added tangent between two circles

This commit is contained in:
Artyom Degtyarev 2023-02-13 23:17:13 +03:00
parent 784d397ab1
commit 50579f4712
2 changed files with 116 additions and 0 deletions

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

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/*
* Copyright 2018-2023 KMath contributors.
* Use of this source code is governed by the Apache 2.0 license that can be found in the license/LICENSE.txt file.
*/
package space.kscience.kmath.geometry
import space.kscience.kmath.geometry.Euclidean2DSpace.vector
import kotlin.test.Test
import kotlin.test.assertEquals
class TangentTest {
@Test
fun tangent() {
val c1 = Circle2D(vector(0.0, 0.0), 1.0)
val c2 = Circle2D(vector(4.0, 0.0), 1.0)
val routes = arrayListOf<String>("RSR", "RSL", "LSR", "LSL")
val segments = arrayListOf<Segment>(
Segment(startPoint = vector(0.0, 1.0),
terminalPoint = vector(4.0, 1.0)),
Segment(startPoint = vector(0.5, 0.8660254),
terminalPoint = vector(3.5, -0.8660254)),
Segment(startPoint = vector(0.5, -0.8660254),
terminalPoint = vector(3.5, 0.8660254)),
Segment(startPoint = vector(0.0, -1.0),
terminalPoint = vector(4.0, -1.0))
)
val tangentMap = tangentsToCircles(c1, c2)
val tangentMapKeys = tangentMap.keys.toList()
val tangentMapValues = tangentMap.values.toList()
assertEquals(routes, tangentMapKeys)
for (i in segments.indices) {
assertEquals(segments[i], tangentMapValues[i])
}
// assertEquals(segments, tangentMapValues)
}
}