Merge pull request #111 from quietshu/master

Geometry, basic Bézier-curve algorithm (and its test)

Author: felipernb

src/algorithms/geometry/bezier_curve.js

@@ -0,0 +1,59 @@
+'use strict';
+
+/**
+ * 2D bezier-curve, https://en.wikipedia.org/wiki/B%C3%A9zier_curve
+ * Usage:
+ *   var b = new BezierCurve([ [0, 0], [10, 3] ]);
+ *   b.get(0.5); // [5, 1.5]
+ */
+
+/**
+ * Generates a bezier-curve from a series of points
+ * @param Array array of control points ([[x0, y0], [x1, y1]])
+ */
+var BezierCurve = function (array) {
+    var n = array.length;
+
+    // The binomial coefficient
+    var c = [1];
+    var i, j;
+    for (i = 1; i < n; ++i) {
+        c.push(0);
+        for (j = i; j >= 1; --j) {
+            c[j] += c[j - 1];
+        }
+    }
+
+    // the i-th control point times the coefficient
+    var p = [];
+    for (i = 0; i < n; ++i) {
+        p.push([c[i] * array[i][0], c[i] * array[i][1]]);
+    }
+
+    this.p = p;
+    this.n = n;
+};
+
+/**
+ * @param Number float variable from 0 to 1
+ */
+BezierCurve.prototype.get = function (t) {
+    var res = [0, 0], i;
+    var a = 1, b = 1;
+
+    // The coefficient
+    var c = [];
+    for (i = 0; i < this.n; ++i) {
+        c.push(a);
+        a *= t;
+    }
+
+    for (i = this.n - 1; i >= 0; --i) {
+        res[0] += this.p[i][0] * c[i] * b;
+        res[1] += this.p[i][1] * c[i] * b;
+        b *= 1 - t;
+    }
+    return res;
+};
+
+module.exports = BezierCurve;

src/geometry.js

@@ -0,0 +1,6 @@
+'use strict';
+
+// Geometry algorithms
+module.exports = {
+    bezierCurve: require('./algorithms/geometry/bezier_curve')
+};

src/index.js

@@ -3,6 +3,7 @@
 var lib = {
   DataStructures: require('./data_structures'),
   Graph: require('./graph'),
+  Geometry: require('./geometry'),
   Math: require('./math'),
   Search: require('./search'),
   Sorting: require('./sorting'),

src/test/algorithms/geometry/bezier_curve.js

@@ -0,0 +1,35 @@
+'use strict';
+
+var root = require('../../../'),
+    BezierCurve = root.Geometry.bezierCurve,
+    assert = require('assert');
+
+// Testing with http://pomax.github.io/bezierjs/
+
+describe('Bézier-Curve Algorithm', function () {
+    it('should get a linear Bézier-curve', function () {
+        var b = new BezierCurve([[0, 0], [10, 3]]);
+
+        // Ends
+        assert.deepEqual(b.get(0), [0, 0]);
+        assert.deepEqual(b.get(1), [10, 3]);
+
+        // Middle
+        assert.deepEqual(b.get(0.5), [5, 1.5]);
+
+        // 1/4 and 3/4
+        assert.deepEqual(b.get(0.25), [2.5, 0.75]);
+        assert.deepEqual(b.get(0.75), [7.5, 2.25]);
+    });
+    it('should get a quadratic Bézier-curve', function () {
+        var b = new BezierCurve([[150, 40], [80, 30], [105, 150]]);
+
+        assert.deepEqual(b.get(0.5), [103.75, 62.5]);
+        assert.deepEqual(b.get(0.25), [120.9375, 43.125]);
+    });
+    it('should get a cubic Bézier-curve', function () {
+        var b = new BezierCurve([[150, 40], [80, 30], [105, 150], [100, 100]]);
+
+        assert.deepEqual(b.get(0.5), [100.625, 85]);
+    });
+});