Merge branch 'triangulation' of https://github.com/jahting/three.js into dev

src/extras/FontUtils.js

@@ -424,11 +424,13 @@ THREE.FontUtils.generateShapes = function( text, parameters ) {
 
 		for ( p = 0; p < n; p++ ) {
 
-			if( (p === u) || (p === v) || (p === w) ) continue;
-
 			px = contour[ verts[ p ] ].x
 			py = contour[ verts[ p ] ].y
 
+			if ( ( (px === ax) && (py === ay) ) ||
+				 ( (px === bx) && (py === by) ) ||
+				 ( (px === cx) && (py === cy) ) )	continue;
+
 			apx = px - ax;  apy = py - ay;
 			bpx = px - bx;  bpy = py - by;
 			cpx = px - cx;  cpy = py - cy;

src/extras/core/Shape.js

@@ -316,7 +316,7 @@ THREE.Shape.Utils = {
 
 	},
 
-	triangulateShape: function ( contour, holes ) {
+	triangulateShape_OLD: function ( contour, holes ) {
 
 		var shapeWithoutHoles = THREE.Shape.Utils.removeHoles( contour, holes );
 
@@ -400,6 +400,374 @@ THREE.Shape.Utils = {
 
 	}, // end triangulate shapes
 
+	/*
+	 *		Modified Triangulation.
+	 *
+	 *		basically rewritten 'removeHoles':
+	 *		- doesn't cut out an area anymore, but slices from shape to hole by adding two edges
+	 *		  - ATTENTION: this requires small change to 'THREE.FontUtils.snip' to account for duplicate coordinates
+	 *		- checks whether such a cut line lies inside the shape doesn't intersect any other edge (shape and holes)
+	 */
+	triangulateShape: function ( contour, holes ) {
+
+		function point_in_segment_2D( inSegPt1, inSegPt2, inOtherPt ) {
+			// inOtherPt needs to be colinear to the inSegment
+			if ( inSegPt1.x != inSegPt2.x ) {
+				if ( inSegPt1.x < inSegPt2.x ) {
+					return	( ( inSegPt1.x <= inOtherPt.x ) && ( inOtherPt.x <= inSegPt2.x ) );
+				} else {
+					return	( ( inSegPt2.x <= inOtherPt.x ) && ( inOtherPt.x <= inSegPt1.x ) );
+				}
+			} else {
+				if ( inSegPt1.y < inSegPt2.y ) {
+					return	( ( inSegPt1.y <= inOtherPt.y ) && ( inOtherPt.y <= inSegPt2.y ) );
+				} else {
+					return	( ( inSegPt2.y <= inOtherPt.y ) && ( inOtherPt.y <= inSegPt1.y ) );
+				}
+			}
+		}
+
+		function intersect_segments_2D( inSeg1Pt1, inSeg1Pt2, inSeg2Pt1, inSeg2Pt2, inExcludeAdjacentSegs ) {
+			var EPSILON = 0.0000000001;
+
+			var seg1dx = inSeg1Pt2.x - inSeg1Pt1.x,   seg1dy = inSeg1Pt2.y - inSeg1Pt1.y;
+			var seg2dx = inSeg2Pt2.x - inSeg2Pt1.x,   seg2dy = inSeg2Pt2.y - inSeg2Pt1.y;
+
+			var seg1seg2dx = inSeg1Pt1.x - inSeg2Pt1.x;
+			var seg1seg2dy = inSeg1Pt1.y - inSeg2Pt1.y;
+
+			var limit		= seg1dy * seg2dx - seg1dx * seg2dy;
+			var perpSeg1	= seg1dy * seg1seg2dx - seg1dx * seg1seg2dy;
+
+			if ( Math.abs(limit) > EPSILON ) {			// not parallel
+
+				var perpSeg2;
+				if ( limit > 0 ) {
+					if ( ( perpSeg1 < 0 ) || ( perpSeg1 > limit ) ) 		return [];
+					perpSeg2 = seg2dy * seg1seg2dx - seg2dx * seg1seg2dy;
+					if ( ( perpSeg2 < 0 ) || ( perpSeg2 > limit ) ) 		return [];
+				} else {
+					if ( ( perpSeg1 > 0 ) || ( perpSeg1 < limit ) ) 		return [];
+					perpSeg2 = seg2dy * seg1seg2dx - seg2dx * seg1seg2dy;
+					if ( ( perpSeg2 > 0 ) || ( perpSeg2 < limit ) ) 		return [];
+				}
+
+				// intersection at endpoint ?
+				if ( perpSeg2 == 0 ) {
+					if ( ( inExcludeAdjacentSegs ) &&
+						 ( ( perpSeg1 == 0 ) || ( perpSeg1 == limit ) ) )		return [];
+					return  [ inSeg1Pt1 ];
+				}
+				if ( perpSeg2 == limit ) {
+					if ( ( inExcludeAdjacentSegs ) &&
+						 ( ( perpSeg1 == 0 ) || ( perpSeg1 == limit ) ) )		return [];
+					return  [ inSeg1Pt2 ];
+				}
+
+				// return real intersection point
+				var factorSeg1 = perpSeg2 / limit;
+				return	[ { x: inSeg1Pt1.x + factorSeg1 * seg1dx,
+							y: inSeg1Pt1.y + factorSeg1 * seg1dy } ];
+
+			} else {		// parallel or colinear
+				if ( perpSeg1 != 0 )							 			return [];
+
+				// they are collinear or degenerate
+				var seg1Pt = ( (seg1dx == 0) && (seg1dy == 0) );	// segment1 ist just a point?
+				var seg2Pt = ( (seg2dx == 0) && (seg2dy == 0) );	// segment2 ist just a point?
+				// both segments are points
+				if ( seg1Pt && seg2Pt ) {
+					if ( (inSeg1Pt1.x != inSeg2Pt1.x) ||
+						 (inSeg1Pt1.y != inSeg2Pt1.y) )		return [];   	// they are distinct  points
+					return  [ inSeg1Pt1 ];                 					// they are the same point
+				}
+				// segment#1  is a single point
+				if ( seg1Pt ) {
+					if (! point_in_segment_2D( inSeg2Pt1, inSeg2Pt2, inSeg1Pt1 ) )		return [];		// but not in segment#2
+					return  [ inSeg1Pt1 ];
+				}
+				// segment#2  is a single point
+				if ( seg2Pt ) {
+					if (! point_in_segment_2D( inSeg1Pt1, inSeg1Pt2, inSeg2Pt1 ) )		return [];		// but not in segment#1
+					return  [ inSeg2Pt1 ];
+				}
+
+				// they are collinear segments, which might overlap
+				var seg1min, seg1max, seg1minVal, seg1maxVal;
+				var seg2min, seg2max, seg2minVal, seg2maxVal;
+				if (seg1dx != 0) {		// the segments are NOT on a vertical line
+					if ( inSeg1Pt1.x < inSeg1Pt2.x ) {
+						seg1min = inSeg1Pt1; seg1minVal = inSeg1Pt1.x;
+						seg1max = inSeg1Pt2; seg1maxVal = inSeg1Pt2.x;
+					} else {
+						seg1min = inSeg1Pt2; seg1minVal = inSeg1Pt2.x;
+						seg1max = inSeg1Pt1; seg1maxVal = inSeg1Pt1.x;
+					}
+					if ( inSeg2Pt1.x < inSeg2Pt2.x ) {
+						seg2min = inSeg2Pt1; seg2minVal = inSeg2Pt1.x;
+						seg2max = inSeg2Pt2; seg2maxVal = inSeg2Pt2.x;
+					} else {
+						seg2min = inSeg2Pt2; seg2minVal = inSeg2Pt2.x;
+						seg2max = inSeg2Pt1; seg2maxVal = inSeg2Pt1.x;
+					}
+				} else {				// the segments are on a vertical line
+					if ( inSeg1Pt1.y < inSeg1Pt2.y ) {
+						seg1min = inSeg1Pt1; seg1minVal = inSeg1Pt1.y;
+						seg1max = inSeg1Pt2; seg1maxVal = inSeg1Pt2.y;
+					} else {
+						seg1min = inSeg1Pt2; seg1minVal = inSeg1Pt2.y;
+						seg1max = inSeg1Pt1; seg1maxVal = inSeg1Pt1.y;
+					}
+					if ( inSeg2Pt1.y < inSeg2Pt2.y ) {
+						seg2min = inSeg2Pt1; seg2minVal = inSeg2Pt1.y;
+						seg2max = inSeg2Pt2; seg2maxVal = inSeg2Pt2.y;
+					} else {
+						seg2min = inSeg2Pt2; seg2minVal = inSeg2Pt2.y;
+						seg2max = inSeg2Pt1; seg2maxVal = inSeg2Pt1.y;
+					}
+				}
+				if ( seg1minVal <= seg2minVal ) {
+					if ( seg1maxVal <  seg2minVal )	return [];
+					if ( seg1maxVal == seg2minVal )	{
+						if ( inExcludeAdjacentSegs )		return [];
+						return [ seg2min ];
+					}
+					if ( seg1maxVal <= seg2maxVal )	return [ seg2min, seg1max ];
+					return	[ seg2min, seg2max ];
+				} else {
+					if ( seg1minVal >  seg2maxVal )	return [];
+					if ( seg1minVal == seg2maxVal )	{
+						if ( inExcludeAdjacentSegs )		return [];
+						return [ seg1min ];
+					}
+					if ( seg1maxVal <= seg2maxVal )	return [ seg1min, seg1max ];
+					return	[ seg1min, seg2max ];
+				}
+			}
+		}
+
+		function isPointInsideAngle( inVertex, inLegFromPt, inLegToPt, inOtherPt ) {
+			// The order of legs is important
+
+			var EPSILON = 0.0000000001;
+
+			// translation of all points, so that Vertex is at (0,0)
+			var legFromPtX	= inLegFromPt.x - inVertex.x,  legFromPtY	= inLegFromPt.y - inVertex.y;
+			var legToPtX	= inLegToPt.x	- inVertex.x,  legToPtY		= inLegToPt.y	- inVertex.y;
+			var otherPtX	= inOtherPt.x	- inVertex.x,  otherPtY		= inOtherPt.y	- inVertex.y;
+
+			// main angle >0: < 180 deg.; 0: 180 deg.; <0: > 180 deg.
+			var from2toAngle	= legFromPtX * legToPtY - legFromPtY * legToPtX;
+			var from2otherAngle	= legFromPtX * otherPtY - legFromPtY * otherPtX;
+
+			if ( Math.abs(from2toAngle) > EPSILON ) {			// angle != 180 deg.
+
+				var other2toAngle		= otherPtX * legToPtY - otherPtY * legToPtX;
+				// console.log( "from2to: " + from2toAngle + ", from2other: " + from2otherAngle + ", other2to: " + other2toAngle );
+
+				if ( from2toAngle > 0 ) {				// main angle < 180 deg.
+					return	( ( from2otherAngle >= 0 ) && ( other2toAngle >= 0 ) );
+				} else {								// main angle > 180 deg.
+					return	( ( from2otherAngle >= 0 ) || ( other2toAngle >= 0 ) );
+				}
+			} else {										// angle == 180 deg.
+				// console.log( "from2to: 180 deg., from2other: " + from2otherAngle  );
+				return	( from2otherAngle > 0 );
+			}
+		}
+
+
+		function removeHoles( contour, holes ) {
+
+			var shape = contour.concat(); // work on this shape
+			var hole;
+
+			function isCutLineInsideAngles( inShapeIdx, inHoleIdx ) {
+				// Check if hole point lies within angle around shape point
+				var lastShapeIdx = shape.length - 1;
+
+				var prevShapeIdx = inShapeIdx - 1;
+				if ( prevShapeIdx < 0 )			prevShapeIdx = lastShapeIdx;
+
+				var nextShapeIdx = inShapeIdx + 1;
+				if ( nextShapeIdx > lastShapeIdx )	nextShapeIdx = 0;
+
+				var insideAngle = isPointInsideAngle( shape[inShapeIdx], shape[ prevShapeIdx ], shape[ nextShapeIdx ], hole[inHoleIdx] );
+				if (! insideAngle ) {
+					// console.log( "Vertex (Shape): " + inShapeIdx + ", Point: " + hole[inHoleIdx].x + "/" + hole[inHoleIdx].y );
+					return	false;
+				}
+
+				// Check if shape point lies within angle around hole point
+				var lastHoleIdx = hole.length - 1;
+
+				var prevHoleIdx = inHoleIdx - 1;
+				if ( prevHoleIdx < 0 )			prevHoleIdx = lastHoleIdx;
+
+				var nextHoleIdx = inHoleIdx + 1;
+				if ( nextHoleIdx > lastHoleIdx )	nextHoleIdx = 0;
+
+				insideAngle = isPointInsideAngle( hole[inHoleIdx], hole[ prevHoleIdx ], hole[ nextHoleIdx ], shape[inShapeIdx] );
+				if (! insideAngle ) {
+					// console.log( "Vertex (Hole): " + inHoleIdx + ", Point: " + shape[inShapeIdx].x + "/" + shape[inShapeIdx].y );
+					return	false;
+				}
+
+				return	true;
+			}
+
+			function intersectsShapeEdge( inShapePt, inHolePt ) {
+				// checks for intersections with shape edges
+				var sIdx, nextIdx, intersection;
+				for ( sIdx = 0; sIdx < shape.length; sIdx++ ) {
+					nextIdx = sIdx+1; nextIdx %= shape.length;
+					intersection = intersect_segments_2D( inShapePt, inHolePt, shape[sIdx], shape[nextIdx], true );
+					if ( intersection.length > 0 )		return	true;
+				}
+
+				return	false;
+			}
+
+			var indepHoles = [];
+
+			function intersectsHoleEdge( inShapePt, inHolePt ) {
+				// checks for intersections with hole edges
+				var ihIdx, chkHole,
+					hIdx, nextIdx, intersection;
+				for ( ihIdx = 0; ihIdx < indepHoles.length; ihIdx++ ) {
+					chkHole = holes[indepHoles[ihIdx]];
+					for ( hIdx = 0; hIdx < chkHole.length; hIdx++ ) {
+						nextIdx = hIdx+1; nextIdx %= chkHole.length;
+						intersection = intersect_segments_2D( inShapePt, inHolePt, chkHole[hIdx], chkHole[nextIdx], true );
+						if ( intersection.length > 0 )		return	true;
+					}
+				}
+				return	false;
+			}
+
+			var holeIndex, shapeIndex,
+				shapePt, h, h2, holePt,
+				holeIdx, cutKey, failedCuts = [],
+				tmpShape1, tmpShape2,
+				tmpHole1, tmpHole2;
+
+			for (h in holes) { indepHoles.push( h ); }
+
+			var counter = indepHoles.length * 2;
+			while ( indepHoles.length > 0 ) {
+				counter --;
+				if ( counter < 0 ) {
+					console.log( "Infinite Loop! Holes left:" + indepHoles.length + ", Probably Hole outside Shape!" );
+					break;
+				}
+
+				// search for shape-vertex and hole-vertex,
+				// which can be connected without intersections
+				for ( shapeIndex = 0; shapeIndex < shape.length; shapeIndex++ ) {
+
+					shapePt = shape[ shapeIndex ];
+					holeIndex	= -1;
+
+					// search for hole which can be reached without intersections
+					for ( h = 0; h < indepHoles.length; h++ ) {
+						holeIdx = indepHoles[h];
+
+						// prevent multiple checks
+						cutKey = shapePt.x + ":" + shapePt.y + ":" + holeIdx;
+						if ( failedCuts[cutKey] !== undefined )			continue;
+
+						hole = holes[holeIdx];
+						for ( h2 = 0; h2 < hole.length; h2 ++ ) {
+							holePt = hole[ h2 ];
+							if (! isCutLineInsideAngles( shapeIndex, h2 ) )		continue;
+							if ( intersectsShapeEdge( shapePt, holePt ) )		continue;
+							if ( intersectsHoleEdge( shapePt, holePt ) )		continue;
+
+							holeIndex = h2;
+							indepHoles.splice(h,1);
+
+							tmpShape1 = shape.slice( 0, shapeIndex+1 );
+							tmpShape2 = shape.slice( shapeIndex );
+							tmpHole1 = hole.slice( holeIndex );
+							tmpHole2 = hole.slice( 0, holeIndex+1 );
+
+							shape = tmpShape1.concat( tmpHole1 ).concat( tmpHole2 ).concat( tmpShape2 );
+
+							// Debug only, to show the selected cuts
+							// glob_CutLines.push( [ shapePt, holePt ] );
+
+							break;
+						}
+						if ( holeIndex >= 0 )	break;		// hole-vertex found
+
+						failedCuts[cutKey] = true;			// remember failure
+					}
+					if ( holeIndex >= 0 )	break;		// hole-vertex found
+				}
+			}
+
+			return shape; 			/* shape with no holes */
+		}
+
+
+		var i, il, f, face,
+			key, index,
+			allPointsMap = {};
+
+		// To maintain reference to old shape, one must match coordinates, or offset the indices from original arrays. It's probably easier to do the first.
+
+		var allpoints = contour.concat();
+		for (var h in holes) { Array.prototype.push.apply( allpoints, holes[h] ); }
+		//console.log( "allpoints",allpoints, allpoints.length );
+
+		// prepare all points map
+
+		for ( i = 0, il = allpoints.length; i < il; i ++ ) {
+
+			key = allpoints[ i ].x + ":" + allpoints[ i ].y;
+
+			if ( allPointsMap[ key ] !== undefined ) {
+
+				console.log( "Duplicate point", key );
+
+			}
+
+			allPointsMap[ key ] = i;
+
+		}
+
+		// remove holes by cutting paths to holes and adding them to the shape
+		var shapeWithoutHoles = removeHoles( contour, holes );
+
+		var triangles = THREE.FontUtils.Triangulate( shapeWithoutHoles, false ); // True returns indices for points of spooled shape
+		//console.log( "triangles",triangles, triangles.length );
+
+		// check all face vertices against all points map
+
+		for ( i = 0, il = triangles.length; i < il; i ++ ) {
+
+			face = triangles[ i ];
+
+			for ( f = 0; f < 3; f ++ ) {
+
+				key = face[ f ].x + ":" + face[ f ].y;
+
+				index = allPointsMap[ key ];
+
+				if ( index !== undefined ) {
+
+					face[ f ] = index;
+
+				}
+
+			}
+
+		}
+
+		return triangles.concat();
+
+	}, // end triangulate shapes
+
 	/*
 	triangulate2 : function( pts, holes ) {