forked from kscience/kmath
added tangent between two circles
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/*
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* Copyright 2018-2023 KMath contributors.
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* Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file.
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*/
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package space.kscience.kmath.geometry
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import space.kscience.kmath.geometry.Euclidean2DSpace.distanceTo
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import space.kscience.kmath.linear.DoubleLinearSpace.plus
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import space.kscience.kmath.linear.Point
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import kotlin.math.absoluteValue
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import kotlin.math.atan2
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import kotlin.math.pow
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import kotlin.math.sign
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import kotlin.math.sin
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import kotlin.math.cos
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import space.kscience.kmath.geometry.Euclidean2DSpace.vector
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import space.kscience.kmath.geometry.Euclidean2DSpace.dot
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import space.kscience.kmath.geometry.Euclidean2DSpace.scale
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import space.kscience.kmath.geometry.Euclidean2DSpace.add
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public class Segment(
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public val startPoint: DoubleVector2D,
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public val terminalPoint: DoubleVector2D,
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public val length: Double = startPoint.distanceTo(terminalPoint)
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) {
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public override operator fun equals(other: Any?): Boolean {
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return if (other is Segment) {
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startPoint.x.equalFloat(other.startPoint.x) && startPoint.y.equalFloat(other.startPoint.y) &&
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terminalPoint.x.equalFloat(other.terminalPoint.x) && terminalPoint.y.equalFloat(other.terminalPoint.y)
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} else {
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false
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}
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}
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}
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public const val maxFloatDelta: Double = 0.000001
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public fun Double.equalFloat(other: Double): Boolean = kotlin.math.abs(this - other) < maxFloatDelta
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public fun tangentsToCircles(
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startCircle: Circle2D,
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terminalCircle: Circle2D
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): kotlin.collections.MutableMap<String, Segment> {
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val R1 = startCircle.radius
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val R2 = terminalCircle.radius
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val d = Segment(startCircle.center, terminalCircle.center).length
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val angle1 = atan2(terminalCircle.center.x - startCircle.center.x, terminalCircle.center.y - startCircle.center.y)
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var r: Double
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var angle2: Double
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val routes = mapOf("RSR" to Pair(R1, R2),
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"RSL" to Pair(R1, -R2),
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"LSR" to Pair(-R1, R2),
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"LSL" to Pair(-R1, -R2))
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val segments = mutableMapOf<String, Segment>()
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for ((route, r1r2) in routes) {
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val r1 = r1r2.first
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val r2 = r1r2.second
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r = if (r1.sign == r2.sign) {
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r1.absoluteValue - r2.absoluteValue
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} else {
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r1.absoluteValue + r2.absoluteValue
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}
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val L = (d * d - r * r).pow(0.5)
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angle2 = if (r1.absoluteValue > r2.absoluteValue) {
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angle1 + r1.sign * atan2(r.absoluteValue, L)
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} else {
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angle1 - r2.sign * atan2(r.absoluteValue, L)
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}
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val W = vector(-cos(angle2), sin(angle2))
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segments[route] = Segment(add(startCircle.center, scale(W, r1)),
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add(terminalCircle.center, scale(W, r2)))
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}
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return segments
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}
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@ -0,0 +1,39 @@
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/*
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* Copyright 2018-2023 KMath contributors.
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* Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file.
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*/
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package space.kscience.kmath.geometry
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import space.kscience.kmath.geometry.Euclidean2DSpace.vector
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import kotlin.test.Test
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import kotlin.test.assertEquals
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class TangentTest {
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@Test
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fun tangent() {
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val c1 = Circle2D(vector(0.0, 0.0), 1.0)
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val c2 = Circle2D(vector(4.0, 0.0), 1.0)
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val routes = arrayListOf<String>("RSR", "RSL", "LSR", "LSL")
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val segments = arrayListOf<Segment>(
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Segment(startPoint = vector(0.0, 1.0),
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terminalPoint = vector(4.0, 1.0)),
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Segment(startPoint = vector(0.5, 0.8660254),
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terminalPoint = vector(3.5, -0.8660254)),
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Segment(startPoint = vector(0.5, -0.8660254),
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terminalPoint = vector(3.5, 0.8660254)),
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Segment(startPoint = vector(0.0, -1.0),
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terminalPoint = vector(4.0, -1.0))
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)
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val tangentMap = tangentsToCircles(c1, c2)
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val tangentMapKeys = tangentMap.keys.toList()
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val tangentMapValues = tangentMap.values.toList()
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assertEquals(routes, tangentMapKeys)
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for (i in segments.indices) {
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assertEquals(segments[i], tangentMapValues[i])
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}
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// assertEquals(segments, tangentMapValues)
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}
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}
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