Add VideoSensing math module

- motionVector takes motion component and returns a 2d vector
- scratchAtan2 takes a y and x value and returns an angle in degrees
  referencing Scratch's coordinate system

src/extensions/scratch3_video_sensing/math.js

@@ -0,0 +1,76 @@
+/**
+ * A constant value helping to transform a value in radians to degrees.
+ * @type {number}
+ */
+const TO_DEGREE = 180 / Math.PI;
+
+/**
+ * A object reused to save on memory allocation returning u and v vector from
+ * motionVector.
+ * @type {UV}
+ */
+const _motionVectorOut = {u: 0, v: 0};
+
+/**
+ * Determine a motion vector combinations of the color component difference on
+ * the x axis, y axis, and temporal axis.
+ * @param {number} A2 - a sum of x axis squared
+ * @param {number} A1B2 - a sum of x axis times y axis
+ * @param {number} B1 - a sum of y axis squared
+ * @param {number} C2 - a sum of x axis times temporal axis
+ * @param {number} C1 - a sum of y axis times temporal axis
+ * @param {UV} out - optional object to store return UV info in
+ * @returns {UV} a uv vector representing the motion for the given input
+ */
+const motionVector = function (A2, A1B2, B1, C2, C1, out = _motionVectorOut) {
+    // Compare sums of X * Y and sums of X squared and Y squared.
+    const delta = ((A1B2 * A1B2) - (A2 * B1));
+    if (delta) {
+        // System is not singular - solving by Kramer method.
+        const deltaX = -((C1 * A1B2) - (C2 * B1));
+        const deltaY = -((A1B2 * C2) - (A2 * C1));
+        const Idelta = 8 / delta;
+        out.u = deltaX * Idelta;
+        out.v = deltaY * Idelta;
+    } else {
+        // Singular system - find optical flow in gradient direction.
+        const Norm = ((A1B2 + A2) * (A1B2 + A2)) + ((B1 + A1B2) * (B1 + A1B2));
+        if (Norm) {
+            const IGradNorm = 8 / Norm;
+            const temp = -(C1 + C2) * IGradNorm;
+            out.u = (A1B2 + A2) * temp;
+            out.v = (B1 + A1B2) * temp;
+        } else {
+            out.u = 0;
+            out.v = 0;
+        }
+    }
+    return out;
+};
+
+/**
+ * Translate an angle in degrees with the range -180 to 180 rotated to
+ * Scratch's reference angle.
+ * @param {number} degrees - angle in range -180 to 180
+ * @returns {number} angle from Scratch's reference angle
+ */
+const scratchDegrees = function (degrees) {
+    return ((degrees + 270) % 360) - 180;
+};
+
+/**
+ * Get the angle of the y and x component of a 2d vector in degrees in
+ * Scratch's coordinate plane.
+ * @param {number} y - the y component of a 2d vector
+ * @param {number} x - the x component of a 2d vector
+ * @returns {number} angle in degrees in Scratch's coordinate plane
+ */
+const scratchAtan2 = function (y, x) {
+    return scratchDegrees(Math.atan2(y, x) * TO_DEGREE);
+};
+
+module.exports = {
+    motionVector,
+    scratchDegrees,
+    scratchAtan2
+};