[orx-shapes] Add circle inversion primitives and demo examples
This commit is contained in:
Edwin Jakobs
81
orx-shapes/src/commonTest/kotlin/TestCircleInvert.kt
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81
orx-shapes/src/commonTest/kotlin/TestCircleInvert.kt
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import org.openrndr.math.Vector2
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import org.openrndr.shape.Circle
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import org.openrndr.extra.shapes.primitives.invert
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import kotlin.math.abs
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import kotlin.test.Test
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import kotlin.test.assertEquals
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import kotlin.test.assertFailsWith
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import kotlin.test.assertTrue
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class TestCircleInvert {
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@Test
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fun testInvertPointOutsideCircle() {
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val circle = Circle(100.0, 100.0, 50.0)
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val point = Vector2(200.0, 100.0) // Point outside the circle
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val inverted = circle.invert(point)
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// The inverted point should be at (125.0, 100.0)
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// This is because:
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// - The point is 100 units away from the center
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// - The radius is 50
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// - The inverted distance is 50²/100 = 25
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// - So the inverted point is 25 units from the center in the same direction
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assertEquals(125.0, inverted.x, 1e-10)
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assertEquals(100.0, inverted.y, 1e-10)
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// Verify the inversion property: |OPʹ| × |OP| = r²
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val distanceToPoint = (point - circle.center).length
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val distanceToInverted = (inverted - circle.center).length
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assertTrue(abs(distanceToPoint * distanceToInverted - circle.radius * circle.radius) < 1e-10)
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}
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@Test
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fun testInvertPointInsideCircle() {
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val circle = Circle(100.0, 100.0, 50.0)
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val point = Vector2(125.0, 100.0) // Point inside the circle
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val inverted = circle.invert(point)
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// The inverted point should be at (200.0, 100.0)
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// This is because:
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// - The point is 25 units away from the center
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// - The radius is 50
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// - The inverted distance is 50²/25 = 100
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// - So the inverted point is 100 units from the center in the same direction
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assertEquals(200.0, inverted.x, 1e-10)
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assertEquals(100.0, inverted.y, 1e-10)
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// Verify the inversion property: |OPʹ| × |OP| = r²
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val distanceToPoint = (point - circle.center).length
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val distanceToInverted = (inverted - circle.center).length
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assertTrue(abs(distanceToPoint * distanceToInverted - circle.radius * circle.radius) < 1e-10)
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}
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@Test
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fun testInvertPointOnCircle() {
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val circle = Circle(100.0, 100.0, 50.0)
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val point = Vector2(150.0, 100.0) // Point on the circle
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val inverted = circle.invert(point)
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// The inverted point should be the same as the original point
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// This is because points on the circle invert to themselves
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assertEquals(150.0, inverted.x, 1e-10)
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assertEquals(100.0, inverted.y, 1e-10)
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// Verify the inversion property: |OPʹ| × |OP| = r²
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val distanceToPoint = (point - circle.center).length
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val distanceToInverted = (inverted - circle.center).length
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assertTrue(abs(distanceToPoint * distanceToInverted - circle.radius * circle.radius) < 1e-10)
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}
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@Test
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fun testInvertPointAtCenter() {
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val circle = Circle(100.0, 100.0, 50.0)
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val point = Vector2(100.0, 100.0) // Point at the center
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// Inverting a point at the center should throw an exception
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assertFailsWith<IllegalArgumentException> {
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circle.invert(point)
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}
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}
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}
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import org.openrndr.math.Vector2
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import org.openrndr.shape.Circle
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import org.openrndr.extra.shapes.primitives.invertConformal
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import kotlin.math.abs
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import kotlin.test.Test
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import kotlin.test.assertEquals
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import kotlin.test.assertFailsWith
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import kotlin.test.assertTrue
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class TestCircleInvertConformal {
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/**
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* Helper function to check if two circles are tangent
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*/
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private fun areTangent(circle1: Circle, circle2: Circle): Boolean {
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val centerDistance = (circle1.center - circle2.center).length
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val radiusSum = circle1.radius + circle2.radius
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val radiusDiff = abs(circle1.radius - circle2.radius)
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// Circles are externally tangent if the distance between centers equals the sum of radii
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val externallyTangent = abs(centerDistance - radiusSum) < 1e-10
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// Circles are internally tangent if the distance between centers equals the difference of radii
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val internallyTangent = abs(centerDistance - radiusDiff) < 1e-10
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return externallyTangent || internallyTangent
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}
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@Test
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fun testInvertConformalPreservesTangency() {
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// Create an inverting circle
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val invertingCircle = Circle(100.0, 100.0, 50.0)
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// Create two externally tangent circles
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val circle1 = Circle(200.0, 100.0, 30.0)
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val circle2 = Circle(260.0, 100.0, 30.0)
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// Verify that the circles are indeed tangent
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assertTrue(areTangent(circle1, circle2), "The test circles should be tangent")
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// Perform conformal inversion
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val inverted1 = invertingCircle.invertConformal(circle1)
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val inverted2 = invertingCircle.invertConformal(circle2)
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// Verify that the inverted circles are also tangent
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assertTrue(areTangent(inverted1, inverted2), "The inverted circles should remain tangent")
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}
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@Test
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fun testInvertConformalPreservesInternalTangency() {
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// Create an inverting circle
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val invertingCircle = Circle(100.0, 100.0, 50.0)
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// Create two internally tangent circles
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// For internal tangency, one circle must be inside the other with their boundaries touching at exactly one point
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val circle1 = Circle(200.0, 100.0, 50.0)
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val circle2 = Circle(230.0, 100.0, 20.0) // Center is at distance (radius1 - radius2) from circle1's center
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// Verify that the circles are indeed tangent
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assertTrue(areTangent(circle1, circle2), "The test circles should be internally tangent")
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// Perform conformal inversion
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val inverted1 = invertingCircle.invertConformal(circle1)
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val inverted2 = invertingCircle.invertConformal(circle2)
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// Verify that the inverted circles are also tangent
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assertTrue(areTangent(inverted1, inverted2), "The inverted circles should remain tangent")
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}
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@Test
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fun testInvertConformalWithCircleAtCenter() {
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// Create an inverting circle
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val invertingCircle = Circle(100.0, 100.0, 50.0)
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// Create a circle centered at the center of the inverting circle
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val circle = Circle(100.0, 100.0, 20.0)
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// Inverting a circle centered at the center of the inverting circle should throw an exception
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assertFailsWith<IllegalArgumentException> {
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invertingCircle.invertConformal(circle)
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}
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}
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}
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