paper.js/src/path/PathItem.Boolean.js

1146 lines
52 KiB
JavaScript

/*
* Paper.js - The Swiss Army Knife of Vector Graphics Scripting.
* http://paperjs.org/
*
* Copyright (c) 2011 - 2016, Juerg Lehni & Jonathan Puckey
* http://scratchdisk.com/ & http://jonathanpuckey.com/
*
* Distributed under the MIT license. See LICENSE file for details.
*
* All rights reserved.
*/
/*
* Boolean Geometric Path Operations
*
* Supported
* - Path and CompoundPath items
* - Boolean Union
* - Boolean Intersection
* - Boolean Subtraction
* - Boolean Exclusion
* - Resolving a self-intersecting Path items
* - Boolean operations on self-intersecting Paths items
*
* @author Harikrishnan Gopalakrishnan <hari.exeption@gmail.com>
* @author Jan Boesenberg <development@iconexperience.com>
* @author Juerg Lehni <juerg@scratchdisk.com>
* http://hkrish.com/playground/paperjs/booleanStudy.html
*/
PathItem.inject(new function() {
var min = Math.min,
max = Math.max,
abs = Math.abs,
// Set up lookup tables for each operator, to decide if a given segment
// is to be considered a part of the solution, or to be discarded, based
// on its winding contribution, as calculated by propagateWinding().
// Boolean operators return true if a segment with the given winding
// contribution contributes to the final result or not. They are applied
// to for each segment after the paths are split at crossings.
operators = {
unite: { 1: true },
intersect: { 2: true },
subtract: { 1: true },
exclude: { 1: true }
};
/*
* Creates a clone of the path that we can modify freely, with its matrix
* applied to its geometry. Calls #reduce() to simplify compound paths and
* remove empty curves, #resolveCrossings() to resolve self-intersection
* make sure all paths have correct winding direction.
*/
function preparePath(path, closed) {
var res = path.clone(false).reduce({ simplify: true })
.transform(null, true, true);
if (closed)
res.setClosed(true);
return closed ? res.resolveCrossings().reorient() : res;
}
function createResult(ctor, paths, reduce, path1, path2) {
var result = new ctor(Item.NO_INSERT);
result.addChildren(paths, true);
// See if the item can be reduced to just a simple Path.
if (reduce)
result = result.reduce({ simplify: true });
// Insert the resulting path above whichever of the two paths appear
// further up in the stack.
result.insertAbove(path2 && path1.isSibling(path2)
&& path1.getIndex() < path2.getIndex() ? path2 : path1);
// Copy over the input path attributes, excluding matrix and we're done.
result.copyAttributes(path1, true);
return result;
}
function computeBoolean(path1, path2, operation) {
// Retrieve the operator lookup table for winding numbers.
var operator = operators[operation];
// Add a simple boolean property to check for a given operation,
// e.g. `if (operator.unite)`
operator[operation] = true;
// If path1 is open, delegate to computeOpenBoolean().
// NOTE: Do not access private _closed property here, since path1 may
// be a CompoundPath.
if (!path1.isClosed())
return computeOpenBoolean(path1, path2, operator);
// We do not modify the operands themselves, but create copies instead,
// fas produced by the calls to preparePath().
// Note that the result paths might not belong to the same type
// i.e. subtraction(A:Path, B:Path):CompoundPath etc.
var _path1 = preparePath(path1, true),
_path2 = path2 && path1 !== path2 && preparePath(path2, true);
// Give both paths the same orientation except for subtraction
// and exclusion, where we need them at opposite orientation.
if (_path2 && (operator.subtract || operator.exclude)
^ (_path2.isClockwise() ^ _path1.isClockwise()))
_path2.reverse();
// Split curves at crossings on both paths. Note that for self-
// intersection, path2 is null and getIntersections() handles it.
var crossings = divideLocations(
CurveLocation.expand(_path1.getCrossings(_path2))),
segments = [],
// Aggregate of all curves in both operands.
curves = [],
paths1 = _path1._children || [_path1],
paths2 = _path2 && (_path2._children || [_path2]),
paths;
function collect(paths) {
for (var i = 0, l = paths.length; i < l; i++) {
var path = paths[i];
segments.push.apply(segments, path._segments);
curves.push.apply(curves, path.getCurves());
// Keep track if there are valid intersections other than
// overlaps in each path.
path._overlapsOnly = path._validOverlapsOnly = true;
}
}
function contains(paths1, paths2) {
return false;
}
// When there are no crossings, and the two paths are not contained
// within each other, the result can be known ahead of tracePaths(),
// largely simplifying the processing required:
if (!crossings.length) {
// If we have two operands, check their bounds to find cases where
// one path is fully contained in another. These cases cannot be
// simplified, we still need tracePaths() for them.
var ok = true;
if (paths2) {
for (var i1 = 0, l1 = paths1.length; i1 < l1 && ok; i1++) {
var bounds1 = paths1[i1].getBounds();
for (var i2 = 0, l2 = paths2.length; i2 < l2 && ok; i2++) {
var bounds2 = paths2[i2].getBounds();
// If either of the bounds fully contains the other,
// skip the simple approach and delegate to tracePaths()
ok = !bounds1._containsRectangle(bounds2) &&
!bounds2._containsRectangle(bounds1);
}
}
}
if (ok) {
paths = operator.unite || operator.exclude ? [_path1, _path2]
: operator.subtract ? [_path1]
// No result, but let's return an empty path to keep
// chainability and transfer styles to the result.
: operator.intersect ? [new Path(Item.NO_INSERT)]
: null;
}
}
if (!paths) {
// Collect all segments and monotonic curves
collect(paths1);
if (paths2)
collect(paths2);
// Propagate the winding contribution. Winding contribution of
// curves does not change between two crossings.
// First, propagate winding contributions for curve chains starting
// in all crossings:
for (var i = 0, l = crossings.length; i < l; i++) {
propagateWinding(crossings[i]._segment, _path1, _path2, curves,
operator);
}
for (var i = 0, l = segments.length; i < l; i++) {
var segment = segments[i],
inter = segment._intersection;
if (segment._winding == null) {
propagateWinding(segment, _path1, _path2, curves, operator);
}
// See if there are any valid segments that aren't part of
// overlaps. Use this information to determine how to deal with
// various edge-cases in tracePaths().
if (!(inter && inter._overlap)) {
var path = segment._path;
path._overlapsOnly = false;
// This is no overlap. If it is valid, take note that this
// path contains valid intersections other than overlaps.
if (operator[segment._winding])
path._validOverlapsOnly = false;
}
}
paths = tracePaths(segments, operator);
}
return createResult(CompoundPath, paths, true, path1, path2);
}
function computeOpenBoolean(path1, path2, operator) {
// Only support subtract and intersect operations between an open
// and a closed path.
if (!path2 || !operator.subtract && !operator.intersect) {
throw new Error('Boolean operations on open paths only support ' +
'subtraction and intersection with another path.');
}
var _path1 = preparePath(path1, false),
_path2 = preparePath(path2, false),
crossings = _path1.getCrossings(_path2),
sub = operator.subtract,
paths = [];
function addPath(path) {
// Simple see if the point halfway across the open path is inside
// path2, and include / exclude the path based on the operator.
if (_path2.contains(path.getPointAt(path.getLength() / 2)) ^ sub) {
paths.unshift(path);
return true;
}
}
// Now loop backwards through all crossings, split the path and check
// the new path that was split off for inclusion.
for (var i = crossings.length - 1; i >= 0; i--) {
var path = crossings[i].split();
if (path) {
// See if we can add the path, and if so, clear the first handle
// at the split, because it might have been a curve.
if (addPath(path))
path.getFirstSegment().setHandleIn(0, 0);
// Clear the other side of the split too, which is always the
// end of the remaining _path1.
_path1.getLastSegment().setHandleOut(0, 0);
}
}
// At the end, check what's left from our path after all the splitting.
addPath(_path1);
return createResult(Group, paths, false, path1, path2);
}
/*
* Creates linked lists between intersections through their _next and _prev
* properties.
*
* @private
*/
function linkIntersections(from, to) {
// Only create the link if it's not already in the existing chain, to
// avoid endless recursions. First walk to the beginning of the chain,
// and abort if we find `to`.
var prev = from;
while (prev) {
if (prev === to)
return;
prev = prev._previous;
}
// Now walk to the end of the existing chain to find an empty spot, but
// stop if we find `to`, to avoid adding it again.
while (from._next && from._next !== to)
from = from._next;
// If we're reached the end of the list, we can add it.
if (!from._next) {
// Go back to beginning of the other chain, and link the two up.
while (to._previous)
to = to._previous;
from._next = to;
to._previous = from;
}
}
/**
* Divides the path-items at the given locations.
*
* @param {CurveLocation[]} locations an array of the locations to split the
* path-item at.
* @param {Function} [include] a function that determines if dividing should
* happen at a given location.
* @return {CurveLocation[]} the locations at which the involved path-items
* were divided
* @private
*/
function divideLocations(locations, include) {
var results = include && [],
tMin = /*#=*/Numerical.CURVETIME_EPSILON,
tMax = 1 - tMin,
noHandles = false,
clearCurves = [],
prevCurve,
prevTime;
for (var i = locations.length - 1; i >= 0; i--) {
var loc = locations[i];
// Call include() before retrieving _curve, because it might cause a
// change in the cached location values (see #resolveCrossings()).
if (include) {
if (!include(loc))
continue;
results.unshift(loc);
}
var curve = loc._curve,
time = loc._time,
origTime = time,
segment;
if (curve !== prevCurve) {
// This is a new curve, update noHandles setting.
noHandles = !curve.hasHandles();
} else if (prevTime >= tMin && prevTime <= tMax ) {
// Scale parameter when we are splitting same curve multiple
// times, but only if splitting was done previously.
time /= prevTime;
}
if (time < tMin) {
segment = curve._segment1;
} else if (time > tMax) {
segment = curve._segment2;
} else {
// Split the curve at time, passing true for _setHandles to
// always set the handles on the sub-curves even if the original
// curve had no handles.
var newCurve = curve.divideAtTime(time, true);
// Keep track of curves without handles, so they can be cleared
// again at the end.
if (noHandles)
clearCurves.push(curve, newCurve);
segment = newCurve._segment1;
}
loc._setSegment(segment);
// Create links from the new segment to the intersection on the
// other curve, as well as from there back. If there are multiple
// intersections on the same segment, we create linked lists between
// the intersections through linkIntersections(), linking both ways.
var inter = segment._intersection,
dest = loc._intersection;
if (inter) {
linkIntersections(inter, dest);
// Each time we add a new link to the linked list, we need to
// add links from all the other entries to the new entry.
var other = inter;
while (other) {
linkIntersections(other._intersection, inter);
other = other._next;
}
} else {
segment._intersection = dest;
}
prevCurve = curve;
prevTime = origTime;
}
// Clear segment handles if they were part of a curve with no handles,
// once we are done with the entire curve.
for (var i = 0, l = clearCurves.length; i < l; i++) {
clearCurves[i].clearHandles();
}
return results || locations;
}
/**
* Returns the winding contribution number of the given point in respect
* to the shapes described by the passed curves.
*
* See #1073#issuecomment-226942348 and #1073#issuecomment-226946965 for a
* detailed description of the approach developed by @iconexperience to
* precisely determine the winding contribution in all known edge cases.
*
* @param {Point} point the location for which to determine the winding
* contribution
* @param {Curve[]} curves the curves that describe the shape against which
* to check, as returned by {@link Path#getCurves()} or
* {@link CompoundPath#getCurves()}
* @param {Number} [dir=0] the direction in which to determine the
* winding contribution, `0`: in x-direction, `1`: in y-direction
* @return {Object} an object containing the calculated winding number, as
* well as an indication whether the point was situated on the contour
* @private
*/
function getWinding(point, curves, dir) {
var epsilon = /*#=*/Numerical.WINDING_EPSILON,
// Determine the index of the abscissa and ordinate values in the
// curve values arrays, based on the direction:
ia = dir ? 1 : 0, // the abscissa index
io = dir ? 0 : 1, // the ordinate index
pv = [point.x, point.y],
pa = pv[ia], // the point's abscissa
po = pv[io], // the point's ordinate
paL = pa - epsilon,
paR = pa + epsilon,
windingL = 0,
windingR = 0,
pathWindingL = 0,
pathWindingR = 0,
onPathWinding = 0,
isOnPath = false,
vPrev,
vClose;
function addWinding(v) {
var o0 = v[io],
o3 = v[io + 6];
if (o0 > po && o3 > po || o0 < po && o3 < po) {
// If curve is outside the ordinates' range, no intersection
// with the ray is possible.
return v;
}
var a0 = v[ia],
a1 = v[ia + 2],
a2 = v[ia + 4],
a3 = v[ia + 6];
if (o0 === o3) {
// A horizontal curve is not necessarily between two non-
// horizontal curves. We have to take cases like these into
// account:
// +-----+
// +----+ |
// +-----+
if (a1 < paR && a3 > paL || a3 < paR && a1 > paL) {
isOnPath = true;
}
// If curve does not change in ordinate direction, windings will
// be added by adjacent curves.
return vPrev;
}
var roots = [],
a = po === o0 ? a0
: po === o3 ? a3
: paL > max(a0, a1, a2, a3) || paR < min(a0, a1, a2, a3)
? (a0 + a3) / 2
: Curve.solveCubic(v, io, po, roots, 0, 1) === 1
? Curve.getPoint(v, roots[0])[dir ? 'y' : 'x']
: (a0 + a3) / 2;
var winding = o0 > o3 ? 1 : -1,
windingPrev = vPrev[io] > vPrev[io + 6] ? 1 : -1,
a3Prev = vPrev[ia + 6];
if (po !== o0) {
// Standard case, curve is not crossed at its starting point.
if (a < paL) {
pathWindingL += winding;
} else if (a > paR) {
pathWindingR += winding;
} else {
isOnPath = true;
pathWindingL += winding;
pathWindingR += winding;
}
} else if (winding !== windingPrev) {
// Curve is crossed at starting point and winding changes from
// previous. Cancel winding contribution from previous curve.
if (a3Prev < paR) {
pathWindingL += winding;
}
if (a3Prev > paL) {
pathWindingR += winding;
}
} else if (a3Prev < paL && a > paL || a3Prev > paR && a < paR) {
// Point is on a horizontal curve between the previous non-
// horizontal and the current curve.
isOnPath = true;
if (a3Prev < paL) {
// left winding was added before, now add right winding.
pathWindingR += winding;
} else if (a3Prev > paR) {
// right winding was added before, not add left winding.
pathWindingL += winding;
}
}
return v;
}
function handleCurve(v) {
// Get the ordinates:
var o0 = v[io],
o1 = v[io + 2],
o2 = v[io + 4],
o3 = v[io + 6];
// Only handle curves that can cross the point's ordinate.
if (po <= max(o0, o1, o2, o3) && po >= min(o0, o1, o2, o3)) {
// Get the abscissas:
var a0 = v[ia],
a1 = v[ia + 2],
a2 = v[ia + 4],
a3 = v[ia + 6],
// Get monotone curves. If the curve is outside the point's
// abscissa, it can be treated as a monotone curve:
monoCurves = paL > max(a0, a1, a2, a3) ||
paR < min(a0, a1, a2, a3)
? [v] : Curve.getMonoCurves(v, dir);
for (var i = 0, l = monoCurves.length; i < l; i++) {
vPrev = addWinding(monoCurves[i]);
}
}
}
for (var i = 0, l = curves.length; i < l; i++) {
var curve = curves[i],
path = curve._path,
v = curve.getValues();
if (i === 0 || curves[i - 1]._path !== path) {
// We're on a new (sub-)path, so we need to determine values of
// the last non-horizontal curve on this path.
vPrev = null;
// If the path is not closed, connect the end points with a
// straight curve, just like how filling open paths works.
if (!path._closed) {
var p1 = path.getLastCurve().getPoint2(),
p2 = curve.getPoint1(),
x1 = p1._x, y1 = p1._y,
x2 = p2._x, y2 = p2._y;
vClose = [x1, y1, x1, y1, x2, y2, x2, y2];
// This closing curve is a potential candidate for the last
// non-horizontal curve.
if (vClose[io] !== vClose[io + 6]) {
vPrev = vClose;
}
}
if (!vPrev) {
// Walk backwards through list of the path's curves until we
// find one that is not horizontal.
// Fall-back to the first curve's values if none is found:
vPrev = v;
var prev = path.getLastCurve();
while (prev && prev !== curve) {
var v2 = prev.getValues();
if (v2[io] !== v2[io + 6]) {
vPrev = v2;
break;
}
prev = prev.getPrevious();
}
}
}
handleCurve(v);
if (i + 1 === l || curves[i + 1]._path !== path) {
// We're at the last curve of the current (sub-)path. If a
// closing curve was calculated at the beginning of it, handle
// it now to treat the path as closed:
if (vClose) {
handleCurve(vClose);
vClose = null;
}
if (!pathWindingL && !pathWindingR && isOnPath) {
// If the point is on the path and the windings canceled
// each other, we treat the point as if it was inside the
// path. A point inside a path has a winding of [+1,-1]
// for clockwise and [-1,+1] for counter-clockwise paths.
// If the ray is cast in y direction (dir == 1), the
// windings always have opposite sign.
var add = path.isClockwise() ^ dir ? 1 : -1;
windingL += add;
windingR -= add;
onPathWinding += add;
} else {
windingL += pathWindingL;
windingR += pathWindingR;
pathWindingL = pathWindingR = 0;
}
isOnPath = false;
}
}
if (!windingL && !windingR) {
windingL = windingR = onPathWinding;
}
windingL = windingL && (2 - abs(windingL) % 2);
windingR = windingR && (2 - abs(windingR) % 2);
// Return both the calculated winding contribution, and also detect if
// we are on the contour of the area by comparing windingL and windingR.
// This is required when handling unite operations, where a winding
// contribution of 2 is not part of the result unless it's the contour:
return {
winding: max(windingL, windingR),
contour: !windingL ^ !windingR
};
}
function propagateWinding(segment, path1, path2, curves, operator) {
// Here we try to determine the most likely winding number contribution
// for the curve-chain starting with this segment. Once we have enough
// confidence in the winding contribution, we can propagate it until the
// next intersection or end of a curve chain.
var chain = [],
start = segment,
totalLength = 0,
winding;
do {
var curve = segment.getCurve(),
length = curve.getLength();
chain.push({ segment: segment, curve: curve, length: length });
totalLength += length;
segment = segment.getNext();
} while (segment && !segment._intersection && segment !== start);
// Sample the point at a middle of the chain to get its winding:
var length = totalLength / 2;
for (var j = 0, l = chain.length; j < l; j++) {
var entry = chain[j],
curveLength = entry.length;
if (length <= curveLength) {
var curve = entry.curve,
path = curve._path,
parent = path._parent,
t = curve.getTimeAt(length),
pt = curve.getPointAtTime(t),
// Determine the direction in which to check the winding
// from the point (horizontal or vertical), based on the
// curve's direction at that point.
dir = abs(curve.getTangentAtTime(t).normalize().y) < 0.5
? 1 : 0;
if (parent instanceof CompoundPath)
path = parent;
// While subtracting, we need to omit this curve if it is
// contributing to the second operand and is outside the
// first operand.
winding = !(operator.subtract && path2 && (
path === path1 && path2._getWinding(pt, dir) ||
path === path2 && !path1._getWinding(pt, dir)))
? getWinding(pt, curves, dir)
: { winding: 0 };
break;
}
length -= curveLength;
}
// Now assign the winding to the entire curve chain.
for (var j = chain.length - 1; j >= 0; j--) {
var seg = chain[j].segment;
seg._winding = winding.winding;
seg._contour = winding.contour;
}
}
/**
* Private method to trace closed paths from a list of segments, according
* to a the their winding number contribution and a custom operator.
*
* @param {Segment[]} segments array of segments to trace closed paths
* @param {Function} operator the operator lookup table that receives as key
* the winding number contribution of a curve and returns a boolean
* value indicating whether the curve should be included in result
* @return {Path[]} the traced closed paths
*/
function tracePaths(segments, operator) {
var paths = [],
start,
otherStart;
function isValid(seg, excludeContour) {
// Unite operations need special handling of segments with a winding
// contribution of two (part of both involved areas) but which are
// also part of the contour of the result. Such segments are not
// chosen as the start of new paths and are not always counted as a
// valid next step, as controlled by the excludeContour parameter.
return !!(seg && !seg._visited && (!operator
|| operator[seg._winding]
|| !excludeContour && operator.unite && seg._contour));
}
function isStart(seg) {
return seg === start || seg === otherStart;
}
// If there are multiple possible intersections, find the one that's
// either connecting back to start or is not visited yet, and will be
// part of the boolean result:
function findBestIntersection(inter, exclude) {
if (!inter._next)
return inter;
while (inter) {
var seg = inter._segment,
nextSeg = seg.getNext(),
nextInter = nextSeg && nextSeg._intersection;
// See if this segment and the next are both not visited yet, or
// are bringing us back to the beginning, and are both valid,
// meaning they are part of the boolean result.
if (seg !== exclude && (isStart(seg) || isStart(nextSeg)
|| nextSeg && !seg._visited && !nextSeg._visited
// Self-intersections (!operator) don't need isValid() calls
&& (!operator || isValid(seg) && (isValid(nextSeg)
// If the next segment isn't valid, its intersection
// to which we may switch might be, so check that.
|| nextInter && isValid(nextInter._segment)))
))
return inter;
// If it's no match, continue with the next linked intersection.
inter = inter._next;
}
return null;
}
// Sort segments to give non-ambiguous segments the preference as
// starting points when tracing: prefer segments with no intersections
// over intersections, and process intersections with overlaps last:
segments.sort(function(seg1, seg2) {
var inter1 = seg1._intersection,
inter2 = seg2._intersection,
over1 = !!(inter1 && inter1._overlap),
over2 = !!(inter2 && inter2._overlap),
path1 = seg1._path,
path2 = seg2._path;
// Use bitwise-or to sort cases where only one segment is an overlap
// or intersection separately, and fall back on natural order within
// the path.
return over1 ^ over2
? over1 ? 1 : -1
: inter1 ^ inter2
? inter1 ? 1 : -1
// All other segments, also when comparing two overlaps
// or two intersections, are sorted by their order.
// Sort by path id to group segments on the same path.
: path1 !== path2
? path1._id - path2._id
: seg1._index - seg2._index;
});
for (var i = 0, l = segments.length; i < l; i++) {
var path = null,
finished = false,
seg = segments[i],
inter = seg._intersection,
handleIn;
// If all encountered segments in a path are overlaps (regardless if
// valid or not), we may have two fully overlapping paths that need
// special handling.
if (!seg._visited && seg._path._overlapsOnly) {
// TODO: Don't we also need to check for multiple overlaps?
var path1 = seg._path,
path2 = inter._segment._path,
segments1 = path1._segments,
segments2 = path2._segments;
if (Base.equals(segments1, segments2)) {
// Only add the path to the result if it has an area.
if ((operator.unite || operator.intersect)
&& path1.getArea()) {
paths.push(path1.clone(false));
}
// Now mark all involved segments as visited.
for (var j = 0, k = segments1.length; j < k; j++) {
segments1[j]._visited = segments2[j]._visited = true;
}
}
}
// Exclude three cases of invalid starting segments:
// - Do not start with invalid segments (segments that were already
// visited, or that are not going to be part of the result).
// - Do not start in segments that have an invalid winding
// contribution but are part of the contour (excludeContour=true).
// - Do not start in overlaps, unless all segments are part of
// overlaps, in which case we have no other choice.
if (!isValid(seg, true))
continue;
start = otherStart = null;
while (true) {
// For each segment we encounter, see if there are multiple
// intersections, and if so, pick the best one:
inter = inter && findBestIntersection(inter, seg) || inter;
// Get the reference to the other segment on the intersection.
var other = inter && inter._segment;
if (isStart(seg)) {
finished = true;
} else if (other) {
if (isStart(other)) {
finished = true;
// Switch the segment, but do not update handleIn
seg = other;
} else if (isValid(other, isValid(seg, true))) {
// Note that we pass `true` for excludeContour here if
// the current segment is valid and not a contour
// segment. See isValid()/getWinding() for explanations.
// We are at a crossing and the other segment is part of
// the boolean result, switch over.
// We need to mark segments as visited when processing
// intersection and subtraction.
if (operator
&& (operator.intersect || operator.subtract)) {
seg._visited = true;
}
seg = other;
}
}
// Bail out if we're done, or if we encounter an already visited
// next segment.
if (finished || seg._visited) {
// It doesn't hurt to set again to share some code.
seg._visited = true;
break;
}
// If there are only valid overlaps and we encounter and invalid
// segment, bail out immediately. Otherwise we need to be more
// tolerant due to complex situations of crossing,
// see findBestIntersection()
if (seg._path._validOverlapsOnly && !isValid(seg))
break;
if (!path) {
path = new Path(Item.NO_INSERT);
start = seg;
otherStart = other;
}
// Add the segment to the path, and mark it as visited.
// But first we need to look ahead. If we encounter the end of
// an open path, we need to treat it the same way as the fill of
// an open path would: Connecting the last and first segment
// with a straight line, ignoring the handles.
var next = seg.getNext();
path.add(new Segment(seg._point, handleIn,
next && seg._handleOut));
seg._visited = true;
// If this is the end of an open path, go back to its first
// segment but ignore its handleIn (see above for handleOut).
seg = next || seg._path.getFirstSegment();
handleIn = next && next._handleIn;
inter = seg._intersection;
}
if (finished) {
// Finish with closing the paths, and carrying over the last
// handleIn to the first segment.
path.firstSegment.setHandleIn(handleIn);
path.setClosed(true);
} else if (path) {
// Only complain about open paths if they would actually contain
// an area when closed. Open paths that can silently discarded
// can occur due to epsilons, e.g. when two segments are so
// close to each other that they are considered the same
// location, but the winding calculation still produces a valid
// number due to their slight differences producing a tiny area.
var area = path.getArea(true);
if (abs(area) >= /*#=*/Numerical.GEOMETRIC_EPSILON) {
// This path wasn't finished and is hence invalid.
// Report the error to the console for the time being.
console.error('Boolean operation resulted in open path',
'segments =', path._segments.length,
'length =', path.getLength(),
'area=', area);
}
path = null;
}
// Add the path to the result, while avoiding stray segments and
// paths that are incomplete or cover no area.
// As an optimization, only check paths with 8 or less segments
// for their area, and assume that they cover an area when more.
if (path && (path._segments.length > 8
|| !Numerical.isZero(path.getArea()))) {
paths.push(path);
path = null;
}
}
return paths;
}
return /** @lends PathItem# */{
/**
* Returns the winding contribution number of the given point in respect
* to this PathItem.
*
* @param {Point} point the location for which to determine the winding
* contribution
* @param {Number} [dir=0] the direction in which to determine the
* winding contribution, `0`: in x-direction, `1`: in y-direction
* @return {Number} the winding number
*/
_getWinding: function(point, dir) {
return getWinding(point, this.getCurves(), dir).winding;
},
/**
* {@grouptitle Boolean Path Operations}
*
* Merges the geometry of the specified path with this path's geometry
* and returns the result as a new path item.
*
* @param {PathItem} path the path to unite with
* @return {PathItem} the resulting path item
*/
unite: function(path) {
return computeBoolean(this, path, 'unite');
},
/**
* Intersects the geometry of the specified path with this path's
* geometry and returns the result as a new path item.
*
* @param {PathItem} path the path to intersect with
* @return {PathItem} the resulting path item
*/
intersect: function(path) {
return computeBoolean(this, path, 'intersect');
},
/**
* Subtracts the geometry of the specified path from this path's
* geometry and returns the result as a new path item.
*
* @param {PathItem} path the path to subtract
* @return {PathItem} the resulting path item
*/
subtract: function(path) {
return computeBoolean(this, path, 'subtract');
},
/**
* Excludes the intersection of the geometry of the specified path with
* this path's geometry and returns the result as a new path item.
*
* @param {PathItem} path the path to exclude the intersection of
* @return {PathItem} the resulting group item
*/
exclude: function(path) {
return computeBoolean(this, path, 'exclude');
},
/**
* Splits the geometry of this path along the geometry of the specified
* path returns the result as a new group item. This is equivalent to
* calling {@link #subtract(path)} and {@link #subtract(path)} and
* putting the results into a new group.
*
* @param {PathItem} path the path to divide by
* @return {Group} the resulting group item
*/
divide: function(path) {
return createResult(Group, [this.subtract(path),
this.intersect(path)], true, this, path);
},
/*
* Resolves all crossings of a path item by splitting the path or
* compound-path in each self-intersection and tracing the result.
* If possible, the existing path / compound-path is modified if the
* amount of resulting paths allows so, otherwise a new path /
* compound-path is created, replacing the current one.
*
* @return {PahtItem} the resulting path item
*/
resolveCrossings: function() {
var children = this._children,
// Support both path and compound-path items
paths = children || [this];
function hasOverlap(seg) {
var inter = seg && seg._intersection;
return inter && inter._overlap;
}
// First collect all overlaps and crossings while taking not of the
// existence of both.
var hasOverlaps = false,
hasCrossings = false,
intersections = this.getIntersections(null, function(inter) {
return inter._overlap && (hasOverlaps = true) ||
inter.isCrossing() && (hasCrossings = true);
});
intersections = CurveLocation.expand(intersections);
if (hasOverlaps) {
// First divide in all overlaps, and then remove the inside of
// the resulting overlap ranges.
var overlaps = divideLocations(intersections, function(inter) {
return inter._overlap;
});
for (var i = overlaps.length - 1; i >= 0; i--) {
var seg = overlaps[i]._segment,
prev = seg.getPrevious(),
next = seg.getNext();
if (seg._path && hasOverlap(prev) && hasOverlap(next)) {
seg.remove();
prev._handleOut._set(0, 0);
next._handleIn._set(0, 0);
var curve = prev.getCurve();
if (curve.isStraight() && curve.getLength() === 0) {
// Transfer handleIn when removing segment:
next._handleIn.set(prev._handleIn);
prev.remove();
}
}
}
}
if (hasCrossings) {
// Divide any remaining intersections that are still part of
// valid paths after the removal of overlaps.
divideLocations(intersections, hasOverlaps && function(inter) {
// Check both involved curves to see if they're still valid,
// meaning they are still part of their paths.
var curve1 = inter.getCurve(),
// Do not call getCurve() on the other intersection yet,
// as it too is in the intersections array and will be
// divided later. But do check if its current curve is
// still valid. This is required by some very rare edge
// cases, related to intersections on the same curve.
curve2 = inter._intersection._curve,
seg = inter._segment;
if (curve1 && curve2 && curve1._path && curve2._path) {
return true;
} else if (seg) {
// Remove all intersections that were involved in the
// handling of overlaps, to not confuse tracePaths().
seg._intersection = null;
}
});
// Finally resolve self-intersections through tracePaths()
paths = tracePaths(Base.each(paths, function(path) {
this.push.apply(this, path._segments);
}, []));
}
// Determine how to return the paths: First try to recycle the
// current path / compound-path, if the amount of paths does not
// require a conversion.
var length = paths.length,
item;
if (length > 1 && children) {
if (paths !== children) {
// TODO: Fix automatic child-orientation in CompoundPath,
// and stop passing true for _preserve.
this.setChildren(paths, true); // Preserve orientation
}
item = this;
} else if (length === 1 && !children) {
if (paths[0] !== this)
this.setSegments(paths[0].removeSegments());
item = this;
}
// Otherwise create a new compound-path and see if we can reduce it,
// and attempt to replace this item with it.
if (!item) {
item = new CompoundPath(Item.NO_INSERT);
item.addChildren(paths, true); // Preserve orientation
item = item.reduce();
item.copyAttributes(this);
this.replaceWith(item);
}
return item;
},
/**
* Fixes the orientation of the sub-paths of a compound-path, by first
* ordering them according to the area they cover, and then making sure
* that all sub-paths are of different winding direction than the first,
* biggest path, except for when individual sub-paths are disjoint,
* i.e. islands, which are reoriented so that:
*
* - The holes have opposite winding direction.
* - Islands have to have the same winding direction as the first child.
*
* @return {PahtItem} a reference to the item itself, reoriented
*/
reorient: function() {
var children = this._children;
if (children && children.length > 1) {
// First order the paths by their areas.
children = this.removeChildren().sort(function (a, b) {
return abs(b.getArea()) - abs(a.getArea());
});
var first = children[0],
paths = [first],
excluded = {},
isNonZero = this.getFillRule() === 'nonzero',
windings = isNonZero && Base.each(children, function(path) {
this.push(path.isClockwise() ? 1 : -1);
}, []);
// Walk through children, from largest to smallest.
// The first, largest child can be skipped.
for (var i = 1, l = children.length; i < l; i++) {
var path = children[i],
point = path.getInteriorPoint(),
isContained = false,
container = null,
exclude = false;
for (var j = i - 1; j >= 0 && !container; j--) {
// We run through the paths from largest to smallest,
// meaning that for any current path, all potentially
// containing paths have already been processed and
// their orientation has been fixed. Since we want to
// achieve alternating orientation of contained paths,
// all we have to do is to find one include path that
// contains the current path, and then set the
// orientation to the opposite of the containing path.
if (children[j].contains(point)) {
if (isNonZero && !isContained) {
windings[i] += windings[j];
// Remove path if rule is nonzero and winding
// of path and containing path is not zero.
if (windings[i] && windings[j]) {
exclude = excluded[i] = true;
break;
}
}
isContained = true;
// If the containing path is not excluded, we're
// done searching for the orientation defining path.
container = !excluded[j] && children[j];
}
}
if (!exclude) {
// Set to the opposite orientation of containing path,
// or the same orientation as the first path if the path
// is not contained in any other path.
path.setClockwise(container ? !container.isClockwise()
: first.isClockwise());
paths.push(path);
}
}
this.setChildren(paths, true); // Preserve orientation
}
return this;
},
/**
* Returns a point that is guaranteed to be inside the path.
*
* @bean
* @type Point
*/
getInteriorPoint: function() {
var bounds = this.getBounds(),
point = bounds.getCenter(true);
if (!this.contains(point)) {
// Since there is no guarantee that a poly-bezier path contains
// the center of its bounding rectangle, we shoot a ray in x
// direction and select a point between the first consecutive
// intersections of the ray on the left.
var curves = this.getCurves(),
y = point.y,
intercepts = [],
roots = [];
// Process all y-monotone curves that intersect the ray at y:
for (var i = 0, l = curves.length; i < l; i++) {
var v = curves[i].getValues(),
o0 = v[1],
o1 = v[3],
o2 = v[5],
o3 = v[7];
if (y >= min(o0, o1, o2, o3) && y <= max(o0, o1, o2, o3)) {
var monoCurves = Curve.getMonoCurves(v);
for (var j = 0, m = monoCurves.length; j < m; j++) {
var mv = monoCurves[j],
mo0 = mv[1],
mo3 = mv[7];
// Only handle curves that are not horizontal and
// that can cross the point's ordinate.
if ((mo0 !== mo3) &&
(y >= mo0 && y <= mo3 || y >= mo3 && y <= mo0)){
var x = y === mo0 ? mv[0]
: y === mo3 ? mv[6]
: Curve.solveCubic(mv, 1, y, roots, 0, 1)
=== 1
? Curve.getPoint(mv, roots[0]).x
: (mv[0] + mv[6]) / 2;
intercepts.push(x);
}
}
}
}
if (intercepts.length > 1) {
intercepts.sort(function(a, b) { return a - b; });
point.x = (intercepts[0] + intercepts[1]) / 2;
}
}
return point;
}
};
});