Add vector product to Euclidean3DSpace

gradle.properties

@@ -9,7 +9,7 @@ kotlin.native.ignoreDisabledTargets=true
 org.gradle.configureondemand=true
 org.gradle.jvmargs=-Xmx4096m
 
-toolsVersion=0.14.2-kotlin-1.8.10
+toolsVersion=0.14.3-kotlin-1.8.20-RC
 
 
 org.gradle.parallel=true

kmath-geometry/src/commonMain/kotlin/space/kscience/kmath/geometry/Euclidean3DSpace.kt

@@ -78,8 +78,11 @@ public object Euclidean3DSpace : GeometrySpace<DoubleVector3D>, ScaleOperations<
         }
     }
 
+    public fun vector(x: Double, y: Double, z: Double): DoubleVector3D =
+        Vector3DImpl(x, y, z)
+
     public fun vector(x: Number, y: Number, z: Number): DoubleVector3D =
-        Vector3DImpl(x.toDouble(), y.toDouble(), z.toDouble())
+        vector(x.toDouble(), y.toDouble(), z.toDouble())
 
     override val zero: DoubleVector3D by lazy { vector(0.0, 0.0, 0.0) }
 
@@ -100,6 +103,48 @@ public object Euclidean3DSpace : GeometrySpace<DoubleVector3D>, ScaleOperations<
     override fun DoubleVector3D.dot(other: DoubleVector3D): Double =
         x * other.x + y * other.y + z * other.z
 
+    private fun leviCivita(i: Int, j: Int, k: Int): Int = when {
+        // even permutation
+        i == 0 && j == 1 && k == 2 -> 1
+        i == 1 && j == 2 && k == 0 -> 1
+        i == 2 && j == 0 && k == 1 -> 1
+        // odd permutations
+        i == 2 && j == 1 && k == 0 -> -1
+        i == 0 && j == 2 && k == 1 -> -1
+        i == 1 && j == 0 && k == 2 -> -1
+
+        else -> 0
+    }
+
+    /**
+     * Compute vector product of [first] and [second]. The basis assumed to be right-handed if [rightBasis] is true and
+     * left-handed otherwise
+     */
+    public fun vectorProduct(
+        first: DoubleVector3D,
+        second: DoubleVector3D,
+        rightBasis: Boolean = true,
+    ): DoubleVector3D {
+        var x = 0.0
+        var y = 0.0
+        var z = 0.0
+
+        for (j in (0..2)) {
+            for (k in (0..2)) {
+                x += leviCivita(0, j, k) * first[j] * second[k]
+                y += leviCivita(1, j, k) * first[j] * second[k]
+                z += leviCivita(2, j, k) * first[j] * second[k]
+            }
+        }
+
+        return vector(x, y, z) * (if (rightBasis) 1 else -1)
+    }
+
+    /**
+     * Vector product with right basis
+     */
+    public infix fun DoubleVector3D.cross(other: DoubleVector3D): Vector3D<Double> = vectorProduct(this, other)
+
     public val xAxis: DoubleVector3D = vector(1.0, 0.0, 0.0)
     public val yAxis: DoubleVector3D = vector(0.0, 1.0, 0.0)
     public val zAxis: DoubleVector3D = vector(0.0, 0.0, 1.0)

kmath-geometry/src/commonTest/kotlin/space/kscience/kmath/geometry/Euclidean3DSpaceTest.kt

@@ -57,23 +57,39 @@ internal class Euclidean3DSpaceTest {
     }
 
     @Test
-    fun add() {
+    fun add() = with(Euclidean3DSpace) {
-        with(Euclidean3DSpace) {
+        assertVectorEquals(
-            assertVectorEquals(
+            vector(1.0, -2.0, 0.001),
-                vector(1.0, -2.0, 0.001),
+            vector(1.0, -2.0, 0.001) + zero
-                vector(1.0, -2.0, 0.001) + zero
+        )
-            )
+        assertVectorEquals(
-            assertVectorEquals(
+            vector(8.0, -3.0, 3.001),
-                vector(8.0, -3.0, 3.001),
+            vector(1.0, 2.0, 3.0) + vector(7.0, -5.0, 0.001)
-                vector(1.0, 2.0, 3.0) + vector(7.0, -5.0, 0.001)
+        )
-            )
-        }
     }
 
     @Test
-    fun multiply() {
+    fun multiply() = with(Euclidean3DSpace) {
-        with(Euclidean3DSpace) {
+        assertVectorEquals(vector(2.0, -4.0, 0.0), vector(1.0, -2.0, 0.0) * 2)
-            assertVectorEquals(vector(2.0, -4.0, 0.0), vector(1.0, -2.0, 0.0) * 2)
-        }
     }
+
+    @Test
+    fun vectorProduct() = with(Euclidean3DSpace) {
+        assertVectorEquals(zAxis, vectorProduct(xAxis, yAxis))
+        assertVectorEquals(zAxis, xAxis cross yAxis)
+        assertVectorEquals(-zAxis, vectorProduct(yAxis, xAxis))
+        assertVectorEquals(zAxis, vectorProduct(yAxis, xAxis, rightBasis = false))
+    }
+
+    @Test
+    fun doubleVectorProduct() = with(Euclidean3DSpace) {
+        val a = vector(1, 2, -3)
+        val b = vector(-1, 0, 1)
+        val c = vector(4, 5, 6)
+
+        val res = a cross (b cross c)
+        val expected = b * (a dot c) - c * (a dot b)
+        assertVectorEquals(expected, res)
+    }
+
 }