added tangent between two circles

kmath-geometry/src/commonMain/kotlin/space/kscience/kmath/geometry/Tangent.kt

@@ -0,0 +1,77 @@
+/*
+ * 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
+}

kmath-geometry/src/commonTest/kotlin/space/kscience/kmath/geometry/TangentTest.kt

@@ -0,0 +1,39 @@
+/*
+ * 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)
+    }
+}