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Make Curve#_getCrossings() a static method and have it work on curve values directly.
This commit is contained in:
Jürg Lehni
parent
d6db007765
commit
610e396d94
2 changed files with 79 additions and 84 deletions
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@ -286,87 +286,11 @@ var Curve = Base.extend(/** @lends Curve# */{
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&& this._segment2._handleIn.isZero();
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},
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isZero: function() {
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return this._segment1._point.equals(this._segment2._point)
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&& this.isLinear();
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},
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getIntersections: function(curve) {
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return Curve.getIntersections(this.getValues(), curve.getValues(),
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this, curve, []);
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},
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_getCrossings: function(point, previous, roots) {
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// Implementation of the crossing number algorithm:
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// http://en.wikipedia.org/wiki/Point_in_polygon
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// Solve the y-axis cubic polynomial for point.y and count all solutions
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// to the right of point.x as crossings.
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var vals = this.getValues(),
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count = Curve.solveCubic(vals, 1, point.y, roots),
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crossings = 0,
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tolerance = /*#=*/ Numerical.TOLERANCE,
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abs = Math.abs;
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// Checks the y-slope between the current curve and the previous for a
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// change of orientation, when a solution is found at t == 0
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function changesOrientation(tangent) {
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return Curve.evaluate(previous.getValues(), 1, true, 1).y
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* tangent.y > 0;
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}
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// TODO: See if this speeds up code, or slows it down:
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// var bounds = this.getBounds();
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// if (point.y < bounds.getTop() || point.y > bounds.getBottom()
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// || point.x > bounds.getRight())
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// return 0;
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if (count === -1) {
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// Infinite solutions, so we have a horizontal curve.
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// Find parameter through getParameterOf()
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roots[0] = Curve.getParameterOf(vals, point.x, point.y);
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count = roots[0] !== null ? 1 : 0;
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}
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for (var i = 0; i < count; i++) {
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var t = roots[i];
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if (t > -tolerance && t < 1 - tolerance) {
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var pt = Curve.evaluate(vals, t, true, 0);
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if (point.x < pt.x + tolerance) {
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// Passing 1 for Curve.evaluate() type calculates tangents
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var tan = Curve.evaluate(vals, t, true, 1);
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// Handle all kind of edge cases when points are on contours
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// or rays are touching countours, to termine wether the
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// crossing counts or not.
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// See if the actual point is on the countour:
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if (abs(pt.x - point.x) < tolerance) {
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// Do not count the crossing if it is on the left hand
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// side of the shape (tangent pointing upwards), since
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// the ray will go out the other end, count as
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// crossing there, and the point is on the contour, so
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// to be considered inside.
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var angle = tan.getAngle();
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if (angle > -180 && angle < 0
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// Handle special case where point is on a corner,
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// in which case this crossing is skipped if both
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// tangents have the same orientation.
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&& (t > tolerance || changesOrientation(tan)))
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continue;
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} else {
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// Skip touching stationary points:
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if (abs(tan.y) < tolerance
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// Check derivate for stationary points. If root is
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// close to 0 and not changing vertical orientation
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// from the previous curve, do not count this root,
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// as it's touching a corner.
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|| t < tolerance && !changesOrientation(tan))
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continue;
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}
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crossings++;
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}
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}
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}
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return crossings;
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},
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// TODO: adjustThroughPoint
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/**
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@ -670,6 +594,70 @@ statics: {
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return new Rectangle(min[0], min[1], max[0] - min[0], max[1] - min[1]);
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},
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_getCrossings: function(v, prev, x, y, roots) {
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// Implementation of the crossing number algorithm:
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// http://en.wikipedia.org/wiki/Point_in_polygon
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// Solve the y-axis cubic polynomial for y and count all solutions
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// to the right of x as crossings.
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var count = Curve.solveCubic(v, 1, y, roots),
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crossings = 0,
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tolerance = /*#=*/ Numerical.TOLERANCE,
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abs = Math.abs;
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// Checks the y-slope between the current curve and the previous for a
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// change of orientation, when a solution is found at t == 0
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function changesOrientation(tangent) {
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return Curve.evaluate(prev, 1, true, 1).y
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* tangent.y > 0;
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}
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if (count === -1) {
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// Infinite solutions, so we have a horizontal curve.
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// Find parameter through getParameterOf()
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roots[0] = Curve.getParameterOf(v, x, y);
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count = roots[0] !== null ? 1 : 0;
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}
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for (var i = 0; i < count; i++) {
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var t = roots[i];
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if (t > -tolerance && t < 1 - tolerance) {
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var pt = Curve.evaluate(v, t, true, 0);
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if (x < pt.x + tolerance) {
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// Pass 1 for Curve.evaluate() type to calculate tangent
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var tan = Curve.evaluate(v, t, true, 1);
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// Handle all kind of edge cases when points are on
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// contours or rays are touching countours, to termine
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// wether the crossing counts or not.
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// See if the actual point is on the countour:
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if (abs(pt.x - x) < tolerance) {
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// Do not count the crossing if it is on the left hand
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// side of the shape (tangent pointing upwards), since
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// the ray will go out the other end, count as crossing
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// there, and the point is on the contour, so to be
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// considered inside.
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var angle = tan.getAngle();
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if (angle > -180 && angle < 0
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// Handle special case where point is on a corner,
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// in which case this crossing is skipped if both
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// tangents have the same orientation.
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&& (t > tolerance || changesOrientation(tan)))
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continue;
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} else {
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// Skip touching stationary points:
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if (abs(tan.y) < tolerance
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// Check derivate for stationary points. If root is
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// close to 0 and not changing vertical orientation
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// from the previous curve, do not count this root,
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// as it's touching a corner.
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|| t < tolerance && !changesOrientation(tan))
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continue;
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}
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crossings++;
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}
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}
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}
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return crossings;
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},
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/**
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* Private helper for both Curve.getBounds() and Path.getBounds(), which
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* finds the 0-crossings of the derivative of a bezier curve polynomial, to
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@ -1613,22 +1613,29 @@ var Path = PathItem.extend(/** @lends Path# */{
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crossings = 0,
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// Reuse one array for root-finding, give garbage collector a break
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roots = new Array(3),
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last = closed
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last = (closed
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? curves[curves.length - 1]
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// Create a straight closing line for open paths, just like
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// how filling open paths works.
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: new Curve(segments[segments.length - 1]._point,
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segments[0]._point),
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segments[0]._point)).getValues(),
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previous = last;
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for (var i = 0, l = curves.length; i < l; i++) {
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var curve = curves[i];
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if (!curve.isZero()) {
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crossings += curve._getCrossings(point, previous, roots);
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previous = curve;
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var vals = curves[i].getValues(),
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x = vals[0],
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y = vals[1];
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// Filter out curves with 0-lenght (all 4 points in the same place):
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if (!(x === vals[2] && y === vals[3] && x === vals[4]
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&& y === vals[5] && x === vals[6] && y === vals[7])) {
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crossings += Curve._getCrossings(vals, previous,
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point.x, point.y, roots);
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previous = vals;
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}
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}
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if (!closed)
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crossings += last._getCrossings(point, previous, roots);
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if (!closed) {
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crossings += Curve._getCrossings(last, previous, point.x, point.y,
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roots);
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}
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return (crossings & 1) === 1;
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},
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