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

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This commit is contained in:
Edwin Jakobs
2025-08-20 21:38:58 +02:00
parent e17644a247
commit 307b3fc282
3 changed files with 138 additions and 11 deletions
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76
orx-shapes/src/commonMain/kotlin/primitives/CircleInversion.kt
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@@ -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 Circle(farPoint, 1e6)
return Line2D(this.center, direction)
}
// 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 Circle(farPoint, 1e6)
return Line2D(this.center, direction)
}
// For conformal inversion that preserves tangency, we use the standard circle inversion formula
@@ -141,4 +143,60 @@ fun Circle.invertConformal(circle: Circle): Circle {
val newRadius = abs(this.radius * this.radius * circle.radius / power)
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()
}

10
orx-shapes/src/jvmDemo/kotlin/primitives/DemoCircleInversion02.kt
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@@ -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)
}
}
}
}

63
orx-shapes/src/jvmDemo/kotlin/primitives/DemoCircleInversion03.kt Normal file
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@@ -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")
}
}
}
}
}