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paper.js/Boolean.js

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/*!
*
* Vector boolean operations on paperjs objects
* This is mostly written for clarity (I hope it is clear) and compatibility,
* not optimised for performance, and has to be tested heavily for stability.
* (Looking up to Java's Area path boolean algorithms for stability,
* but the code is too complex —mainly because the operations are stored and
* enumerable, such as quadraticCurveTo, cubicCurveTo etc.; and is largely
* undocumented to directly adapt from)
*
* Supported
* - paperjs Path objects
* - Boolean Union operations
* - Boolean Intersection operations
* - handles path complexity quite nicely
*
* Not supported yet ( which I would like to see supported )
* - Compound Paths as input ( however compound paths are correctly handled in the output )
* - Self-intersecting Paths
* - Boolean Subtraction operation ( depends on compound paths as input )
* - Paths are clones of each other that ovelap exactly on top of each other!
*
* In the Not-supported-yet list, the first three can be easily implemented,
* as for the last point, I need help! Thanks! :)
*
* ------
* Harikrishnan Gopalakrishnan
* http://hkrish.com/playground/paperbool.html
*
* ------
* Paperjs
* Copyright (c) 2011, Juerg Lehni & Jonathan Puckey
* http://paperjs.org/license/
*
*/
/**
* BooleanOps defines the boolean operator functions to use.
* A boolean operator is a function f( link:Link, isInsidePath1:Boolean, isInsidePath2:Boolean ) :
* should return a Boolean value indicating whether to keep the link or not.
* return true - keep the path
* return false - discard the path
*/
var BooleanOps = {
Union: function( lnk, isInsidePath1, isInsidePath2 ){
if( isInsidePath1 || isInsidePath2 ){
return false;
}
return true;
},
Intersection: function( lnk, isInsidePath1, isInsidePath2 ){
if( !isInsidePath1 && !isInsidePath2 ){
return false;
}
return true;
}
};
/**
* The datastructure for boolean computation:
* Graph - List of Links
* Link - Connects 2 Nodes, represents a Curve
* Node - Connects 2 Links, represents a Segment
*/
var NORMAL_NODE = 1;
var INTERSECTION_NODE = 2;
var IntersectionID = 1;
var UNIQUE_ID = 1;
/**
* Nodes in the graph are analogous to Segment objects
* with additional linkage information to track intersections etc.
* (enough to do a complete graph traversal)
* @param {Point} _point
* @param {Point} _handleIn
* @param {Point} _handleOut
* @param {Any} _id
*/
function Node( _point, _handleIn, _handleOut, _id, _childId ){
this.id = _id;
this.childId = _childId;
this.type = NORMAL_NODE;
this.point = _point;
this.handleIn = _handleIn; // handleIn
this.handleOut = _handleOut; // handleOut
this.linkIn = null; // aka linkIn
this.linkOut = null; // linkOut
this.uniqueID = ++UNIQUE_ID;
// In case of an intersection this will be a merged node.
// And we need space to save the "other Node's" parameters before merging.
this.idB = null;
// this.pointB = this.point; // point should be the same
this.handleBIn = null;
this.handleBOut = null;
this.linkBIn = null;
this.linkBOut = null;
this._segment = null;
this.getSegment = function( recalculate ){
if( this.type === INTERSECTION_NODE && recalculate ){
// point this.linkIn and this.linkOut to those active ones
// also point this.handleIn and this.handleOut to correct in and out handles
// If a link is null, make sure the corresponding handle is also null
this.handleIn = (this.linkIn)? this.handleIn : null;
this.handleOut = (this.linkOut)? this.handleOut : null;
this.handleBIn = (this.linkBIn)? this.handleBIn : null;
this.handleBOut = (this.linkBOut)? this.handleBOut : null;
// Select the valid links
this.linkIn = this.linkIn || this.linkBIn; // linkIn
this.linkOut = this.linkOut || this.linkBOut; // linkOut
// Also update the references in links to point to "this" Node
this.linkIn.nodeOut = this; // linkIn.nodeEnd
this.linkOut.nodeIn = this; // linkOut.nodeStart
this.handleIn = this.handleIn || this.handleBIn;
this.handleOut = this.handleOut || this.handleBOut;
}
this._segment = this._segment || new Segment( this.point, this.handleIn, this.handleOut );
return this._segment;
};
}
/**
* Links in the graph are analogous to CUrve objects
* @param {Node} _nodeIn
* @param {Node} _nodeOut
* @param {Any} _id
*/
function Link( _nodeIn, _nodeOut, _id, _childId ) {
this.id = _id;
this.childId = _childId;
this.nodeIn = _nodeIn; // nodeStart
this.nodeOut = _nodeOut; // nodeEnd
this.nodeIn.linkOut = this; // nodeStart.linkOut
this.nodeOut.linkIn = this; // nodeEnd.linkIn
this._curve = null;
this.intersections = [];
// for reusing the paperjs function we need to (temperorily) build a Curve object from this Link
// for performance reasons we cache it.
this.getCurve = function() {
this._curve = this._curve || new Curve( this.nodeIn.getSegment(), this.nodeOut.getSegment() );
return this._curve;
};
}
/**
* makes a graph. Only works on paths, for compound paths we need to
* make graphs for each of the child paths and merge them.
* @param {Path} path
* @param {Integer} id
* @return {Array} Links
*/
function makeGraph( path, id, childId ){
var graph = [];
var segs = path.segments, prevNode = null, firstNode = null, nuLink, nuNode;
for( i = 0, l = segs.length; i < l; i++ ){
var nuSeg = segs[i].clone();
nuNode = new Node( nuSeg.point, nuSeg.handleIn, nuSeg.handleOut, id, childId );
if( prevNode ) {
nuLink = new Link( prevNode, nuNode, id, childId );
graph.push( nuLink );
}
prevNode = nuNode;
if( !firstNode ){
firstNode = nuNode;
}
}
// the path is closed
nuLink = new Link( prevNode, firstNode, id, childId );
graph.push( nuLink );
return graph;
}
/**
* Calculates the Union of two paths
* Boolean API.
* @param {Path} path1
* @param {Path} path2
* @return {CompoundPath} union of path1 & path2
*/
function boolUnion( path1, path2 ){
return computeBoolean( path1, path2, BooleanOps.Union );
}
/**
* Calculates the Intersection between two paths
* Boolean API.
* @param {Path} path1
* @param {Path} path2
* @return {CompoundPath} Intersection of path1 & path2
*/
function boolIntersection( path1, path2 ){
return computeBoolean( path1, path2, BooleanOps.Intersection );
}
/**
* Actual function that computes the boolean
* @param {Path} _path1 (cannot be self-intersecting at the moment)
* @param {Path} _path2 (cannot be self-intersecting at the moment)
* @param {BooleanOps type} operator
* @return {CompoundPath} boolean result
*/
function computeBoolean( _path1, _path2, operator ){
IntersectionID = 1;
UNIQUE_ID = 1;
// The boolean operation may modify the original paths
var path1 = _path1.clone();
var path2 = _path2.clone();
// if( !path1.clockwise ){ path1.reverse(); }
// if( !path2.clockwise ){ path2.reverse(); }
//
var i, j, k, l, lnk, crv, node, nuNode, leftLink, rightLink;
// Prepare the graphs. Graphs are list of Links that retains
// full connectivity information. The order of links in a graph is not important
// That allows us to sort and merge graphs and 'splice' links with their splits easily.
// Also, this is the place to resolve self-intersecting paths
var graph = [], path1Children, path2Children;
if( path1 instanceof CompoundPath ){
path1Children = path1.children;
for (i = 0, l = path1Children.length; i < l; i++) {
path1Children[i].closed = true;
graph = graph.concat( makeGraph( path1Children[i], 1, i + 1 ) );
}
} else {
path1.closed = true;
path1.clockwise = true;
graph = graph.concat( makeGraph( path1, 1, 1 ) );
}
// TODO: if operator === BooleanOps.subtract, then for path2, clockwise must be false
if( path2 instanceof CompoundPath ){
path2Children = path2.children;
for (i = 0, l = path2Children.length; i < l; i++) {
path2Children[i].closed = true;
graph = graph.concat( makeGraph( path2Children[i], 2, i + 1 ) );
}
} else {
path2.closed = true;
path2.clockwise = true;
graph = graph.concat( makeGraph( path2, 2, 1 ) );
}
window.g = graph
// Sort function to sort intersections according to the 'parameter'(t) in a link (curve)
function ixSort( a, b ){ return a._parameter - b._parameter; }
/*
* Pass 1:
* Calculate the intersections for all graphs
* TODO: test if this takes are of self intersecting paths - NO
* And since it doesn't take self-intersecting curves, we need to only calculate
* intersections if the "id" of the links differ.
* The rest of the algorithm can easily be modified to resolve self-intersections
*/
for ( i = graph.length - 1; i >= 0; i--) {
var c1 = graph[i].getCurve();
var v1 = c1.getValues();
for ( j = i -1; j >= 0; j-- ) {
if( graph[j].id === graph[i].id ){ continue; }
var c2 = graph[j].getCurve();
var v2 = c2.getValues();
var loc = [];
Curve._addIntersections( v1, v2, loc );
if( loc.length ){
for (k = 0, l=loc.length; k<l; k++) {
var loc1 = loc[k].clone();
loc1._intersectionID = loc[k]._intersectionID;
loc1._parameter = c1.getNearestLocation( loc[k] ).parameter; // For sorting on curve1
graph[i].intersections.push( loc1 );
var loc2 = loc[k].clone();
loc2._intersectionID = loc[k]._intersectionID;
loc2._parameter = c2.getNearestLocation( loc[k] ).parameter; // For sorting on curve2
graph[j].intersections.push( loc2 );
}
}
}
}
/*
* Pass 2:
* Walk the graph, sort the intersections on each individual link.
* for each link that intersects with another one, replace it with new split links.
*/
for ( i = graph.length - 1; i >= 0; i--) {
if( graph[i].intersections.length ){
var ix = graph[i].intersections;
ix.sort( ixSort );
// Remove the graph link, this link has to be split and replaced with the splits
lnk = graph.splice( i, 1 )[0];
for (j =0, l=ix.length; j<l && lnk; j++) {
var splitLinks = [];
crv = lnk.getCurve();
// We need to recalculate parameter after each curve split
// This operation (except for recalculating the curve parameter),
// is fairly similar to Curve.split method, except that it operates on Node and Link objects.
var param = crv.getNearestLocation( ix[j] ).parameter;
if( param === 0.0 || param === 1.0) {
// Intersection falls on an existing node
// there is no need to split the link
nuNode = ( param === 0.0 )? lnk.nodeIn : lnk.nodeOut;
nuNode.type = INTERSECTION_NODE;
nuNode._intersectionID = ix[j]._intersectionID;
if( param === 1.0 ){
leftLink = null;
rightLink = lnk;
} else {
leftLink = lnk;
rightLink = null;
}
} else {
var parts = Curve.subdivide(crv.getValues(), param);
var left = parts[0];
var right = parts[1];
// Make new link and convert handles from absolute to relative
// TODO: check if link is linear and set handles to null
var ixPoint = new Point( left[6], left[7] );
nuNode = new Node( ixPoint, new Point(left[4] - ixPoint.x, left[5] - ixPoint.y),
new Point(right[2] - ixPoint.x, right[3] - ixPoint.y), lnk.id, lnk.childId );
nuNode.type = INTERSECTION_NODE;
nuNode._intersectionID = ix[j]._intersectionID;
// clear the cached Segment on original end nodes and Update their handles
lnk.nodeIn._segment = null;
var tmppnt = lnk.nodeIn.point;
lnk.nodeIn.handleOut = new Point( left[2] - tmppnt.x, left[3] - tmppnt.y );
lnk.nodeOut._segment = null;
tmppnt = lnk.nodeOut.point;
lnk.nodeOut.handleIn = new Point( right[4] - tmppnt.x, right[5] - tmppnt.y );
// Make new links after the split
leftLink = new Link( lnk.nodeIn, nuNode, lnk.id, lnk.childId);
rightLink = new Link( nuNode, lnk.nodeOut, lnk.id, lnk.childId );
}
// Add the first split link back to the graph, since we sorted the intersections
// already, this link should contain no more intersections to the left.
if( leftLink ){
graph.splice( i, 0, leftLink );
}
// continue with the second split link, to see if
// there are more intersections to deal with
lnk = rightLink;
}
// Add the last split link back to the graph
if( lnk ){
graph.splice( i, 0, lnk );
}
}
}
/**
* Pass 3:
* Merge matching intersection Node Pairs (type is INTERSECTION_NODE &&
* a._intersectionID == b._intersectionID )
*
* Mark each Link(Curve) according to whether it is
* case 1. inside Path1 ( and only Path1 )
* 2. inside Path2 ( and only Path2 )
* 3. inside both ( fully contained holes that completely overlap )
* 4. outside (normal case)
*
* Take a test function "operator" which will discard links
* according to the above
* * Union -> discard cases 1, 2 and 3
* * Intersection -> discard case 4
* * Path1-Path2 -> discard cases 2, 3[Path1] and 4[Path2]‡
* * Path2-Path1 -> discard cases 1, 3[Path2] and 4[Path1]
* ‡ - 4[Path2] means curves of case 4 that belongs to Path2
*/
// step 1: discard invalid links according to the boolean operator
for ( i = graph.length - 1; i >= 0; i--) {
lnk = graph[i];
crv = lnk.getCurve();
// var midPoint = new Point(lnk.nodeIn.point);
var midPoint = crv.getPoint( 0.5 );
var insidePath1 = (lnk.id === 1 )? false : path1.contains( midPoint );
var insidePath2 = (lnk.id === 2 )? false : path2.contains( midPoint );
if( !operator( lnk, insidePath1, insidePath2 ) ){
// lnk = graph.splice( i, 1 )[0];
lnk.INVALID = true;
lnk.nodeIn.linkOut = null;
lnk.nodeOut.linkIn = null;
}
}
// step 2: Match nodes according to their _intersectionID and merge them together
var len = graph.length;
while( len-- ){
node = graph[len].nodeIn;
if( node.type === INTERSECTION_NODE ){
var otherNode = null;
for (i = len - 1; i >= 0; i--) {
var tmpnode = graph[i].nodeIn;
if( tmpnode._intersectionID === node._intersectionID &&
tmpnode.uniqueID !== node.uniqueID ) {
otherNode = tmpnode;
break;
}
}
if( otherNode ) {
//Check if it is a self-intersecting Node
if( node.id === otherNode.id ){
// Swap the outgoing links, this will resolve a knot and create two paths,
// the portion of the original path on one side of a self crossing is counter-clockwise,
// so one of the resulting paths will also be counter-clockwise
var tmp = otherNode.linkOut;
otherNode.linkOut = node.linkOut;
node.linkOut = tmp;
tmp = otherNode.handleOut;
otherNode.handleOut = node.handleOut;
node.handleOut = tmp;
node.type = otherNode.type = NORMAL_NODE;
node._intersectionID = null;
node._segment = otherNode._segment = null;
} else {
// Merge the nodes together, by adding this node's information to the other node
otherNode.idB = node.id;
otherNode.handleBIn = node.handleIn;
otherNode.handleBOut = node.handleOut;
otherNode.linkBIn = node.linkIn;
otherNode.linkBOut = node.linkOut;
otherNode._segment = null;
if( node.linkIn ){ node.linkIn.nodeOut = otherNode; }
if( node.linkOut ){ node.linkOut.nodeIn = otherNode; }
// Clear this node's intersectionID, so that we won't iterate over it again
node._intersectionID = null;
}
}
}
}
// Final step: Retrieve the resulting paths from the graph
// TODO: start from a path where childId === 1
var boolResult = new CompoundPath();
var firstNode = true, nextNode, foundBasePath = false;
while( firstNode ){
firstNode = nextNode = null;
len = graph.length;
while( len-- ){
if( !graph[len].INVALID && !graph[len].nodeIn.visited && !firstNode ){
if( !foundBasePath && graph[len].childId === 1 ){
firstNode = graph[len].nodeIn;
foundBasePath = true;
break;
} else if(foundBasePath){
firstNode = graph[len].nodeIn;
break;
}
}
}
if( firstNode ){
var path = new Path();
path.add( firstNode.getSegment( true ) );
firstNode.visited = true;
nextNode = firstNode.linkOut.nodeOut;
while( firstNode.uniqueID !== nextNode.uniqueID ){
path.add( nextNode.getSegment( true ) );
nextNode.visited = true;
nextNode = nextNode.linkOut.nodeOut;
}
path.closed = true;
// path.clockwise = true;
boolResult.addChild( path );
}
}
boolResult = boolResult.reduce();
return boolResult;
}
function markPoint( pnt, t, c, tc, remove ) {
if( !pnt ) return;
c = c || '#000';
if( remove === undefined ){ remove = true; }
var cir = new Path.Circle( pnt, 2 );
cir.style.fillColor = c;
cir.style.strokeColor = tc;
if( t !== undefined || t !== null ){
var text = new PointText( pnt.add([0, -3]) );
text.justification = 'center';
text.fillColor = c;
text.content = t;
if( remove ){
text.removeOnMove();
}
}
if( remove ) {
cir.removeOnMove();
}
}
// Same as the paperjs' Numerical class,
// added here because I can't access the original from this scope
var Numerical = {
TOLERANCE : 10e-6
};
// paperjs' Curve._addIntersections modified to return just intersection Point with a
// unique id.
paper.Curve._addIntersections = function(v1, v2, locations) {
var bounds1 = Curve.getBounds(v1),
bounds2 = Curve.getBounds(v2);
if (bounds1.touches(bounds2)) {
// See if both curves are flat enough to be treated as lines.
if (Curve.isFlatEnough(v1, /*#=*/ Numerical.TOLERANCE) &&
Curve.isFlatEnough(v2, /*#=*/ Numerical.TOLERANCE)) {
// See if the parametric equations of the lines interesct.
var point = new Line(v1[0], v1[1], v1[6], v1[7], false)
.intersect(new Line(v2[0], v2[1], v2[6], v2[7], false),
// Filter out beginnings of the curves, to avoid
// duplicate solutions where curves join.
true, false);
if (point){
point._intersectionID = IntersectionID++;
locations.push( point );
}
} else {
// Subdivide both curves, and see if they intersect.
var v1s = Curve.subdivide(v1),
v2s = Curve.subdivide(v2);
for (var i = 0; i < 2; i++)
for (var j = 0; j < 2; j++)
this._addIntersections(v1s[i], v2s[j], locations);
}
}
return locations;
};
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