--- /dev/null
+/*! JointJS v0.9.3 - JavaScript diagramming library 2015-05-22
+
+
+This Source Code Form is subject to the terms of the Mozilla Public
+License, v. 2.0. If a copy of the MPL was not distributed with this
+file, You can obtain one at http://mozilla.org/MPL/2.0/.
+ */
+// Geometry library.
+// (c) 2011-2013 client IO
+
+(function(root, factory) {
+
+ if (typeof define === 'function' && define.amd) {
+
+ // AMD. Register as an anonymous module.
+ define([], factory);
+
+ } else if (typeof exports === 'object') {
+
+ // Node. Does not work with strict CommonJS, but
+ // only CommonJS-like environments that support module.exports,
+ // like Node.
+ module.exports = factory();
+
+ } else {
+
+ // Browser globals.
+ root.g = factory();
+
+ }
+
+}(this, function() {
+
+ // Declare shorthands to the most used math functions.
+ var math = Math;
+ var abs = math.abs;
+ var cos = math.cos;
+ var sin = math.sin;
+ var sqrt = math.sqrt;
+ var mmin = math.min;
+ var mmax = math.max;
+ var atan = math.atan;
+ var atan2 = math.atan2;
+ var acos = math.acos;
+ var round = math.round;
+ var floor = math.floor;
+ var PI = math.PI;
+ var random = math.random;
+ var toDeg = function(rad) { return (180 * rad / PI) % 360; };
+ var toRad = function(deg, over360) {
+ over360 = over360 || false;
+ deg = over360 ? deg : (deg % 360);
+ return deg * PI / 180;
+ };
+ var snapToGrid = function(val, gridSize) { return gridSize * Math.round(val / gridSize); };
+ var normalizeAngle = function(angle) { return (angle % 360) + (angle < 0 ? 360 : 0); };
+
+ // Point
+ // -----
+
+ // Point is the most basic object consisting of x/y coordinate,.
+
+ // Possible instantiations are:
+
+ // * `point(10, 20)`
+ // * `new point(10, 20)`
+ // * `point('10 20')`
+ // * `point(point(10, 20))`
+ function point(x, y) {
+ if (!(this instanceof point))
+ return new point(x, y);
+ var xy;
+ if (y === undefined && Object(x) !== x) {
+ xy = x.split(x.indexOf('@') === -1 ? ' ' : '@');
+ this.x = parseInt(xy[0], 10);
+ this.y = parseInt(xy[1], 10);
+ } else if (Object(x) === x) {
+ this.x = x.x;
+ this.y = x.y;
+ } else {
+ this.x = x;
+ this.y = y;
+ }
+ }
+
+ point.prototype = {
+ toString: function() {
+ return this.x + '@' + this.y;
+ },
+ // If point lies outside rectangle `r`, return the nearest point on the boundary of rect `r`,
+ // otherwise return point itself.
+ // (see Squeak Smalltalk, Point>>adhereTo:)
+ adhereToRect: function(r) {
+ if (r.containsPoint(this)) {
+ return this;
+ }
+ this.x = mmin(mmax(this.x, r.x), r.x + r.width);
+ this.y = mmin(mmax(this.y, r.y), r.y + r.height);
+ return this;
+ },
+ // Compute the angle between me and `p` and the x axis.
+ // (cartesian-to-polar coordinates conversion)
+ // Return theta angle in degrees.
+ theta: function(p) {
+ p = point(p);
+ // Invert the y-axis.
+ var y = -(p.y - this.y);
+ var x = p.x - this.x;
+ // Makes sure that the comparison with zero takes rounding errors into account.
+ var PRECISION = 10;
+ // Note that `atan2` is not defined for `x`, `y` both equal zero.
+ var rad = (y.toFixed(PRECISION) == 0 && x.toFixed(PRECISION) == 0) ? 0 : atan2(y, x);
+
+ // Correction for III. and IV. quadrant.
+ if (rad < 0) {
+ rad = 2 * PI + rad;
+ }
+ return 180 * rad / PI;
+ },
+ // Returns distance between me and point `p`.
+ distance: function(p) {
+ return line(this, p).length();
+ },
+ // Returns a manhattan (taxi-cab) distance between me and point `p`.
+ manhattanDistance: function(p) {
+ return abs(p.x - this.x) + abs(p.y - this.y);
+ },
+ // Offset me by the specified amount.
+ offset: function(dx, dy) {
+ this.x += dx || 0;
+ this.y += dy || 0;
+ return this;
+ },
+ magnitude: function() {
+ return sqrt((this.x * this.x) + (this.y * this.y)) || 0.01;
+ },
+ update: function(x, y) {
+ this.x = x || 0;
+ this.y = y || 0;
+ return this;
+ },
+ round: function(decimals) {
+ this.x = decimals ? this.x.toFixed(decimals) : round(this.x);
+ this.y = decimals ? this.y.toFixed(decimals) : round(this.y);
+ return this;
+ },
+ // Scale the line segment between (0,0) and me to have a length of len.
+ normalize: function(len) {
+ var s = (len || 1) / this.magnitude();
+ this.x = s * this.x;
+ this.y = s * this.y;
+ return this;
+ },
+ difference: function(p) {
+ return point(this.x - p.x, this.y - p.y);
+ },
+ // Return the bearing between me and point `p`.
+ bearing: function(p) {
+ return line(this, p).bearing();
+ },
+ // Converts rectangular to polar coordinates.
+ // An origin can be specified, otherwise it's 0@0.
+ toPolar: function(o) {
+ o = (o && point(o)) || point(0, 0);
+ var x = this.x;
+ var y = this.y;
+ this.x = sqrt((x - o.x) * (x - o.x) + (y - o.y) * (y - o.y)); // r
+ this.y = toRad(o.theta(point(x, y)));
+ return this;
+ },
+ // Rotate point by angle around origin o.
+ rotate: function(o, angle) {
+ angle = (angle + 360) % 360;
+ this.toPolar(o);
+ this.y += toRad(angle);
+ var p = point.fromPolar(this.x, this.y, o);
+ this.x = p.x;
+ this.y = p.y;
+ return this;
+ },
+ // Move point on line starting from ref ending at me by
+ // distance distance.
+ move: function(ref, distance) {
+ var theta = toRad(point(ref).theta(this));
+ return this.offset(cos(theta) * distance, -sin(theta) * distance);
+ },
+ // Returns change in angle from my previous position (-dx, -dy) to my new position
+ // relative to ref point.
+ changeInAngle: function(dx, dy, ref) {
+ // Revert the translation and measure the change in angle around x-axis.
+ return point(this).offset(-dx, -dy).theta(ref) - this.theta(ref);
+ },
+ equals: function(p) {
+ return this.x === p.x && this.y === p.y;
+ },
+ snapToGrid: function(gx, gy) {
+ this.x = snapToGrid(this.x, gx);
+ this.y = snapToGrid(this.y, gy || gx);
+ return this;
+ },
+ // Returns a point that is the reflection of me with
+ // the center of inversion in ref point.
+ reflection: function(ref) {
+ return point(ref).move(this, this.distance(ref));
+ }
+ };
+ // Alternative constructor, from polar coordinates.
+ // @param {number} r Distance.
+ // @param {number} angle Angle in radians.
+ // @param {point} [optional] o Origin.
+ point.fromPolar = function(r, angle, o) {
+ o = (o && point(o)) || point(0, 0);
+ var x = abs(r * cos(angle));
+ var y = abs(r * sin(angle));
+ var deg = normalizeAngle(toDeg(angle));
+
+ if (deg < 90) {
+ y = -y;
+ } else if (deg < 180) {
+ x = -x;
+ y = -y;
+ } else if (deg < 270) {
+ x = -x;
+ }
+
+ return point(o.x + x, o.y + y);
+ };
+
+ // Create a point with random coordinates that fall into the range `[x1, x2]` and `[y1, y2]`.
+ point.random = function(x1, x2, y1, y2) {
+ return point(floor(random() * (x2 - x1 + 1) + x1), floor(random() * (y2 - y1 + 1) + y1));
+ };
+
+ // Line.
+ // -----
+ function line(p1, p2) {
+ if (!(this instanceof line))
+ return new line(p1, p2);
+ this.start = point(p1);
+ this.end = point(p2);
+ }
+
+ line.prototype = {
+ toString: function() {
+ return this.start.toString() + ' ' + this.end.toString();
+ },
+ // @return {double} length of the line
+ length: function() {
+ return sqrt(this.squaredLength());
+ },
+ // @return {integer} length without sqrt
+ // @note for applications where the exact length is not necessary (e.g. compare only)
+ squaredLength: function() {
+ var x0 = this.start.x;
+ var y0 = this.start.y;
+ var x1 = this.end.x;
+ var y1 = this.end.y;
+ return (x0 -= x1) * x0 + (y0 -= y1) * y0;
+ },
+ // @return {point} my midpoint
+ midpoint: function() {
+ return point((this.start.x + this.end.x) / 2,
+ (this.start.y + this.end.y) / 2);
+ },
+ // @return {point} Point where I'm intersecting l.
+ // @see Squeak Smalltalk, LineSegment>>intersectionWith:
+ intersection: function(l) {
+ var pt1Dir = point(this.end.x - this.start.x, this.end.y - this.start.y);
+ var pt2Dir = point(l.end.x - l.start.x, l.end.y - l.start.y);
+ var det = (pt1Dir.x * pt2Dir.y) - (pt1Dir.y * pt2Dir.x);
+ var deltaPt = point(l.start.x - this.start.x, l.start.y - this.start.y);
+ var alpha = (deltaPt.x * pt2Dir.y) - (deltaPt.y * pt2Dir.x);
+ var beta = (deltaPt.x * pt1Dir.y) - (deltaPt.y * pt1Dir.x);
+
+ if (det === 0 ||
+ alpha * det < 0 ||
+ beta * det < 0) {
+ // No intersection found.
+ return null;
+ }
+ if (det > 0) {
+ if (alpha > det || beta > det) {
+ return null;
+ }
+ } else {
+ if (alpha < det || beta < det) {
+ return null;
+ }
+ }
+ return point(this.start.x + (alpha * pt1Dir.x / det),
+ this.start.y + (alpha * pt1Dir.y / det));
+ },
+
+ // @return the bearing (cardinal direction) of the line. For example N, W, or SE.
+ // @returns {String} One of the following bearings : NE, E, SE, S, SW, W, NW, N.
+ bearing: function() {
+
+ var lat1 = toRad(this.start.y);
+ var lat2 = toRad(this.end.y);
+ var lon1 = this.start.x;
+ var lon2 = this.end.x;
+ var dLon = toRad(lon2 - lon1);
+ var y = sin(dLon) * cos(lat2);
+ var x = cos(lat1) * sin(lat2) - sin(lat1) * cos(lat2) * cos(dLon);
+ var brng = toDeg(atan2(y, x));
+
+ var bearings = ['NE', 'E', 'SE', 'S', 'SW', 'W', 'NW', 'N'];
+
+ var index = brng - 22.5;
+ if (index < 0)
+ index += 360;
+ index = parseInt(index / 45);
+
+ return bearings[index];
+ },
+
+ // @return {point} my point at 't' <0,1>
+ pointAt: function(t) {
+ var x = (1 - t) * this.start.x + t * this.end.x;
+ var y = (1 - t) * this.start.y + t * this.end.y;
+ return point(x, y);
+ },
+
+ // @return {number} the offset of the point `p` from the line. + if the point `p` is on the right side of the line, - if on the left and 0 if on the line.
+ pointOffset: function(p) {
+ // Find the sign of the determinant of vectors (start,end), where p is the query point.
+ return ((this.end.x - this.start.x) * (p.y - this.start.y) - (this.end.y - this.start.y) * (p.x - this.start.x)) / 2;
+ }
+ };
+
+ // Rectangle.
+ // ----------
+ function rect(x, y, w, h) {
+ if (!(this instanceof rect))
+ return new rect(x, y, w, h);
+ if (y === undefined) {
+ y = x.y;
+ w = x.width;
+ h = x.height;
+ x = x.x;
+ }
+ this.x = x;
+ this.y = y;
+ this.width = w;
+ this.height = h;
+ }
+
+ rect.prototype = {
+ toString: function() {
+ return this.origin().toString() + ' ' + this.corner().toString();
+ },
+ origin: function() {
+ return point(this.x, this.y);
+ },
+ corner: function() {
+ return point(this.x + this.width, this.y + this.height);
+ },
+ topRight: function() {
+ return point(this.x + this.width, this.y);
+ },
+ bottomLeft: function() {
+ return point(this.x, this.y + this.height);
+ },
+ center: function() {
+ return point(this.x + this.width / 2, this.y + this.height / 2);
+ },
+ // @return {boolean} true if rectangles intersect
+ intersect: function(r) {
+ var myOrigin = this.origin();
+ var myCorner = this.corner();
+ var rOrigin = r.origin();
+ var rCorner = r.corner();
+
+ if (rCorner.x <= myOrigin.x ||
+ rCorner.y <= myOrigin.y ||
+ rOrigin.x >= myCorner.x ||
+ rOrigin.y >= myCorner.y) return false;
+ return true;
+ },
+ // @return {string} (left|right|top|bottom) side which is nearest to point
+ // @see Squeak Smalltalk, Rectangle>>sideNearestTo:
+ sideNearestToPoint: function(p) {
+ p = point(p);
+ var distToLeft = p.x - this.x;
+ var distToRight = (this.x + this.width) - p.x;
+ var distToTop = p.y - this.y;
+ var distToBottom = (this.y + this.height) - p.y;
+ var closest = distToLeft;
+ var side = 'left';
+
+ if (distToRight < closest) {
+ closest = distToRight;
+ side = 'right';
+ }
+ if (distToTop < closest) {
+ closest = distToTop;
+ side = 'top';
+ }
+ if (distToBottom < closest) {
+ closest = distToBottom;
+ side = 'bottom';
+ }
+ return side;
+ },
+ // @return {bool} true if point p is insight me
+ containsPoint: function(p) {
+ p = point(p);
+ if (p.x >= this.x && p.x <= this.x + this.width &&
+ p.y >= this.y && p.y <= this.y + this.height) {
+ return true;
+ }
+ return false;
+ },
+ // Algorithm ported from java.awt.Rectangle from OpenJDK.
+ // @return {bool} true if rectangle `r` is inside me.
+ containsRect: function(r) {
+ var nr = rect(r).normalize();
+ var W = nr.width;
+ var H = nr.height;
+ var X = nr.x;
+ var Y = nr.y;
+ var w = this.width;
+ var h = this.height;
+ if ((w | h | W | H) < 0) {
+ // At least one of the dimensions is negative...
+ return false;
+ }
+ // Note: if any dimension is zero, tests below must return false...
+ var x = this.x;
+ var y = this.y;
+ if (X < x || Y < y) {
+ return false;
+ }
+ w += x;
+ W += X;
+ if (W <= X) {
+ // X+W overflowed or W was zero, return false if...
+ // either original w or W was zero or
+ // x+w did not overflow or
+ // the overflowed x+w is smaller than the overflowed X+W
+ if (w >= x || W > w) return false;
+ } else {
+ // X+W did not overflow and W was not zero, return false if...
+ // original w was zero or
+ // x+w did not overflow and x+w is smaller than X+W
+ if (w >= x && W > w) return false;
+ }
+ h += y;
+ H += Y;
+ if (H <= Y) {
+ if (h >= y || H > h) return false;
+ } else {
+ if (h >= y && H > h) return false;
+ }
+ return true;
+ },
+ // @return {point} a point on my boundary nearest to p
+ // @see Squeak Smalltalk, Rectangle>>pointNearestTo:
+ pointNearestToPoint: function(p) {
+ p = point(p);
+ if (this.containsPoint(p)) {
+ var side = this.sideNearestToPoint(p);
+ switch (side){
+ case 'right': return point(this.x + this.width, p.y);
+ case 'left': return point(this.x, p.y);
+ case 'bottom': return point(p.x, this.y + this.height);
+ case 'top': return point(p.x, this.y);
+ }
+ }
+ return p.adhereToRect(this);
+ },
+ // Find point on my boundary where line starting
+ // from my center ending in point p intersects me.
+ // @param {number} angle If angle is specified, intersection with rotated rectangle is computed.
+ intersectionWithLineFromCenterToPoint: function(p, angle) {
+ p = point(p);
+ var center = point(this.x + this.width / 2, this.y + this.height / 2);
+ var result;
+ if (angle) p.rotate(center, angle);
+
+ // (clockwise, starting from the top side)
+ var sides = [
+ line(this.origin(), this.topRight()),
+ line(this.topRight(), this.corner()),
+ line(this.corner(), this.bottomLeft()),
+ line(this.bottomLeft(), this.origin())
+ ];
+ var connector = line(center, p);
+
+ for (var i = sides.length - 1; i >= 0; --i) {
+ var intersection = sides[i].intersection(connector);
+ if (intersection !== null) {
+ result = intersection;
+ break;
+ }
+ }
+ if (result && angle) result.rotate(center, -angle);
+ return result;
+ },
+ // Move and expand me.
+ // @param r {rectangle} representing deltas
+ moveAndExpand: function(r) {
+ this.x += r.x || 0;
+ this.y += r.y || 0;
+ this.width += r.width || 0;
+ this.height += r.height || 0;
+ return this;
+ },
+ round: function(decimals) {
+ this.x = decimals ? this.x.toFixed(decimals) : round(this.x);
+ this.y = decimals ? this.y.toFixed(decimals) : round(this.y);
+ this.width = decimals ? this.width.toFixed(decimals) : round(this.width);
+ this.height = decimals ? this.height.toFixed(decimals) : round(this.height);
+ return this;
+ },
+ // Normalize the rectangle; i.e., make it so that it has a non-negative width and height.
+ // If width < 0 the function swaps the left and right corners,
+ // and it swaps the top and bottom corners if height < 0
+ // like in http://qt-project.org/doc/qt-4.8/qrectf.html#normalized
+ normalize: function() {
+ var newx = this.x;
+ var newy = this.y;
+ var newwidth = this.width;
+ var newheight = this.height;
+ if (this.width < 0) {
+ newx = this.x + this.width;
+ newwidth = -this.width;
+ }
+ if (this.height < 0) {
+ newy = this.y + this.height;
+ newheight = -this.height;
+ }
+ this.x = newx;
+ this.y = newy;
+ this.width = newwidth;
+ this.height = newheight;
+ return this;
+ },
+ // Find my bounding box when I'm rotated with the center of rotation in the center of me.
+ // @return r {rectangle} representing a bounding box
+ bbox: function(angle) {
+ var theta = toRad(angle || 0);
+ var st = abs(sin(theta));
+ var ct = abs(cos(theta));
+ var w = this.width * ct + this.height * st;
+ var h = this.width * st + this.height * ct;
+ return rect(this.x + (this.width - w) / 2, this.y + (this.height - h) / 2, w, h);
+ }
+ };
+
+ // Ellipse.
+ // --------
+ function ellipse(c, a, b) {
+ if (!(this instanceof ellipse))
+ return new ellipse(c, a, b);
+ c = point(c);
+ this.x = c.x;
+ this.y = c.y;
+ this.a = a;
+ this.b = b;
+ }
+
+ ellipse.prototype = {
+ toString: function() {
+ return point(this.x, this.y).toString() + ' ' + this.a + ' ' + this.b;
+ },
+ bbox: function() {
+ return rect(this.x - this.a, this.y - this.b, 2 * this.a, 2 * this.b);
+ },
+ // Find point on me where line from my center to
+ // point p intersects my boundary.
+ // @param {number} angle If angle is specified, intersection with rotated ellipse is computed.
+ intersectionWithLineFromCenterToPoint: function(p, angle) {
+ p = point(p);
+ if (angle) p.rotate(point(this.x, this.y), angle);
+ var dx = p.x - this.x;
+ var dy = p.y - this.y;
+ var result;
+ if (dx === 0) {
+ result = this.bbox().pointNearestToPoint(p);
+ if (angle) return result.rotate(point(this.x, this.y), -angle);
+ return result;
+ }
+ var m = dy / dx;
+ var mSquared = m * m;
+ var aSquared = this.a * this.a;
+ var bSquared = this.b * this.b;
+ var x = sqrt(1 / ((1 / aSquared) + (mSquared / bSquared)));
+
+ x = dx < 0 ? -x : x;
+ var y = m * x;
+ result = point(this.x + x, this.y + y);
+ if (angle) return result.rotate(point(this.x, this.y), -angle);
+ return result;
+ }
+ };
+
+ // Bezier curve.
+ // -------------
+ var bezier = {
+ // Cubic Bezier curve path through points.
+ // Ported from C# implementation by Oleg V. Polikarpotchkin and Peter Lee (http://www.codeproject.com/KB/graphics/BezierSpline.aspx).
+ // @param {array} points Array of points through which the smooth line will go.
+ // @return {array} SVG Path commands as an array
+ curveThroughPoints: function(points) {
+ var controlPoints = this.getCurveControlPoints(points);
+ var path = ['M', points[0].x, points[0].y];
+
+ for (var i = 0; i < controlPoints[0].length; i++) {
+ path.push('C', controlPoints[0][i].x, controlPoints[0][i].y, controlPoints[1][i].x, controlPoints[1][i].y, points[i + 1].x, points[i + 1].y);
+ }
+ return path;
+ },
+
+ // Get open-ended Bezier Spline Control Points.
+ // @param knots Input Knot Bezier spline points (At least two points!).
+ // @param firstControlPoints Output First Control points. Array of knots.length - 1 length.
+ // @param secondControlPoints Output Second Control points. Array of knots.length - 1 length.
+ getCurveControlPoints: function(knots) {
+ var firstControlPoints = [];
+ var secondControlPoints = [];
+ var n = knots.length - 1;
+ var i;
+
+ // Special case: Bezier curve should be a straight line.
+ if (n == 1) {
+ // 3P1 = 2P0 + P3
+ firstControlPoints[0] = point((2 * knots[0].x + knots[1].x) / 3,
+ (2 * knots[0].y + knots[1].y) / 3);
+ // P2 = 2P1 – P0
+ secondControlPoints[0] = point(2 * firstControlPoints[0].x - knots[0].x,
+ 2 * firstControlPoints[0].y - knots[0].y);
+ return [firstControlPoints, secondControlPoints];
+ }
+
+ // Calculate first Bezier control points.
+ // Right hand side vector.
+ var rhs = [];
+
+ // Set right hand side X values.
+ for (i = 1; i < n - 1; i++) {
+ rhs[i] = 4 * knots[i].x + 2 * knots[i + 1].x;
+ }
+ rhs[0] = knots[0].x + 2 * knots[1].x;
+ rhs[n - 1] = (8 * knots[n - 1].x + knots[n].x) / 2.0;
+ // Get first control points X-values.
+ var x = this.getFirstControlPoints(rhs);
+
+ // Set right hand side Y values.
+ for (i = 1; i < n - 1; ++i) {
+ rhs[i] = 4 * knots[i].y + 2 * knots[i + 1].y;
+ }
+ rhs[0] = knots[0].y + 2 * knots[1].y;
+ rhs[n - 1] = (8 * knots[n - 1].y + knots[n].y) / 2.0;
+ // Get first control points Y-values.
+ var y = this.getFirstControlPoints(rhs);
+
+ // Fill output arrays.
+ for (i = 0; i < n; i++) {
+ // First control point.
+ firstControlPoints.push(point(x[i], y[i]));
+ // Second control point.
+ if (i < n - 1) {
+ secondControlPoints.push(point(2 * knots [i + 1].x - x[i + 1],
+ 2 * knots[i + 1].y - y[i + 1]));
+ } else {
+ secondControlPoints.push(point((knots[n].x + x[n - 1]) / 2,
+ (knots[n].y + y[n - 1]) / 2));
+ }
+ }
+ return [firstControlPoints, secondControlPoints];
+ },
+
+ // Solves a tridiagonal system for one of coordinates (x or y) of first Bezier control points.
+ // @param rhs Right hand side vector.
+ // @return Solution vector.
+ getFirstControlPoints: function(rhs) {
+ var n = rhs.length;
+ // `x` is a solution vector.
+ var x = [];
+ var tmp = [];
+ var b = 2.0;
+
+ x[0] = rhs[0] / b;
+ // Decomposition and forward substitution.
+ for (var i = 1; i < n; i++) {
+ tmp[i] = 1 / b;
+ b = (i < n - 1 ? 4.0 : 3.5) - tmp[i];
+ x[i] = (rhs[i] - x[i - 1]) / b;
+ }
+ for (i = 1; i < n; i++) {
+ // Backsubstitution.
+ x[n - i - 1] -= tmp[n - i] * x[n - i];
+ }
+ return x;
+ },
+
+ // Solves an inversion problem -- Given the (x, y) coordinates of a point which lies on
+ // a parametric curve x = x(t)/w(t), y = y(t)/w(t), find the parameter value t
+ // which corresponds to that point.
+ // @param control points (start, control start, control end, end)
+ // @return a function accepts a point and returns t.
+ getInversionSolver: function(p0, p1, p2, p3) {
+ var pts = arguments;
+ function l(i, j) {
+ // calculates a determinant 3x3
+ // [p.x p.y 1]
+ // [pi.x pi.y 1]
+ // [pj.x pj.y 1]
+ var pi = pts[i];
+ var pj = pts[j];
+ return function(p) {
+ var w = (i % 3 ? 3 : 1) * (j % 3 ? 3 : 1);
+ var lij = p.x * (pi.y - pj.y) + p.y * (pj.x - pi.x) + pi.x * pj.y - pi.y * pj.x;
+ return w * lij;
+ };
+ }
+ return function solveInversion(p) {
+ var ct = 3 * l(2, 3)(p1);
+ var c1 = l(1, 3)(p0) / ct;
+ var c2 = -l(2, 3)(p0) / ct;
+ var la = c1 * l(3, 1)(p) + c2 * (l(3, 0)(p) + l(2, 1)(p)) + l(2, 0)(p);
+ var lb = c1 * l(3, 0)(p) + c2 * l(2, 0)(p) + l(1, 0)(p);
+ return lb / (lb - la);
+ };
+ },
+
+ // Divide a Bezier curve into two at point defined by value 't' <0,1>.
+ // Using deCasteljau algorithm. http://math.stackexchange.com/a/317867
+ // @param control points (start, control start, control end, end)
+ // @return a function accepts t and returns 2 curves each defined by 4 control points.
+ getCurveDivider: function(p0, p1, p2, p3) {
+ return function divideCurve(t) {
+ var l = line(p0, p1).pointAt(t);
+ var m = line(p1, p2).pointAt(t);
+ var n = line(p2, p3).pointAt(t);
+ var p = line(l, m).pointAt(t);
+ var q = line(m, n).pointAt(t);
+ var r = line(p, q).pointAt(t);
+ return [{ p0: p0, p1: l, p2: p, p3: r }, { p0: r, p1: q, p2: n, p3: p3 }];
+ };
+ }
+ };
+
+ // Scale.
+ var scale = {
+
+ // Return the `value` from the `domain` interval scaled to the `range` interval.
+ linear: function(domain, range, value) {
+
+ var domainSpan = domain[1] - domain[0];
+ var rangeSpan = range[1] - range[0];
+ return (((value - domain[0]) / domainSpan) * rangeSpan + range[0]) || 0;
+ }
+ };
+
+ return {
+ toDeg: toDeg,
+ toRad: toRad,
+ snapToGrid: snapToGrid,
+ normalizeAngle: normalizeAngle,
+ point: point,
+ line: line,
+ rect: rect,
+ ellipse: ellipse,
+ bezier: bezier,
+ scale: scale
+ };
+
+}));
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Code Review / groupbasedpolicy.git / blobdiff