[orx-shapes] Extend circle inversion functionalities and update demos

orx-shapes/src/commonMain/kotlin/primitives/CircleInversion.kt

@@ -1,8 +1,14 @@
 package org.openrndr.extra.shapes.primitives
 
+import org.openrndr.math.GeometricPrimitive2D
 import org.openrndr.math.Vector2
 import org.openrndr.shape.Circle
+import org.openrndr.shape.Line2D
+import org.openrndr.shape.LineSegment
 import kotlin.math.abs
+import kotlin.math.atan2
+import kotlin.math.max
+import kotlin.math.min
 import kotlin.math.sqrt
 
 
@@ -53,7 +59,7 @@ fun Circle.invert(point: Vector2): Vector2 {
  * @return The inverted circle
  * @throws IllegalArgumentException if the circle to be inverted is centered at the center of the inverting circle
  */
-fun Circle.invert(circle: Circle): Circle {
+fun Circle.invert(circle: Circle): GeometricPrimitive2D {
     // Vector from this circle's center to the other circle's center
     val v = circle.center - this.center
 
@@ -73,8 +79,7 @@ fun Circle.invert(circle: Circle): Circle {
         // Special case: the result would be a line, which we can't represent as a Circle
         // We'll approximate it as a very large circle
         val direction = v.normalized
-        val farPoint = this.center + direction * 1e6
+        return Line2D(this.center, direction)
-        return Circle(farPoint, 1e6)
     }
 
     // Calculate power of the point (center of the inverting circle) with respect to the circle being inverted
@@ -101,7 +106,7 @@ fun Circle.invert(circle: Circle): Circle {
  * @return The conformally inverted circle
  * @throws IllegalArgumentException if the circle to be inverted is centered at the center of the inverting circle
  */
-fun Circle.invertConformal(circle: Circle): Circle {
+fun Circle.invertConformal(circle: Circle): GeometricPrimitive2D {
     // Vector from this circle's center to the other circle's center
     val v = circle.center - this.center
 
@@ -118,11 +123,8 @@ fun Circle.invertConformal(circle: Circle): Circle {
 
     // Check if the circle to be inverted passes through the center of the inverting circle
     if (abs(circle.radius - distance) < 1e-10) {
-        // Special case: the result would be a line, which we can't represent as a Circle
-        // We'll approximate it as a very large circle
         val direction = v.normalized
-        val farPoint = this.center + direction * 1e6
+        return Line2D(this.center, direction)
-        return Circle(farPoint, 1e6)
     }
 
     // For conformal inversion that preserves tangency, we use the standard circle inversion formula
@@ -142,3 +144,59 @@ fun Circle.invertConformal(circle: Circle): Circle {
 
     return Circle(newCenter, newRadius)
 }
+
+fun Circle.invert(segment: LineSegment): GeometricPrimitive2D {
+    val a = segment.start
+    val b = segment.end
+    val c = segment.position(0.5)
+
+    // Direction of the line (normalized)
+    val dir = (b - a)
+    val dirLen = dir.length
+    if (dirLen < 1e-10) {
+        // Degenerate segment: treat as a point inversion
+        return invert(a)
+    }
+    val u = dir / dirLen
+
+    // Foot of the perpendicular from circle center to the infinite line AB
+    val ao = center - a
+    val t = ao.dot(u)
+    val foot = a + u * t
+
+    val perpVec = center - foot
+    val dist = perpVec.length
+
+    // If the line passes through the center of inversion, it maps to a line
+    if (dist < 1e-10) {
+        val aInv = invert(a)
+        val bInv = invert(b)
+        return LineSegment(aInv, bInv)
+    }
+
+    // Inverse of a line not through the center is a circle passing through the center
+    val rPrime = (radius * radius) / (2.0 * dist)
+    val n = (foot - center).normalized // direction from center towards the line
+    val circleCenter = center + n * rPrime
+
+    // The circle radius equals rPrime (since it passes through the center)
+    val aInv = invert(a)
+    val bInv = invert(b)
+    val cInv = invert(c)
+
+    // Compute angles (in degrees) for the arc between inverted endpoints
+    val angleA = atan2(aInv.y - circleCenter.y, aInv.x - circleCenter.x) * 180.0 / kotlin.math.PI
+    val angleB = atan2(bInv.y - circleCenter.y, bInv.x - circleCenter.x) * 180.0 / kotlin.math.PI
+    val angleC = atan2(cInv.y - circleCenter.y, cInv.x - circleCenter.x) * 180.0 / kotlin.math.PI
+
+    var angle0 = min(angleA, angleB)
+    var angle1 = max(angleA, angleB)
+
+    if (angleC in angle0..angle1) {
+        angle1 -= 360.0
+    }
+
+
+    return Arc(circleCenter, rPrime, angle0, angle1).conjugate()
+
+}

orx-shapes/src/jvmDemo/kotlin/primitives/DemoCircleInversion02.kt

@@ -25,7 +25,10 @@ fun main() = application {
                         drawer.clear(ColorRGBa.WHITE)
                         drawer.fill = ColorRGBa.BLACK
                         drawer.stroke = null
-                        drawer.circle(mc.invertConformal(c))
+                        val ci = mc.invertConformal(c)
+                        when (ci) {
+                            is Circle -> drawer.circle(ci)
+                        }
                         break
                     }
                 }
@@ -39,7 +42,10 @@ fun main() = application {
                 for (i in 0 until 10) {
                     val c = Circle(i * width / 10.0 + width / 20.0, j * height / 10.0 + height / 20.0, 36.0)
                     if (p !in c) {
-                        drawer.circle(mc.invertConformal(c))
+                        val ci = mc.invertConformal(c)
+                        when (ci) {
+                            is Circle -> drawer.circle(ci)
+                        }
                     }
                 }
             }

orx-shapes/src/jvmDemo/kotlin/primitives/DemoCircleInversion03.kt

@@ -0,0 +1,63 @@
+package primitives
+
+import org.openrndr.application
+import org.openrndr.color.ColorRGBa
+import org.openrndr.draw.isolated
+import org.openrndr.extra.shapes.primitives.Arc
+import org.openrndr.extra.shapes.primitives.grid
+import org.openrndr.extra.shapes.primitives.invert
+import org.openrndr.math.Polar
+import org.openrndr.shape.Circle
+import org.openrndr.shape.LineSegment
+import kotlin.math.cos
+import kotlin.math.sin
+
+fun main() = application {
+    configure {
+        width = 720
+        height = 720
+    }
+    program {
+        extend {
+
+            val p = Polar(seconds * 36.0, 100.0).cartesian + drawer.bounds.center
+            val c = Circle(p, 180.0)
+            for (i in 0 until 10) {
+                val s = sin(seconds + i) * 0.25 + 0.25
+                drawer.fill = null
+                val ls = drawer.bounds.horizontal((i + 0.5) / 10.0).sub(0.5-s,0.5+s)
+                drawer.stroke = ColorRGBa.PINK
+
+                val cir = c.invert(ls)
+                when (cir) {
+                    is Circle -> drawer.circle(cir)
+                    is Arc -> drawer.contour(cir.contour)
+                    is LineSegment -> drawer.lineSegment(cir)
+                    else -> error("unsupported result")
+                }
+            }
+            drawer.isolated {
+                val pts = drawer.bounds.grid(10, 10).flatten().map {
+                    c.invert(it.center)
+                }
+                drawer.fill = ColorRGBa.BLACK
+                drawer.stroke = null
+                drawer.circles(pts, 5.0)
+
+            }
+            for (i in 0 until 10) {
+                drawer.fill = null
+                val s = cos(seconds + i) * 0.25 + 0.25
+                val ls = drawer.bounds.vertical((i + 0.5) / 10.0).sub(0.5-s,0.5+s)
+                drawer.stroke = ColorRGBa.PINK
+                val cir = c.invert(ls)
+                when (cir) {
+                    is Circle -> drawer.circle(cir)
+                    is Arc -> drawer.contour(cir.contour)
+                    is LineSegment -> drawer.lineSegment(cir)
+                    else -> error("unsupported result")
+                }
+            }
+        }
+    }
+}