mirror of
https://github.com/scratchfoundation/paper.js.git
synced 2025-01-07 13:22:07 -05:00
Expose the previously private evalutate() function through Curve.evaluate(), make it work with curve value arrays, and use it the for various evaluation methods (#getPoint/Tangent/Normal).
This commit is contained in:
Jürg Lehni
parent
14816a872e
commit
cb3834f41c
1 changed files with 262 additions and 251 deletions
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@ -260,6 +260,43 @@ var Curve = this.Curve = Base.extend({
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return Curve.getParameter.apply(Curve, args);
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return Curve.getParameter.apply(Curve, args);
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},
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},
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_evaluate: function(parameter, type) {
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var args = this.getCurveValues();
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args.push(parameter, type);
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return Curve.evaluate.apply(Curve, args);
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},
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/**
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* Returns the point on the curve at the specified position.
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*
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* @param {Number} parameter the position at which to find the point as
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* a value between {@code 0} and {@code 1}.
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* @return {Point}
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*/
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getPoint: function(parameter) {
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return this._evaluate(parameter, 0);
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},
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/**
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* Returns the tangent point on the curve at the specified position.
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*
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* @param {Number} parameter the position at which to find the tangent
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* point as a value between {@code 0} and {@code 1}.
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*/
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getTangent: function(parameter) {
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return this._evaluate(parameter, 1);
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},
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/**
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* Returns the normal point on the curve at the specified position.
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*
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* @param {Number} parameter the position at which to find the normal
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* point as a value between {@code 0} and {@code 1}.
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*/
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getNormal: function(parameter) {
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return this._evaluate(parameter, 2);
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},
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// TODO: getParameter(point, precision)
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// TODO: getParameter(point, precision)
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// TODO: getLocation
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// TODO: getLocation
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// TODO: getIntersections
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// TODO: getIntersections
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@ -320,76 +357,179 @@ var Curve = this.Curve = Base.extend({
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curve._segment1 = segment1;
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curve._segment1 = segment1;
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curve._segment2 = segment2;
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curve._segment2 = segment2;
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return curve;
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return curve;
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},
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getCurveValues: function(segment1, segment2) {
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var p1 = segment1._point,
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h1 = segment1._handleOut,
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h2 = segment2._handleIn,
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p2 = segment2._point;
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return [
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p1._x, p1._y,
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p1._x + h1._x, p1._y + h1._y,
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p2._x + h2._x, p2._y + h2._y,
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p2._x, p2._y
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];
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},
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evaluate: function(p1x, p1y, c1x, c1y, c2x, c2y, p2x, p2y, t, type) {
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var x, y;
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// Handle special case at beginning / end of curve
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// PORT: Change in Sg too, so 0.000000000001 won't be
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// required anymore
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if (t == 0 || t == 1) {
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var point;
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switch (type) {
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case 0: // point
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x = t == 0 ? p1x : p2x;
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y = t == 0 ? p1y : p2y;
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break;
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case 1: // tangent
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case 2: // normal
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var px, py;
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if (t == 0) {
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if (c1x == p1x && c1y == p1y) { // handle1 = 0
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if (c2x == p2x && c2y == p2y) { // handle2 = 0
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px = p2x; py = p2y; // p2
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} else {
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px = c2x; py = c2y; // c2
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}
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} else {
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px = c1x; py = c1y; // handle1
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}
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x = px - p1x;
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y = py - p1y;
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} else {
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if (c2x == p2x && c2y == p2y) { // handle2 = 0
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if (c1x == p1x && c1y == p1y) { // handle1 = 0
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px = p1x; py = p1y; // p1
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} else {
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px = c1x; py = c1y; // c1
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}
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} else { // handle2
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px = c2x; py = c2y;
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}
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x = px - p2x;
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y = py - p2y;
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}
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break;
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}
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} else {
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// Calculate the polynomial coefficients.
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var cx = 3 * (c1x - p1x),
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bx = 3 * (c2x - c1x) - cx,
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ax = p2x - p1x - cx - bx,
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cy = 3 * (c1y - p1y),
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by = 3 * (c2y - c1y) - cy,
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ay = p2y - p1y - cy - by;
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switch (type) {
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case 0: // point
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// Calculate the curve point at parameter value t
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x = ((ax * t + bx) * t + cx) * t + p1x;
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y = ((ay * t + by) * t + cy) * t + p1y;
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break;
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case 1: // tangent
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case 2: // normal
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// Simply use the derivation of the bezier function for both
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// the x and y coordinates:
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x = (3 * ax * t + 2 * bx) * t + cx;
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y = (3 * ay * t + 2 * by) * t + cy;
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break;
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}
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}
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// The normal is simply the rotated tangent:
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// TODO: Rotate normals the other way in Scriptographer too?
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// (Depending on orientation, I guess?)
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return type == 2 ? new Point(y, -x) : new Point(x, y);
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},
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subdivide: function(p1x, p1y, c1x, c1y, c2x, c2y, p2x, p2y, t) {
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if (t === undefined)
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t = 0.5;
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var u = 1 - t,
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// Interpolate from 4 to 3 points
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p3x = u * p1x + t * c1x,
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p3y = u * p1y + t * c1y,
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p4x = u * c1x + t * c2x,
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p4y = u * c1y + t * c2y,
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p5x = u * c2x + t * p2x,
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p5y = u * c2y + t * p2y,
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// Interpolate from 3 to 2 points
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p6x = u * p3x + t * p4x,
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p6y = u * p3y + t * p4y,
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p7x = u * p4x + t * p5x,
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p7y = u * p4y + t * p5y,
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// Interpolate from 2 points to 1 point
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p8x = u * p6x + t * p7x,
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p8y = u * p6y + t * p7y;
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// We now have all the values we need to build the subcurves:
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return [
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[p1x, p1y, p3x, p3y, p6x, p6y, p8x, p8y], // left
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[p8x, p8y, p7x, p7y, p5x, p5y, p2x, p2y] // right
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];
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},
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// TODO: Find better name
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getPart: function(p1x, p1y, c1x, c1y, c2x, c2y, p2x, p2y, from, to) {
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var curve = [p1x, p1y, c1x, c1y, c2x, c2y, p2x, p2y];
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if (from > 0) {
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// 8th argument of Curve.subdivide() == t, and values can be
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// directly used as arguments list for apply().
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curve[8] = from;
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curve = Curve.subdivide.apply(Curve, curve)[1]; // right
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}
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if (to < 1) {
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// Se above about curve[8].
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// Interpolate the parameter at 'to' in the new curve and
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// cut there
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curve[8] = (to - from) / (1 - from);
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curve = Curve.subdivide.apply(Curve, curve)[0]; // left
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}
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return curve;
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},
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isSufficientlyFlat: function(p1x, p1y, c1x, c1y, c2x, c2y, p2x, p2y) {
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// Inspired by Skia, but to be tested:
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// Calculate 1/3 (m1) and 2/3 (m2) along the line between start (p1)
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// and end (p2), measure distance from there the control points and
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// see if they are further away than 1/2.
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// Seems all very inaccurate, especially since the distance
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// measurement is just the bigger one of x / y...
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// TODO: Find a more accurate and still fast way to determine this.
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var vx = (p2x - p1x) / 3,
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vy = (p2y - p1y) / 3,
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m1x = p1x + vx,
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m1y = p1y + vy,
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m2x = p2x - vx,
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m2y = p2y - vy;
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return Math.max(
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Math.abs(m1x - c1x), Math.abs(m1y - c1y),
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Math.abs(m2x - c1x), Math.abs(m1y - c1y)) < 1 / 2;
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/*
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// Thanks to Kaspar Fischer for the following:
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// http://www.inf.ethz.ch/personal/fischerk/pubs/bez.pdf
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var ux = 3 * c1x - 2 * p1x - p2x;
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ux *= ux;
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var uy = 3 * c1y - 2 * p1y - p2y;
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uy *= uy;
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var vx = 3 * c2x - 2 * p2x - p1x;
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vx *= vx;
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var vy = 3 * c2y - 2 * p2y - p1y;
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vy *= vy;
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if (ux < vx)
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ux = vx;
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if (uy < vy)
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uy = vy;
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// Tolerance is 16 * tol ^ 2
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return ux + uy <= 16 * Numerical.TOLERNACE * Numerical.TOLERNACE;
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*/
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}
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}
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}
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}
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}, new function() {
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}, new function() {
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function evaluate(that, t, type) {
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// Calculate the polynomial coefficients. caution: handles are relative
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// to points
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var point1 = that._segment1._point,
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handle1 = that._segment1._handleOut,
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handle2 = that._segment2._handleIn,
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point2 = that._segment2._point,
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x, y;
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// Handle special case at beginning / end of curve
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// PORT: Change in Sg too, so 0.000000000001 won't be
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// required anymore
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if (t == 0 || t == 1) {
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var point;
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switch (type) {
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case 0: // point
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point = t == 0 ? point1 : point2;
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break;
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case 1: // tangent
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case 2: // normal
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point = t == 0
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? handle1.isZero()
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? handle2.isZero()
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? point2.subtract(point1)
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: point2.add(handle2).subtract(point1)
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: handle1
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: handle2.isZero() // t == 1
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? handle1.isZero()
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? point1.subtract(point2)
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: point1.add(handle1).subtract(point2)
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: handle2;
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break;
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}
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x = point._x;
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y = point._y;
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} else {
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var dx = point2._x - point1._x,
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cx = 3 * handle1._x,
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bx = 3 * (dx + handle2._x - handle1._x) - cx,
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ax = dx - cx - bx,
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dy = point2._y - point1._y,
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cy = 3 * handle1._y,
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by = 3 * (dy + handle2._y - handle1._y) - cy,
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ay = dy - cy - by;
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switch (type) {
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case 0: // point
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x = ((ax * t + bx) * t + cx) * t + point1._x;
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y = ((ay * t + by) * t + cy) * t + point1._y;
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break;
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case 1: // tangent
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case 2: // normal
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// Simply use the derivation of the bezier function for both
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// the x and y coordinates:
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x = (3 * ax * t + 2 * bx) * t + cx;
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y = (3 * ay * t + 2 * by) * t + cy;
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break;
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}
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}
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// The normal is simply the rotated tangent:
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// TODO: Rotate normals the other way in Scriptographer too?
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// (Depending on orientation, I guess?)
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return type == 2 ? new Point(y, -x) : new Point(x, y);
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}
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function getLengthIntegrand(p1x, p1y, c1x, c1y, c2x, c2y, p2x, p2y) {
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function getLengthIntegrand(p1x, p1y, c1x, c1y, c2x, c2y, p2x, p2y) {
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// Calculate the coefficients of a Bezier derivative.
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// Calculate the coefficients of a Bezier derivative.
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var ax = 9 * (c1x - c2x) + 3 * (p2x - p1x),
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var ax = 9 * (c1x - c2x) + 3 * (p2x - p1x),
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@ -417,193 +557,64 @@ var Curve = this.Curve = Base.extend({
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}
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}
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return {
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return {
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/** @lends Curve# */
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statics: true,
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/**
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getLength: function(p1x, p1y, c1x, c1y, c2x, c2y, p2x, p2y, a, b) {
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* Returns the point on the curve at the specified position.
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if (a === undefined)
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*
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a = 0;
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* @param {Number} parameter the position at which to find the point as
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if (b === undefined)
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* a value between {@code 0} and {@code 1}.
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b = 1;
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* @return {Point}
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if (p1x == c1x && p1y == c1y && p2x == c2x && p2y == c2y) {
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*/
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// Straight line
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getPoint: function(parameter) {
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var dx = p2x - p1x,
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return evaluate(this, parameter, 0);
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dy = p2y - p1y;
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},
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return (b - a) * Math.sqrt(dx * dx + dy * dy);
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/**
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* Returns the tangent point on the curve at the specified position.
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*
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* @param {Number} parameter the position at which to find the tangent
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* point as a value between {@code 0} and {@code 1}.
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*/
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getTangent: function(parameter) {
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return evaluate(this, parameter, 1);
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},
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/**
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* Returns the normal point on the curve at the specified position.
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*
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* @param {Number} parameter the position at which to find the normal
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* point as a value between {@code 0} and {@code 1}.
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*/
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getNormal: function(parameter) {
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return evaluate(this, parameter, 2);
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},
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statics: {
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getCurveValues: function(segment1, segment2) {
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var p1 = segment1._point,
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h1 = segment1._handleOut,
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h2 = segment2._handleIn,
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p2 = segment2._point;
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return [
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p1._x, p1._y,
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p1._x + h1._x, p1._y + h1._y,
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p2._x + h2._x, p2._y + h2._y,
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p2._x, p2._y
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];
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},
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getLength: function(p1x, p1y, c1x, c1y, c2x, c2y, p2x, p2y, a, b) {
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if (a === undefined)
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a = 0;
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if (b === undefined)
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b = 1;
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||||||
if (p1x == c1x && p1y == c1y && p2x == c2x && p2y == c2y) {
|
|
||||||
// Straight line
|
|
||||||
var dx = p2x - p1x,
|
|
||||||
dy = p2y - p1y;
|
|
||||||
return (b - a) * Math.sqrt(dx * dx + dy * dy);
|
|
||||||
}
|
|
||||||
var ds = getLengthIntegrand(
|
|
||||||
p1x, p1y, c1x, c1y, c2x, c2y, p2x, p2y);
|
|
||||||
return Numerical.integrate(ds, a, b, getIterations(a, b));
|
|
||||||
},
|
|
||||||
|
|
||||||
getParameter: function(p1x, p1y, c1x, c1y, c2x, c2y, p2x, p2y,
|
|
||||||
length, start) {
|
|
||||||
if (length == 0)
|
|
||||||
return start;
|
|
||||||
// See if we're going forward or backward, and handle cases
|
|
||||||
// differently
|
|
||||||
var forward = length > 0,
|
|
||||||
a = forward ? start : 0,
|
|
||||||
b = forward ? 1 : start,
|
|
||||||
length = Math.abs(length),
|
|
||||||
// Use integrand to calculate both range length and part
|
|
||||||
// lengths in f(t) below.
|
|
||||||
ds = getLengthIntegrand(
|
|
||||||
p1x, p1y, c1x, c1y, c2x, c2y, p2x, p2y),
|
|
||||||
// Get length of total range
|
|
||||||
rangeLength = Numerical.integrate(ds, a, b,
|
|
||||||
getIterations(a, b));
|
|
||||||
if (length >= rangeLength)
|
|
||||||
return forward ? b : a;
|
|
||||||
// Use length / rangeLength for an initial guess for t, to
|
|
||||||
// bring us closer:
|
|
||||||
var guess = length / rangeLength,
|
|
||||||
len = 0;
|
|
||||||
// Iteratively calculate curve range lengths, and add them up,
|
|
||||||
// using integration precision depending on the size of the
|
|
||||||
// range. This is much faster and also more precise than not
|
|
||||||
// modifing start and calculating total length each time.
|
|
||||||
function f(t) {
|
|
||||||
var count = getIterations(start, t);
|
|
||||||
if (start < t) {
|
|
||||||
len += Numerical.integrate(ds, start, t, count);
|
|
||||||
} else {
|
|
||||||
len -= Numerical.integrate(ds, t, start, count);
|
|
||||||
}
|
|
||||||
start = t;
|
|
||||||
return len - length;
|
|
||||||
}
|
|
||||||
return Numerical.findRoot(f, ds,
|
|
||||||
forward ? a + guess : b - guess, // Initial guess for x
|
|
||||||
a, b, 16, Numerical.TOLERANCE);
|
|
||||||
},
|
|
||||||
|
|
||||||
subdivide: function(p1x, p1y, c1x, c1y, c2x, c2y, p2x, p2y, t) {
|
|
||||||
if (t === undefined)
|
|
||||||
t = 0.5;
|
|
||||||
var u = 1 - t,
|
|
||||||
// Interpolate from 4 to 3 points
|
|
||||||
p3x = u * p1x + t * c1x,
|
|
||||||
p3y = u * p1y + t * c1y,
|
|
||||||
p4x = u * c1x + t * c2x,
|
|
||||||
p4y = u * c1y + t * c2y,
|
|
||||||
p5x = u * c2x + t * p2x,
|
|
||||||
p5y = u * c2y + t * p2y,
|
|
||||||
// Interpolate from 3 to 2 points
|
|
||||||
p6x = u * p3x + t * p4x,
|
|
||||||
p6y = u * p3y + t * p4y,
|
|
||||||
p7x = u * p4x + t * p5x,
|
|
||||||
p7y = u * p4y + t * p5y,
|
|
||||||
// Interpolate from 2 points to 1 point
|
|
||||||
p8x = u * p6x + t * p7x,
|
|
||||||
p8y = u * p6y + t * p7y;
|
|
||||||
// We now have all the values we need to build the subcurves:
|
|
||||||
return [
|
|
||||||
[p1x, p1y, p3x, p3y, p6x, p6y, p8x, p8y], // left
|
|
||||||
[p8x, p8y, p7x, p7y, p5x, p5y, p2x, p2y] // right
|
|
||||||
];
|
|
||||||
},
|
|
||||||
|
|
||||||
// TODO: Find better name
|
|
||||||
getPart: function(p1x, p1y, c1x, c1y, c2x, c2y, p2x, p2y, from, to) {
|
|
||||||
var curve = [p1x, p1y, c1x, c1y, c2x, c2y, p2x, p2y];
|
|
||||||
if (from > 0) {
|
|
||||||
// 8th argument of Curve.subdivide() == t, and values can be
|
|
||||||
// directly used as arguments list for apply().
|
|
||||||
curve[8] = from;
|
|
||||||
curve = Curve.subdivide.apply(Curve, curve)[1]; // right
|
|
||||||
}
|
|
||||||
if (to < 1) {
|
|
||||||
// Se above about curve[8].
|
|
||||||
// Interpolate the parameter at 'to' in the new curve and
|
|
||||||
// cut there
|
|
||||||
curve[8] = (to - from) / (1 - from);
|
|
||||||
curve = Curve.subdivide.apply(Curve, curve)[0]; // left
|
|
||||||
}
|
|
||||||
return curve;
|
|
||||||
},
|
|
||||||
|
|
||||||
isSufficientlyFlat: function(p1x, p1y, c1x, c1y, c2x, c2y, p2x, p2y) {
|
|
||||||
// Inspired by Skia, but to be tested:
|
|
||||||
// Calculate 1/3 (m1) and 2/3 (m2) along the line between start
|
|
||||||
// (p1) and end (p2), measure distance from there the control
|
|
||||||
// points and see if they are further away than 1/2.
|
|
||||||
// Seems all very inaccurate, especially since the distance
|
|
||||||
// measurement is just the bigger one of x / y...
|
|
||||||
// TODO: Find a more accurate and still fast way to determine
|
|
||||||
// this.
|
|
||||||
var vx = (p2x - p1x) / 3,
|
|
||||||
vy = (p2y - p1y) / 3,
|
|
||||||
m1x = p1x + vx,
|
|
||||||
m1y = p1y + vy,
|
|
||||||
m2x = p2x - vx,
|
|
||||||
m2y = p2y - vy;
|
|
||||||
return Math.max(
|
|
||||||
Math.abs(m1x - c1x), Math.abs(m1y - c1y),
|
|
||||||
Math.abs(m2x - c1x), Math.abs(m1y - c1y)) < 1 / 2;
|
|
||||||
/*
|
|
||||||
// Thanks to Kaspar Fischer for the following:
|
|
||||||
// http://www.inf.ethz.ch/personal/fischerk/pubs/bez.pdf
|
|
||||||
var ux = 3 * c1x - 2 * p1x - p2x;
|
|
||||||
ux *= ux;
|
|
||||||
var uy = 3 * c1y - 2 * p1y - p2y;
|
|
||||||
uy *= uy;
|
|
||||||
var vx = 3 * c2x - 2 * p2x - p1x;
|
|
||||||
vx *= vx;
|
|
||||||
var vy = 3 * c2y - 2 * p2y - p1y;
|
|
||||||
vy *= vy;
|
|
||||||
if (ux < vx)
|
|
||||||
ux = vx;
|
|
||||||
if (uy < vy)
|
|
||||||
uy = vy;
|
|
||||||
// Tolerance is 16 * tol ^ 2
|
|
||||||
return ux + uy <= 16 * Numerical.TOLERNACE * Numerical.TOLERNACE;
|
|
||||||
*/
|
|
||||||
}
|
}
|
||||||
|
var ds = getLengthIntegrand(
|
||||||
|
p1x, p1y, c1x, c1y, c2x, c2y, p2x, p2y);
|
||||||
|
return Numerical.integrate(ds, a, b, getIterations(a, b));
|
||||||
|
},
|
||||||
|
|
||||||
|
getParameter: function(p1x, p1y, c1x, c1y, c2x, c2y, p2x, p2y,
|
||||||
|
length, start) {
|
||||||
|
if (length == 0)
|
||||||
|
return start;
|
||||||
|
// See if we're going forward or backward, and handle cases
|
||||||
|
// differently
|
||||||
|
var forward = length > 0,
|
||||||
|
a = forward ? start : 0,
|
||||||
|
b = forward ? 1 : start,
|
||||||
|
length = Math.abs(length),
|
||||||
|
// Use integrand to calculate both range length and part
|
||||||
|
// lengths in f(t) below.
|
||||||
|
ds = getLengthIntegrand(
|
||||||
|
p1x, p1y, c1x, c1y, c2x, c2y, p2x, p2y),
|
||||||
|
// Get length of total range
|
||||||
|
rangeLength = Numerical.integrate(ds, a, b,
|
||||||
|
getIterations(a, b));
|
||||||
|
if (length >= rangeLength)
|
||||||
|
return forward ? b : a;
|
||||||
|
// Use length / rangeLength for an initial guess for t, to
|
||||||
|
// bring us closer:
|
||||||
|
var guess = length / rangeLength,
|
||||||
|
len = 0;
|
||||||
|
// Iteratively calculate curve range lengths, and add them up,
|
||||||
|
// using integration precision depending on the size of the
|
||||||
|
// range. This is much faster and also more precise than not
|
||||||
|
// modifing start and calculating total length each time.
|
||||||
|
function f(t) {
|
||||||
|
var count = getIterations(start, t);
|
||||||
|
if (start < t) {
|
||||||
|
len += Numerical.integrate(ds, start, t, count);
|
||||||
|
} else {
|
||||||
|
len -= Numerical.integrate(ds, t, start, count);
|
||||||
|
}
|
||||||
|
start = t;
|
||||||
|
return len - length;
|
||||||
|
}
|
||||||
|
return Numerical.findRoot(f, ds,
|
||||||
|
forward ? a + guess : b - guess, // Initial guess for x
|
||||||
|
a, b, 16, Numerical.TOLERANCE);
|
||||||
}
|
}
|
||||||
};
|
};
|
||||||
});
|
});
|
||||||
|
|
|
||||||
Loading…
Reference in a new issue