA.isIntersect(lineB)
        if (!isIntersect) throw AssertionError("$lineA : $lineB")
    }
    run {
        val lineA = pointAt(1f, 1f) to pointAt(0f, 0f)
        val lineB = pointAt(0f, 0f) to pointAt(1f, -1f)
        // 交点を持つ
        val interceptPoint = lineA.getIntercept(lineB)
        if (interceptPoint != pointAt(0f, 0f)) throw AssertionError("$interceptPoint")
        val isIntersect = lineA.isIntersect(lineB)
        if (!isIntersect) throw AssertionError("$lineA : $lineB")
    }
    run {
        val dist = pointAt(3f, -3f)
        val lineA = pointAt(1f, 1f) to pointAt(-1f, -1f)
        val lineB = pointAt(-1f, 1f).move(dist) to pointAt(1f, -1f).move(dist)
        // 直線上の延長線上に交点を持つが、範囲内では交差しない
        val interceptPoint = lineA.getIntercept(lineB)
        if (interceptPoint != pointAt(0f, 0f)) throw AssertionError("$interceptPoint")
        val isIntersect = lineA.isIntersect(lineB)
        if (isIntersect) throw AssertionError("$lineA : $lineB")
    }
    run {
        val dist = pointAt(-3f, 3f)
        val lineA = pointAt(1f, 1f) to pointAt(-1f, -1f)
        val lineB = pointAt(-1f, 1f).move(dist) to pointAt(1f, -1f).move(dist)
        // 直線上の延長線上に交点を持つが、範囲内では交差しない
        val interceptPoint = lineA.getIntercept(lineB)
        if (interceptPoint != pointAt(0f, 0f)) throw AssertionError("$interceptPoint")
        val isIntersect = lineA.isIntersect(lineB)
        if (isIntersect) throw AssertionError("$lineA : $lineB")
    }
    run {
        val dist = pointAt(-5f, -5f)
        val lineA = pointAt(1f, 1f) to pointAt(-1f, -1f)
        val lineB = pointAt(-1f, 1f).move(dist) to pointAt(1f, -1f).move(dist)
        // 直線上の延長線上に交点を持つが、範囲内では交差しない
        val interceptPoint = lineA.getIntercept(lineB)
        if (interceptPoint != pointAt(-5f, -5f)) throw AssertionError("$interceptPoint")
        val isIntersect = lineA.isIntersect(lineB)
        if (isIntersect) throw AssertionError("$lineA : $lineB")
    }
    run {
        val dist = pointAt(5f, 5f)
        val lineA = pointAt(1f, 1f) to pointAt(-1f, -1f)
        val lineB = pointAt(-1f, 1f).move(dist) to pointAt(1f, -1f).move(dist)
        // 直線上の延長線上に交点を持つが、範囲内では交差しない
        val interceptPoint = lineA.getIntercept(lineB)
        if (interceptPoint != pointAt(5f, 5f)) throw AssertionError("$interceptPoint")
        val isIntersect = lineA.isIntersect(lineB)
        if (isIntersect) throw AssertionError("$lineA : $lineB")
    }
    run {
        val dist = pointAt(5f, 5f)
        val lineA = pointAt(1f, 1f) to pointAt(1f, -1f)
        val lineB = lineA.parallelTransport(dist)
        // 直線上の延長線上に持たず、範囲内では交差しない
        val interceptPoint = lineA.getIntercept(lineB)
        if (interceptPoint != null) throw AssertionError("$interceptPoint")
        val isIntersect = lineA.isIntersect(lineB)
        if (isIntersect) throw AssertionError("$lineA : $lineB")
    }
}