mirror of
https://github.com/scratchfoundation/paper.js.git
synced 2025-01-20 22:39:50 -05:00
Start cleaning up code from #773
- Use Line object isntead of static methods - Do not rely on Math.sign() as it's not supported on all browsers - Wrap lines at 80 char width.
This commit is contained in:
Jürg Lehni
parent
2a7d1c5728
commit
1231153553
2 changed files with 81 additions and 67 deletions
|
|
@ -417,16 +417,16 @@ var Curve = Base.extend(/** @lends Curve# */{
|
|||
* Returns all intersections between two {@link Curve} objects as an array
|
||||
* of {@link CurveLocation} objects.
|
||||
*
|
||||
* If the parameter curve is null, the self intersection of the curve is
|
||||
* returned, if it exists.
|
||||
*
|
||||
* @param {Curve} curve the other curve to find the intersections with
|
||||
* @return {CurveLocation[]} the locations of all intersection between the
|
||||
* @param {Curve} curve the other curve to find the intersections with (if
|
||||
* the curve itself or {@code null} is passed, the self intersection of the
|
||||
* curve is returned, if it exists)
|
||||
* @return {CurveLocation[]} the locations of all intersections between the
|
||||
* curves
|
||||
*/
|
||||
getIntersections: function(curve) {
|
||||
return Curve.getIntersections(this.getValues(), curve ? curve.getValues() : null,
|
||||
this, curve ? curve : this, [], {});
|
||||
return Curve.getIntersections(this.getValues(),
|
||||
curve && curve !== this ? curve.getValues() : null,
|
||||
this, curve, [], {});
|
||||
},
|
||||
|
||||
// TODO: adjustThroughPoint
|
||||
|
|
@ -1756,63 +1756,78 @@ new function() { // Scope for intersection using bezier fat-line clipping
|
|||
}
|
||||
|
||||
return { statics: /** @lends Curve */{
|
||||
// We need to provide the original left curve reference to the
|
||||
// #getIntersections() calls as it is required to create the resulting
|
||||
// CurveLocation objects.
|
||||
getIntersections: function(v1, v2, c1, c2, locations, param) {
|
||||
if (!v2) { // if v2 is null or undefined, search for self intersection
|
||||
// get side of both handles
|
||||
var h1Side = Line.getSide(v1[0], v1[1], v1[6], v1[7], v1[2], v1[3], false);
|
||||
var h2Side = Line.getSide(v1[0], v1[1], v1[6], v1[7], v1[4], v1[5], false);
|
||||
if (h1Side == h2Side) {
|
||||
var edgeSum = (v1[0] - v1[4]) * (v1[3] - v1[7]) + (v1[2] - v1[6]) * (v1[5] - v1[1]);
|
||||
// if both handles are on the same side, the curve can only have a self intersection if
|
||||
// the edge sum and the handles's side have different signs. If the handles are on the
|
||||
// left side, the edge sum must be negative for a self intersection (and vice versa)
|
||||
if (Math.sign(edgeSum) == h1Side) return locations;
|
||||
// If v2 is not provided, search for self intersection on v1.
|
||||
if (!v2) {
|
||||
// Get side of both handles
|
||||
var line = new Line(v1[0], v1[1], v1[6], v1[7], false),
|
||||
side1 = line.getSide(v1[2], v1[3]),
|
||||
side2 = Line.getSide(v1[4], v1[5]);
|
||||
if (side1 === side2) {
|
||||
var edgeSum = (v1[0] - v1[4]) * (v1[3] - v1[7])
|
||||
+ (v1[2] - v1[6]) * (v1[5] - v1[1]);
|
||||
// If both handles are on the same side, the curve can only
|
||||
// have a self intersection if the edge sum and the
|
||||
// handles' sides have different signs. If the handles are
|
||||
// on the left side, the edge sum must be negative for a
|
||||
// self intersection (and vice-versa).
|
||||
if (edgeSum * side1 > 0)
|
||||
return locations;
|
||||
}
|
||||
// As a second condition we check if the curve has an inflection point. If an inflection point
|
||||
// exists, the curve cannot have a self intersection.
|
||||
var ax = v1[6] - 3 * v1[4] + 3 * v1[2] - v1[0];
|
||||
var bx = v1[4] - 2 * v1[2] + v1[0];
|
||||
var cx = v1[2] - v1[0];
|
||||
var ay = v1[7] - 3 * v1[5] + 3 * v1[3] - v1[1];
|
||||
var by = v1[5] - 2 * v1[3] + v1[1];
|
||||
var cy = v1[3] - v1[1];
|
||||
var hasInflectionPoint = (Math.pow(ay * cx - ax * cy, 2) - 4 * (ay * bx - ax * by) * (by * cx - bx * cy) >= 0);
|
||||
if (!hasInflectionPoint) {
|
||||
// the curve may have a self intersection, find parameter to split curve. We search for the
|
||||
// parameter where the velocity has an extremum by finding the roots of the cross product
|
||||
// between the bezier curve's first and second derivative
|
||||
// As a second condition we check if the curve has an inflection
|
||||
// point. If an inflection point exists, the curve cannot have a
|
||||
// self intersection.
|
||||
var ax = v1[6] - 3 * v1[4] + 3 * v1[2] - v1[0],
|
||||
bx = v1[4] - 2 * v1[2] + v1[0],
|
||||
cx = v1[2] - v1[0],
|
||||
ay = v1[7] - 3 * v1[5] + 3 * v1[3] - v1[1],
|
||||
by = v1[5] - 2 * v1[3] + v1[1],
|
||||
cy = v1[3] - v1[1],
|
||||
hasInflection = Math.pow(ay * cx - ax * cy, 2)
|
||||
- 4 * (ay * bx - ax * by) * (by * cx - bx * cy) >= 0;
|
||||
if (!hasInflection) {
|
||||
// The curve may have a self intersection, find parameter to
|
||||
// split curve. We search for the parameter where the
|
||||
// velocity has an extremum by finding the roots of the
|
||||
// cross product between the bezier curve's first and second
|
||||
// derivative.
|
||||
var roots = [],
|
||||
rootCount = Numerical.solveCubic(ax * ax + ay * ay, 3 * (ax * bx + ay * by),
|
||||
(2 * (bx * bx + by * by) + ax * cx + ay * cy), (bx * cx + by * cy), roots, 0, 1);
|
||||
// Select extremum with smallest curvature. This is always on the loop in case of a self intersection
|
||||
var tSplit, maxCurvature;
|
||||
for (var i = 0; i < rootCount; i++) {
|
||||
var curvature = Math.abs(c1.getCurvatureAt(roots[i], true));
|
||||
if (!maxCurvature || curvature > maxCurvature) {
|
||||
rootCount = Numerical.solveCubic(
|
||||
ax * ax + ay * ay,
|
||||
3 * (ax * bx + ay * by),
|
||||
2 * (bx * bx + by * by) + ax * cx + ay * cy,
|
||||
bx * cx + by * cy,
|
||||
roots, 0, 1);
|
||||
// Select extremum with smallest curvature. This is always
|
||||
// on the loop in case of a self intersection.
|
||||
var tSplit;
|
||||
for (var i = 0, maxCurvature = 0; i < rootCount; i++) {
|
||||
var curvature = Math.abs(
|
||||
c1.getCurvatureAt(roots[i], true));
|
||||
if (curvature > maxCurvature) {
|
||||
maxCurvature = curvature;
|
||||
tSplit = roots[i];
|
||||
}
|
||||
}
|
||||
// Divide the curve in two and then apply the normal curve intersection code.
|
||||
// Divide the curve in two and then apply the normal curve
|
||||
// intersection code.
|
||||
var parts = Curve.subdivide(v1, tSplit);
|
||||
if (!param) param = {};
|
||||
// After splitting, the end is always connected:
|
||||
param.endConnected = true;
|
||||
// Since the curve was split above, we need to
|
||||
// adjust the parameters for both locations.
|
||||
param.renormalize = function(t1, t2) {
|
||||
return [t1 * tSplit, t2 * (1 - tSplit) + tSplit];
|
||||
};
|
||||
Curve.getIntersections(parts[0], parts[1], c1, c1, locations, param);
|
||||
Curve.getIntersections(parts[0], parts[1], c1, c1, locations, {
|
||||
startConnected: param.startConnected,
|
||||
// After splitting, the end is always connected:
|
||||
endConnected: true,
|
||||
// Since the curve was split above, we need to
|
||||
// adjust the parameters for both locations.
|
||||
renormalize: function(t1, t2) {
|
||||
return [t1 * tSplit, t2 * (1 - tSplit) + tSplit];
|
||||
}
|
||||
});
|
||||
}
|
||||
} else {
|
||||
// Avoid checking curves if completely out of control bounds.
|
||||
// As a little optimization, we can scale the handles with 0.75
|
||||
// before calculating the control bounds and still be sure that the
|
||||
// curve is fully contained.
|
||||
// Avoid checking curves if completely out of control bounds. As
|
||||
// a little optimization, we can scale the handles with 0.75
|
||||
// before calculating the control bounds and still be sure that
|
||||
// the curve is fully contained.
|
||||
var c1p1x = v1[0], c1p1y = v1[1],
|
||||
c1p2x = v1[6], c1p2y = v1[7],
|
||||
c2p1x = v2[0], c2p1y = v2[1],
|
||||
|
|
@ -1828,18 +1843,18 @@ new function() { // Scope for intersection using bezier fat-line clipping
|
|||
min = Math.min,
|
||||
max = Math.max;
|
||||
if (!(
|
||||
max(c1p1x, c1h1x, c1h2x, c1p2x) >=
|
||||
min(c2p1x, c2h1x, c2h2x, c2p2x) &&
|
||||
min(c1p1x, c1h1x, c1h2x, c1p2x) <=
|
||||
max(c2p1x, c2h1x, c2h2x, c2p2x) &&
|
||||
max(c1p1y, c1h1y, c1h2y, c1p2y) >=
|
||||
min(c2p1y, c2h1y, c2h2y, c2p2y) &&
|
||||
min(c1p1y, c1h1y, c1h2y, c1p2y) <=
|
||||
max(c2p1y, c2h1y, c2h2y, c2p2y)
|
||||
max(c1p1x, c1h1x, c1h2x, c1p2x) >=
|
||||
min(c2p1x, c2h1x, c2h2x, c2p2x) &&
|
||||
min(c1p1x, c1h1x, c1h2x, c1p2x) <=
|
||||
max(c2p1x, c2h1x, c2h2x, c2p2x) &&
|
||||
max(c1p1y, c1h1y, c1h2y, c1p2y) >=
|
||||
min(c2p1y, c2h1y, c2h2y, c2p2y) &&
|
||||
min(c1p1y, c1h1y, c1h2y, c1p2y) <=
|
||||
max(c2p1y, c2h1y, c2h2y, c2p2y)
|
||||
)
|
||||
// Also detect and handle overlaps:
|
||||
// Also detect and handle overlaps:
|
||||
|| !param.startConnected && !param.endConnected
|
||||
&& addOverlap(v1, v2, c1, c2, locations, param))
|
||||
&& addOverlap(v1, v2, c1, c2, locations, param))
|
||||
return locations;
|
||||
var straight1 = Curve.isStraight(v1),
|
||||
straight2 = Curve.isStraight(v2),
|
||||
|
|
|
|||
|
|
@ -88,13 +88,12 @@ var PathItem = Item.extend(/** @lends PathItem# */{
|
|||
values1 = self ? values2[i] : curve1.getValues(matrix1);
|
||||
if (self) {
|
||||
// First check for self-intersections within the same curve
|
||||
var p1 = curve1.getSegment1()._point,
|
||||
p2 = curve1.getSegment2()._point;
|
||||
Curve.getIntersections(values1, null, curve1, curve1,
|
||||
locations, {
|
||||
include: include,
|
||||
// Only possible if there is only one closed curve:
|
||||
startConnected: length1 === 1 && p1.equals(p2)
|
||||
startConnected: length1 === 1 &&
|
||||
curve1.getPoint1().equals(curve1.getPoint2())
|
||||
}
|
||||
);
|
||||
}
|
||||
|
|
|
|||
Loading…
Reference in a new issue