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[orx-math] Add demo and readme texts.

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This commit is contained in:
Abe Pazos
2025-10-05 15:29:32 +02:00
parent 58c65ab393
commit 923e64f37a
8 changed files with 137 additions and 49 deletions
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26
orx-math/src/jvmDemo/kotlin/matrix/DemoLeastSquares01.kt
View File

@@ -11,12 +11,12 @@ import kotlin.math.cos
import kotlin.random.Random
/**
* Demonstrate least squares method to find a regression line through noisy points
* Line drawn in red is the estimated line, in green is the ground-truth line
* Demonstrate least squares method to find a regression line through noisy points.
* The line drawn in red is the estimated line. The green one is the ground-truth.
*
* Ax = b => x = A⁻¹b
* because A is likely inconsistent, we look for an approximate x based on AᵀA, which is consistent.
* x̂ = (AᵀA)⁻¹ Aᵀb
* `Ax = b => x = A⁻¹b`
* because `A` is likely inconsistent, we look for an approximate `x` based on `AᵀA`, which is consistent.
* `x̂ = (AᵀA)⁻¹ Aᵀb`
*/
fun main() {
application {
@@ -26,23 +26,23 @@ fun main() {
}
program {
extend {
val ls = drawer.bounds.horizontal(0.5).rotateBy(cos(seconds)*45.0)
val groundTruth = drawer.bounds.horizontal(0.5).rotateBy(cos(seconds) * 45.0)
val r = Random((seconds*10).toInt())
val r = Random((seconds * 10).toInt())
val pointCount = 100
val A = Matrix(pointCount, 2)
val b = Matrix(pointCount, 1)
for (i in 0 until pointCount) {
val p = ls.position(Double.uniform(0.0, 1.0, r))
val pr = p + Vector2.uniformRing(0.0, 130.0, r)
val point = groundTruth.position(Double.uniform(0.0, 1.0, r))
val pointRandomized = point + Vector2.uniformRing(0.0, 130.0, r)
A[i, 0] = 1.0
A[i, 1] = pr.x
b[i, 0] = pr.y
A[i, 1] = pointRandomized.x
b[i, 0] = pointRandomized.y
drawer.circle(pr, 5.0)
drawer.circle(pointRandomized, 5.0)
}
val At = A.transposed()
val AtA = At * A
@@ -58,7 +58,7 @@ fun main() {
drawer.lineSegment(p0, p1)
drawer.stroke = ColorRGBa.GREEN
drawer.lineSegment(ls)
drawer.lineSegment(groundTruth)
}
}
}

26
orx-math/src/jvmDemo/kotlin/matrix/DemoLeastSquares02.kt
View File

@@ -13,7 +13,17 @@ import kotlin.math.pow
import kotlin.random.Random
/**
* Demonstrate least squares method to fit a cubic bezier to noisy points
* Demonstrate how to use the `least squares` method to fit a cubic bezier to noisy points.
*
* On every animation frame, 10 concentric circles are created centered on the window and converted to contours.
* In OPENRNDR, circular contours are made ouf of 4 cubic-Bezier curves. Each of those curves is considered
* one by one as the ground truth, then 5 points are sampled near those curves.
* Finally, two matrices are constructed using those points and math operations are applied to
* revert the randomization attempting to reconstruct the original curves.
*
* The result is drawn on every animation frame, revealing concentric circles that are more or less similar
* to the ground truth depending on the random values used.
*
*/
fun main() {
application {
@@ -34,8 +44,8 @@ fun main() {
}
extend {
for (z in 0 until 10) {
val c = Circle(drawer.bounds.center, 300.0- z*30.0).contour
for (ls in c.segments) {
val c = Circle(drawer.bounds.center, 300.0 - z * 30.0).contour
for (groundTruth in c.segments) {
val pointCount = 5
val A = Matrix(pointCount, 4)
@@ -46,15 +56,15 @@ fun main() {
pointCount - 1 -> 1.0
else -> Double.uniform(0.0, 1.0, r)
}
val p = ls.position(t)
val pr = p + Vector2.uniformRing(0.0, 0.5, r)
val point = groundTruth.position(t)
val pointRandomized = point + Vector2.uniformRing(0.0, 0.5, r)
A[i, 0] = bernstein(3, 0, t)
A[i, 1] = bernstein(3, 1, t)
A[i, 2] = bernstein(3, 2, t)
A[i, 3] = bernstein(3, 3, t)
b[i, 0] = pr.x
b[i, 1] = pr.y
b[i, 0] = pointRandomized.x
b[i, 1] = pointRandomized.y
}
val At = A.transposed()
val AtA = At * A
@@ -64,11 +74,9 @@ fun main() {
val x = AtAI * Atb
val segment = Segment2D(
//ls.start,
Vector2(x[0, 0], x[0, 1]),
Vector2(x[1, 0], x[1, 1]),
Vector2(x[2, 0], x[2, 1]),
//ls.end
Vector2(x[3, 0], x[3, 1])
)