Boolean Operations.

This is probably a crude integration. Need to resolve some issues,
such as finding the right place for constants, private classes etc.
This commit is contained in:
hkrish 2013-04-29 21:36:12 +02:00
parent 0178386a7a
commit b4dd16bbfb

View file

@ -36,16 +36,16 @@ var PathItem = this.PathItem = Item.extend(/** @lends PathItem# */{
* // {x: 30, y: 25} and a size of {width: 50, height: 50}:
* var path = new Path.Rectangle(new Point(30, 25), new Size(50, 50));
* path.strokeColor = 'black';
*
*
* var secondPath = path.clone();
* var intersectionGroup = new Group();
*
*
* function onFrame(event) {
* secondPath.rotate(3);
*
*
* var intersections = path.getIntersections(secondPath);
* intersectionGroup.removeChildren();
*
*
* for (var i = 0; i < intersections.length; i++) {
* var intersectionPath = new Path.Circle({
* center: intersections[i].point,
@ -88,7 +88,7 @@ var PathItem = this.PathItem = Item.extend(/** @lends PathItem# */{
current = new Point(); // the current position
function getCoord(index, coord, update) {
var val = parseFloat(coords[index]);
var val = parseFloat(coords[index]);
if (relative)
val += current[coord];
if (update)
@ -174,6 +174,616 @@ var PathItem = this.PathItem = Item.extend(/** @lends PathItem# */{
break;
}
}
},
/**
* Calculates the Union of two paths
* Boolean API.
* @param {PathItem} path
* @return {CompoundPath} union of this & path
*/
unite: function( path ){
function UnionOp( lnk, isInsidePath1, isInsidePath2 ){
if( isInsidePath1 || isInsidePath2 ){ return false; }
return true;
}
return this._computeBoolean( this, path, UnionOp, 'unite' );
},
/**
* Calculates the Intersection between two paths
* Boolean API.
* @param {PathItem} path
* @return {CompoundPath} Intersection of this & path
*/
intersect: function( path ){
function IntersectionOp( lnk, isInsidePath1, isInsidePath2 ){
if( !isInsidePath1 && !isInsidePath2 ){
return false;
}
return true;
}
return this._computeBoolean( this, path, IntersectionOp, 'intersect' );
},
/**
* Calculates this <minus> path
* Boolean API.
* @param {PathItem} path
* @return {CompoundPath} this <minus> path
*/
subtract: function( path ){
function SubtractionOp( lnk, isInsidePath1, isInsidePath2 ){
var lnkid = lnk.id;
if( lnkid === 1 && isInsidePath2 ){
return false;
} else if( lnkid === 2 && !isInsidePath1 ){
return false;
}
return true;
}
return this._computeBoolean( this, path, SubtractionOp, 'subtract' );
},
// Some constants
// Need to find a home for these
// for _IntersectionID and _UNIQUE_ID, we could use the Base._uid? // tried; doesn't work.
_NORMAL_NODE: 1,
_INTERSECTION_NODE: 2,
_IntersectionID: 1,
_UNIQUE_ID: 1,
/**
* The datastructure for boolean computation:
* _Node - Connects 2 Links, represents a Segment
* _Link - Connects 2 Nodes, represents a Curve
* Graph - List of Links
*/
/**
* 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
*/
_Node: function( _point, _handleIn, _handleOut, _id, isBaseContour, _uid ){
var _NORMAL_NODE = 1;
var _INTERSECTION_NODE = 2;
this.id = _id;
this.isBaseContour = isBaseContour;
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 = _uid;
// 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.isBaseContourB = false;
// 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
if( !this.linkIn || !this.linkOut ){
throw { name: 'Boolean Error', message: 'No matching link found at ixID: ' +
this._intersectionID + " point: " + this.point.toString() };
}
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.isBaseContour = this.isBaseContour | this.isBaseContourB;
}
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
*/
_Link: function( _nodeIn, _nodeOut, _id, isBaseContour, _winding ) {
this.id = _id;
this.isBaseContour = isBaseContour;
this.winding = _winding;
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
*/
_makeGraph: function( path, id, isBaseContour ){
var graph = [];
var segs = path.segments, prevNode = null, firstNode = null, nuLink, nuNode,
winding = path.clockwise;
for( i = 0, l = segs.length; i < l; i++ ){
// var nuSeg = segs[i].clone();
var nuSeg = segs[i];
nuNode = new this._Node( nuSeg.point, nuSeg.handleIn, nuSeg.handleOut, id, isBaseContour, ++this._UNIQUE_ID );
if( prevNode ) {
nuLink = new this._Link( prevNode, nuNode, id, isBaseContour, winding );
graph.push( nuLink );
}
prevNode = nuNode;
if( !firstNode ){
firstNode = nuNode;
}
}
// the path is closed
nuLink = new this._Link( prevNode, firstNode, id, isBaseContour, winding );
graph.push( nuLink );
return graph;
},
/**
* To deal with a HTML canvas requirement where CompoundPaths' child contours
* has to be of different winding direction for correctly filling holes.
* But if some individual countours are disjoint, i.e. islands, we have to
* reorient them so that
* the holes have opposit winding direction ( already handled by paperjs )
* islands has to have same winding direction ( as the first child of the path )
*
* Does NOT handle selfIntersecting CompoundPaths.
*
* @param {CompoundPath} path - Input CompoundPath, Note: This path could be modified if need be.
* @return {boolean} the winding direction of the base contour( true if clockwise )
*/
_reorientCompoundPath: function( path ){
if( !(path instanceof CompoundPath) ){ return path.clockwise; }
var children = path.children, len = children.length, baseWinding;
var bounds = new Array( len );
var tmparray = new Array( len );
baseWinding = children[0].clockwise;
// Omit the first path
for (i = 0; i < len; i++) {
bounds[i] = children[i].bounds;
tmparray[i] = 0;
}
for (i = 0; i < len; i++) {
var p1 = children[i];
for (j = 0; j < len; j++) {
var p2 = children[j];
if( i !== j && bounds[i].contains( bounds[j] ) ){
tmparray[j]++;
}
}
}
for (i = 1; i < len; i++) {
if ( tmparray[i] % 2 === 0 ) {
children[i].clockwise = baseWinding;
}
}
return baseWinding;
},
_computeBoolean: function( _path1, _path2, operator, operatorName ){
this._IntersectionID = 1;
this._UNIQUE_ID = 1;
// We work on duplicate paths since the algorithm may modify the original paths
var path1 = _path1.clone();
var path2 = _path2.clone();
var i, j, k, l, lnk, crv, node, nuNode, leftLink, rightLink;
var path1Clockwise = true, path2Clockwise = true;
// If one of the operands is empty, resolve self-intersections on the second operand
var childCount1 = (_path1 instanceof CompoundPath)? _path1.children.length : _path1.curves.length;
var childCount2 = (_path2 instanceof CompoundPath)? _path2.children.length : _path2.curves.length;
var resolveSelfIntersections = !childCount1 | !childCount2;
// Reorient the compound paths, i.e. make all the islands wind in the same direction
// and holes in the opposit direction.
// Do this only if we are not resolving selfIntersections:
// Resolving self-intersections work on compound paths, but, we might get different results!
if( !resolveSelfIntersections ){
path1Clockwise = this._reorientCompoundPath( path1 );
path2Clockwise = this._reorientCompoundPath( path2 );
}
// Cache the bounding rectangle of paths
// so we can make the test for containment quite a bit faster
path1._bounds = (childCount1)? path1.bounds : null;
path2._bounds = (childCount2)? path2.bounds : null;
// 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, base;
if( path1 instanceof CompoundPath ){
path1Children = path1.children;
for (i = 0, base = true, l = path1Children.length; i < l; i++, base = false) {
path1Children[i].closed = true;
graph = graph.concat( this._makeGraph( path1Children[i], 1, base ));
}
} else {
path1.closed = true;
path1Clockwise = path1.clockwise;
graph = graph.concat( this._makeGraph( path1, 1, true ) );
}
// if operator is BooleanOps.Subtraction, then reverse path2
// so that the nodes and links will link correctly
var reverse = ( operatorName === 'subtract' )? true: false;
path2Clockwise = (reverse)? !path2Clockwise : path2Clockwise;
if( path2 instanceof CompoundPath ){
path2Children = path2.children;
for (i = 0, base = true, l = path2Children.length; i < l; i++, base = false) {
path2Children[i].closed = true;
if( reverse ){ path2Children[i].reverse(); }
graph = graph.concat( this._makeGraph( path2Children[i], 2, base ));
}
} else {
path2.closed = true;
if( reverse ){ path2.reverse(); }
path2Clockwise = path2.clockwise;
graph = graph.concat( this._makeGraph( path2, 2, true ) );
}
// 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
*/
var ix, loc, loc2, ixCount = 0;
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( !resolveSelfIntersections && graph[j].id === graph[i].id ){ continue; }
var c2 = graph[j].getCurve();
var v2 = c2.getValues();
loc = [];
Curve.getIntersections( v1, v2, c1, loc );
if( loc.length ){
for (k = 0, l=loc.length; k<l; k++) {
// Ignore segment overlaps if both curve are part of same contour
// This is a degenerate case while resolving self-intersections,
// after paperjs rev#8d35d92
if( graph[j].id === graph[i].id &&
( loc[k].parameter === 0.0 || loc[k].parameter === 1.0 )) {
continue;
}
graph[i].intersections.push( loc[k] );
loc2 = new CurveLocation( c2, null, loc[k].point );
loc2._id = loc[k]._id;
graph[j].intersections.push( loc2 );
loc[k]._ixpair = loc2;
loc2._ixpair = loc[k];
++ixCount;
}
}
}
}
/*
* Avoid duplicate intersections when a curve that belongs to one contour
* passes through a segment on another contour
*/
len = graph.length;
while( len-- ){
ix = graph[len].intersections;
for (i =0, l=ix.length; i<l; i++) {
// In case of an over lap over the first segment on a link we
// look for duplicates and mark them INVALID
loc = ix[i];
if ( loc.parameter === 0.0 ){
j = graph.length;
while( j-- ) {
var ix2 = graph[j].intersections;
k = ix2.length;
while ( k-- ) {
loc2 = ix2[k];
if( !loc2.INVALID && loc._id !== loc2._id && loc2.parameter !== 1.0 &&
loc2.point.equals( loc.point ) ) {
loc2.INVALID = loc2._ixpair.INVALID = true;
}
}
}
} // if( loc.parameter === 0.0 ) {
}
}
/*
* 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.
*/
var ixPoint, ixHandleI, ixHandleOut, param, isLinear, parts, left, right;
// variable names are (sort of) acronyms of what thay are relative to the link
// niho - link.NodeInHandleOut, for example.
var values, nix, niy,nox, noy, niho, nohi, nihox, nihoy, nohix, nohiy;
for ( i = graph.length - 1; i >= 0; i--) {
if( graph[i].intersections.length ){
ix = graph[i].intersections;
// Sort the intersections if there is more than one
if( graph[i].intersections.length > 1 ){ ix.sort( ixSort ); }
// Remove the graph link, this link has to be split and replaced with the splits
lnk = graph.splice( i, 1 )[0];
nix = lnk.nodeIn.point.x; niy = lnk.nodeIn.point.y;
nox = lnk.nodeOut.point.x; noy = lnk.nodeOut.point.y;
niho = lnk.nodeIn.handleOut; nohi = lnk.nodeOut.handleIn;
nihox = nihoy = nohix = nohiy = 0;
isLinear = true;
if( niho ){ nihox = niho.x; nihoy = niho.y; isLinear = false; }
if( nohi ){ nohix = nohi.x; nohiy = nohi.y; isLinear = false; }
values = [ nix, niy, nihox + nix, nihoy + niy,
nohix + nox, nohiy + noy, nox, noy ];
for (j =0, l=ix.length; j<l && lnk; j++) {
if( ix[j].INVALID ){ continue; }
param = 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 = this._INTERSECTION_NODE;
nuNode._intersectionID = ix[j]._id;
if( param === 1.0 ){
leftLink = null;
rightLink = lnk;
} else {
leftLink = lnk;
rightLink = null;
}
} else {
parts = Curve.subdivide(values, param);
left = parts[0];
right = parts[1];
// Make new link and convert handles from absolute to relative
ixPoint = new Point( left[6], left[7] );
if( !isLinear ){
ixHandleIn = new Point(left[4] - ixPoint.x, left[5] - ixPoint.y);
ixHandleOut = new Point(right[2] - ixPoint.x, right[3] - ixPoint.y);
} else {
ixHandleIn = ixHandleOut = null;
right[2] = right[0];
right[3] = right[1];
}
nuNode = new this._Node( ixPoint, ixHandleIn, ixHandleOut, lnk.id, lnk.isBaseContour, ++this._UNIQUE_ID );
nuNode.type = this._INTERSECTION_NODE;
nuNode._intersectionID = ix[j]._id;
// clear the cached Segment on original end nodes and Update their handles
lnk.nodeIn._segment = null;
lnk.nodeOut._segment = null;
if( !isLinear ){
var tmppnt = lnk.nodeIn.point;
lnk.nodeIn.handleOut = new Point( left[2] - tmppnt.x, left[3] - tmppnt.y );
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 this._Link( lnk.nodeIn, nuNode, lnk.id, lnk.isBaseContour, lnk.winding );
rightLink = new this._Link( nuNode, lnk.nodeOut, lnk.id, lnk.isBaseContour, lnk.winding );
values = right;
}
// 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;
// Interpolate the rest of the parameters
if( lnk ) {
var one_minus_param = (1.0 - param);
for (k =j + 1, l=ix.length; k<l; k++) {
ix[k]._parameter = ( ix[k].parameter - param ) / one_minus_param;
}
}
}
// 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. outside (normal case)
*
* Take a test function "operator" which will discard links
* according to the above
* * Union -> discard cases 1 and 2
* * Intersection -> discard case 3
* * Path1-Path2 -> discard cases 2, 3[Path2]
*/
// step 1: discard invalid links according to the boolean operator
for ( i = graph.length - 1; i >= 0; i-- ) {
var insidePath1 = false, insidePath2 = false, contains;
lnk = graph[i];
// if( lnk.SKIP_OPERATOR ) { continue; }
if( !lnk.INVALID ) {
crv = lnk.getCurve();
// var midPoint = new Point(lnk.nodeIn.point);
var midPoint = crv.getPoint( 0.5 );
// If on a base curve, consider points on the curve and inside,
// if not —for example a hole, points on the curve falls outside
if( lnk.id !== 1 ){
contains = path1.contains( midPoint );
insidePath1 = (lnk.winding === path1Clockwise)? contains :
contains && !this._testOnContour( path1, midPoint );
}
if( lnk.id !== 2 ){
contains = path2.contains( midPoint );
insidePath2 = (lnk.winding === path2Clockwise)? contains :
contains && !this._testOnContour( path2, midPoint );
}
}
if( lnk.INVALID || !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 === this._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 = this._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
// this node becomes a four-way node, i.e. this node will have two sets of linkIns and linkOuts each.
// In this sense this is a multi-graph!
otherNode.idB = node.id;
otherNode.isBaseContourB = node.isBaseContour;
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;
}
}
}
}
window.g = graph;
// Final step: Retrieve the resulting paths from the graph
var boolResult = new CompoundPath();
var firstNode = true, nextNode, foundBasePath = false;
while( firstNode ){
firstNode = nextNode = null;
len = graph.length;
while( len-- ){
lnk = graph[len];
if( !lnk.INVALID && !lnk.nodeIn.visited && !firstNode ){
if( !foundBasePath && lnk.isBaseContour ){
firstNode = lnk.nodeIn;
foundBasePath = true;
break;
} else if(foundBasePath){
firstNode = lnk.nodeIn;
break;
}
}
}
if( firstNode ){
var path = new Path();
path.add( firstNode.getSegment( true ) );
firstNode.visited = true;
nextNode = firstNode.linkOut.nodeOut;
var linkCount = graph.length + 1;
while( firstNode.uniqueID !== nextNode.uniqueID && linkCount-- ){
path.add( nextNode.getSegment( true ) );
nextNode.visited = true;
if( !nextNode.linkOut ){
throw { name: 'Boolean Error', message: 'No link found at node id: ' + nextNode.id };
}
nextNode = nextNode.linkOut.nodeOut;
}
path.closed = true;
if( path.segments.length > 1 && linkCount >= 0 ){ // avoid stray segments and incomplete paths
if( path.segments.length > 2 || !path.curves[0].isLinear() ){
boolResult.addChild( path );
}
}
}
}
boolResult = boolResult.reduce();
// Remove the paths we duplicated
path1.remove();
path2.remove();
// I think, we're done.
return boolResult;
},
/**
* _testOnContour
* Tests if the point lies on the countour of a path
*/
_testOnContour: function( path, point ){
var res = 0;
var crv = path.getCurves();
var i = 0;
var bounds = path._bounds;
if( bounds && bounds.contains( point ) ){
for( i = 0; i < crv.length && !res; i++ ){
var crvi = crv[i];
if( crvi.bounds.contains( point ) && crvi.getParameterOf( point ) ){
res = 1;
}
}
}
return res;
}
/**
@ -289,16 +899,16 @@ var PathItem = this.PathItem = Item.extend(/** @lends PathItem# */{
* if (myPath) {
* myPath.remove();
* }
*
*
* // Create a new path and add a segment point to it
* // at {x: 150, y: 150):
* myPath = new Path();
* myPath.add(150, 150);
*
*
* // Draw a curve through the position of the mouse to 'toPoint'
* var toPoint = new Point(350, 150);
* myPath.curveTo(event.point, toPoint);
*
*
* // Select the path, so we can see its segments:
* myPath.selected = true;
* }