Non-linear coordinate systems

commons/src/commonMain/kotlin/org/jetbrains/letsPlot/commons/geometry/DoubleVector.kt

@@ -8,6 +8,9 @@ package org.jetbrains.letsPlot.commons.geometry
 import kotlin.math.*
 
 class DoubleVector(val x: Double, val y: Double) {
+    operator fun component1(): Double = x
+    operator fun component2(): Double = y
+
     val isFinite: Boolean get() = x.isFinite() && y.isFinite()
 
     fun add(v: DoubleVector): DoubleVector {

commons/src/commonMain/kotlin/org/jetbrains/letsPlot/commons/intern/math/Math.kt

@@ -42,4 +42,38 @@ fun Int.ipow(e: Int): Double {
     return this.toDouble().pow(e)
 }
 
-fun areEqual(a: Double, b: Double, epsilon: Double = 0.00001) = abs(a - b) < epsilon
+fun areEqual(a: Double, b: Double, epsilon: Double = 0.00001) = abs(a - b) < epsilon
+
+fun pointToLineSqrDistance(x: Double, y: Double, l1x: Double, l1y: Double, l2x: Double, l2y: Double): Double {
+    return if (l1x == l2x && l1y == l2y) {
+        pointSqrDistance(x, y, l1x, l1y)
+    } else {
+        val ortX = l2x - l1x
+        val ortY = -(l2y - l1y)
+
+        val dot = (x - l1x) * ortY + (y - l1y) * ortX
+        val len = ortY * ortY + ortX * ortX
+
+        dot * dot / len
+    }
+}
+
+fun pointSqrDistance(x1: Double, y1: Double, x2: Double, y2: Double): Double {
+    val dx = x1 - x2
+    val dy = y1 - y2
+    return dx * dx + dy * dy
+}
+
+fun yOnLine(p1x: Double, p1y: Double, p2x: Double, p2y: Double, x: Double): Double {
+    // the Equation for the Line
+    // y = m * x + b
+    // Where
+    // m = (y2 - y1) / (x2 - x1)
+    // and b computed by substitution p1 or p2 to the equation of the line
+
+    val m = (p2y - p1y) / ((p2x) - p1x)
+    val b = p2y - m * (p2x)
+
+    // Result
+    return m * x + b
+}

commons/src/commonMain/kotlin/org/jetbrains/letsPlot/commons/intern/spatial/Wrapping.kt

@@ -5,7 +5,7 @@
 
 package org.jetbrains.letsPlot.commons.intern.spatial
 
-import org.jetbrains.letsPlot.commons.intern.typedGeometry.*
+import org.jetbrains.letsPlot.commons.intern.math.yOnLine
 import org.jetbrains.letsPlot.commons.intern.typedGeometry.*
 import kotlin.math.abs
 
@@ -30,20 +30,6 @@ fun <TypeT> wrapPath(path: List<Vec<TypeT>>, domain: Rect<TypeT>): List<List<Vec
     var currentPath = ArrayList<Vec<TypeT>>()
     currentPath.add(path[0])
 
-    fun yOnLine(p1: Vec<TypeT>, p2: Vec<TypeT>, x: Double): Double {
-        // the Equation for the Line
-        // y = m * x + b
-        // Where
-        // m = (y2 - y1) / (x2 - x1)
-        // and b computed by substitution p1 or p2 to the equation of the line
-
-        val m = (p2.y - p1.y) / ((p2.x) - p1.x)
-        val b = p2.y - m * (p2.x)
-
-        // Result
-        return m * x + b
-    }
-
     for (i in 1 until path.size) {
         val p1 = path[i - 1]
         val p2 = path[i]
@@ -54,11 +40,11 @@ fun <TypeT> wrapPath(path: List<Vec<TypeT>>, domain: Rect<TypeT>): List<List<Vec
             val y: Double
 
             if (p1.x < p2.x) {
-                y = yOnLine(p1, p2.copy(x = p2.x - domain.width), x = domain.left)
+                y = yOnLine(p1.x, p1.y, p2.x - domain.width, p2.y, x = domain.left)
                 xa = domain.left
                 xb = domain.right
             } else {
-                y = yOnLine(p1, p2.copy(x = p2.x + domain.width), x = domain.right)
+                y = yOnLine(p1.x, p1.y, p2.x + domain.width, p2.y, x = domain.right)
                 xa = domain.right
                 xb = domain.left
             }

commons/src/commonMain/kotlin/org/jetbrains/letsPlot/commons/intern/typedGeometry/Transforms.kt

@@ -5,8 +5,10 @@
 
 package org.jetbrains.letsPlot.commons.intern.typedGeometry
 
+import org.jetbrains.letsPlot.commons.intern.typedGeometry.VecResampler.Companion.resample
+
 object Transforms {
-    private const val RESAMPLING_PRECISION = 0.001
+    private const val RESAMPLING_PRECISION = 0.004
 
     fun <InT, OutT> transform(
         bbox: Rect<InT>,
@@ -44,6 +46,6 @@ object Transforms {
         resamplingPrecision: Double?
     ): List<Vec<OutT>> = when(resamplingPrecision) {
         null -> path.mapNotNull(transform)
-        else -> VecResampler(transform, resamplingPrecision).resample(path)
+        else -> resample(path, resamplingPrecision, transform)
     }
 }

commons/src/commonMain/kotlin/org/jetbrains/letsPlot/commons/intern/typedGeometry/VecResampler.kt

@@ -8,10 +8,35 @@ package org.jetbrains.letsPlot.commons.intern.typedGeometry
 import org.jetbrains.letsPlot.commons.intern.typedGeometry.algorithms.AdaptiveResampler
 
 
-class VecResampler<InT, OutT>(
+class VecResampler<InT, OutT> private constructor(
     private val transform: (Vec<InT>) -> Vec<OutT>?,
     precision: Double
 ) {
+    companion object {
+        private val VEC_ADAPTER = object : AdaptiveResampler.DataAdapter<Vec<*>> {
+            override fun x(p: Vec<*>): Double = p.x
+            override fun y(p: Vec<*>): Double = p.y
+            override fun create(x: Double, y: Double): Vec<*> = Vec<Untyped>(x, y)
+        }
+
+        fun <InT, OutT> resample(
+            points: List<Vec<InT>>,
+            precision: Double,
+            transform: (Vec<InT>) -> Vec<OutT>?
+        ): List<Vec<OutT>> {
+            return VecResampler(transform, precision).resample(points)
+        }
+
+        fun <InT, OutT> resample(
+            p1: Vec<InT>,
+            p2: Vec<InT>,
+            precision: Double,
+            transform: (Vec<InT>) -> Vec<OutT>?
+        ): List<Vec<OutT>> {
+            return VecResampler(transform, precision).resample(p1, p2)
+        }
+    }
+
     private val resampler = AdaptiveResampler.generic(this::transformWrapper, precision, VEC_ADAPTER)
 
     private fun transformWrapper(v: Vec<*>): Vec<*>? {
@@ -28,12 +53,4 @@ class VecResampler<InT, OutT>(
         @Suppress("UNCHECKED_CAST")
         return resampler.resample(p1, p2) as List<Vec<OutT>>
     }
-
-    private companion object {
-        val VEC_ADAPTER = object : AdaptiveResampler.DataAdapter<Vec<*>> {
-            override fun x(p: Vec<*>): Double = p.x
-            override fun y(p: Vec<*>): Double = p.y
-            override fun create(x: Double, y: Double): Vec<*> = Vec<Untyped>(x, y)
-        }
-    }
 }

commons/src/commonMain/kotlin/org/jetbrains/letsPlot/commons/intern/typedGeometry/algorithms/AdaptiveResampler.kt

@@ -6,92 +6,113 @@
 package org.jetbrains.letsPlot.commons.intern.typedGeometry.algorithms
 
 import org.jetbrains.letsPlot.commons.geometry.DoubleVector
+import org.jetbrains.letsPlot.commons.intern.math.pointSqrDistance
+import org.jetbrains.letsPlot.commons.intern.math.pointToLineSqrDistance
 
 
 class AdaptiveResampler<T> private constructor(
     private val transform: (T) -> T?,
     precision: Double,
     private val dataAdapter: DataAdapter<T>
 ) {
+    private val precisionSqr: Double = precision * precision
+
     companion object {
+        private const val MAX_DEPTH_LIMIT = 9 // 1_025 points maximum (2^(LIMIT + 1) + 1)
+
         private val DOUBLE_VECTOR_ADAPTER = object : DataAdapter<DoubleVector> {
             override fun x(p: DoubleVector) = p.x
             override fun y(p: DoubleVector) = p.y
             override fun create(x: Double, y: Double) = DoubleVector(x, y)
         }
 
-        fun forDoubleVector(transform: (DoubleVector) -> DoubleVector?, precision: Double): AdaptiveResampler<DoubleVector> {
+        private fun forDoubleVector(
+            transform: (DoubleVector) -> DoubleVector?,
+            precision: Double
+        ): AdaptiveResampler<DoubleVector> {
             return AdaptiveResampler(transform, precision, DOUBLE_VECTOR_ADAPTER)
         }
 
         fun <T> generic(transform: (T) -> T?, precision: Double, adapter: DataAdapter<T>): AdaptiveResampler<T> {
             return AdaptiveResampler(transform, precision, adapter)
         }
-    }
-    private val precisionSqr: Double = precision * precision
 
-    fun resample(points: List<T>): List<T> {
-        val result = ArrayList<T>(points.size)
-
-        for (i in 1.until(points.size)) {
-            result.removeLastOrNull()
-
-            resample(points[i - 1], points[i])
-                .forEach(result::add)
+        fun resample(
+            points: List<DoubleVector>,
+            precision: Double,
+            transform: (DoubleVector) -> DoubleVector?
+        ): List<DoubleVector> {
+            return forDoubleVector(transform, precision).resample(points)
         }
 
-        return result
-    }
-
-    fun resample(p1: T, p2: T): List<T> {
-        val result = ArrayList<T>()
-        val temp = ArrayList<T>()
-        result.add(p1)
-        temp.add(p2)
-
-        while (temp.isNotEmpty()) {
-            when (val missingPoint = computeMissingPoint(result.last(), temp.last())) {
-                null -> result.add(temp.removeLast())
-                else -> temp.add(missingPoint)
-            }
+        fun resample(
+            p1: DoubleVector,
+            p2: DoubleVector,
+            precision: Double,
+            transform: (DoubleVector) -> DoubleVector?
+        ): List<DoubleVector> {
+            return forDoubleVector(transform, precision).resample(p1, p2)
         }
-        return result.mapNotNull { transform(it) }
     }
 
-    private fun computeMissingPoint(p1: T, p2: T): T? {
-        val pc = (p1 + p2) / 2.0
-        val q1 = transform(p1) ?: return null
-        val q2 = transform(p2) ?: return null
-        val qc = transform(pc) ?: return null
+    fun resample(points: List<T>): List<T> {
+        var pPrev: T = points.firstOrNull() ?: return emptyList()
+        var tPrev: T = transform(pPrev) ?: return emptyList()
+
+        val pLast = points.lastOrNull() ?: return emptyList()
+        val tLast = transform(pLast) ?: return emptyList()
+
+        val output = ArrayList<T>(points.size)
+        points
+            .asSequence()
+            .drop(1)
+            .forEach { p ->
+                val t = transform(p) ?: return@forEach
+                output.add(tPrev)
+                resample(pPrev, tPrev, p, t, output, MAX_DEPTH_LIMIT)
+
+                pPrev = p
+                tPrev = t
+            }
 
-        val distance = if (q1 == q2) {
-            length(q1, qc)
-        } else {
-            distance(qc, q1, q2)
-        }
+        output.add(tLast)
 
-        return if (distance < precisionSqr) null else pc
+        return output
     }
 
-
-    private fun length(p1: T, p2: T): Double {
-        val x = p2.x - p1.x
-        val y = p2.y - p1.y
-        return x * x + y * y
+    fun resample(p1: T, p2: T): List<T> {
+        val t1 = transform(p1) ?: return emptyList()
+        val t2 = transform(p2) ?: return emptyList()
+
+        val output = mutableListOf<T>()
+        output.add(t1)
+        resample(p1, t1, p2, t2, output, MAX_DEPTH_LIMIT)
+        output.add(t2)
+        return output
     }
 
-    private fun distance(p: T, l1: T, l2: T): Double {
-        val ortX = l2.x - l1.x
-        val ortY = -(l2.y - l1.y)
+    private fun resample(p1: T, t1: T, p2: T, t2: T, output: MutableList<T>, depth: Int) {
+        if (p1 == p2) {
+            return
+        }
 
-        val dot = (p.x - l1.x) * ortY + (p.y - l1.y) * ortX
-        val len = ortY * ortY + ortX * ortX
+        val pm = (p1 + p2) / 2.0
+        val tm = transform(pm) ?: return
 
-        return dot * dot / len
+        if (pointToLineSqrDistance(tm.x, tm.y, t1.x, t1.y, t2.x, t2.y) >= precisionSqr && depth > 0) {
+            resample(p1, t1, pm, tm, output, depth - 1)
+            output.add(tm)
+            resample(pm, tm, p2, t2, output, depth - 1)
+        } else {
+            if (pointSqrDistance(t1.x, t1.y, t2.x, t2.y) > precisionSqr) {
+                output.add(tm)
+            }
+        }
     }
 
     val T.x get() = dataAdapter.x(this)
     val T.y get() = dataAdapter.y(this)
+    private operator fun T.minus(other: T): T = dataAdapter.create(x - other.x, y - other.y)
     private operator fun T.plus(other: T): T = dataAdapter.create(x + other.x, y + other.y)
     private operator fun T.div(other: T): T = dataAdapter.create(x / other.x, y / other.y)
     private operator fun T.div(v: Double): T = dataAdapter.create(x / v, y / v)