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https://github.com/scratchfoundation/paper.js.git
synced 2025-01-07 13:22:07 -05:00
Fat-line clipping. Needs more tests.
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hkrish
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1 changed files with 66 additions and 69 deletions
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@ -3,7 +3,7 @@
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var EPSILON = 10e-12;
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var TOLERANCE = 10e-6;
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var _tolerence = TOLERANCE;
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var _tolerence = EPSILON;
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function getIntersections2( path1, path2 ){
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var locations = [];
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@ -11,11 +11,15 @@ function getIntersections2( path1, path2 ){
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}
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paper.Curve.getIntersections2 = function( v1, v2, curve1, curve2, locations, _t1, _t2, _u1, _u2, tstart ) {
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paper.Curve.getIntersections2 = function( v1, v2, curve1, curve2, locations, _t1, _t2, _u1, _u2 ) {
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_t1 = _t1 || 0; _t2 = _t2 || 1;
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_u1 = _u1 || 0; _u2 = _u2 || 1;
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var ret = _clipFatLine( v1, v2, _t1, _t2, _u1, _u2, (_t2 - _t1), (_u2 - _u1), true, curve1, curve2, locations, tstart );
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if( ret > 1) {
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var loc = { parameter: null };
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var ret = _clipFatLine( v1, v2, 0, 1, 0, 1, true, curve1, curve2, loc );
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if( ret === 1 ){
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var parameter = _t1 + loc.parameter * ( _t2 - _t1 );
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locations.push( new CurveLocation( curve1, parameter, curve1.getPoint(parameter), curve2 ) );
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} else if( ret < 0) {
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// We need to subdivide one of the curves
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// Better if we can subdivide the longest curve
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var v1lx = v1[6] - v1[0];
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@ -25,31 +29,24 @@ paper.Curve.getIntersections2 = function( v1, v2, curve1, curve2, locations, _t1
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var sqrDist1 = v1lx * v1lx + v1ly * v1ly;
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var sqrDist2 = v2lx * v2lx + v2ly * v2ly;
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var parts;
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// This is a quick but dirty way to determine which curve to subdivide
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// A quick and dirty way to determine which curve to subdivide
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if( sqrDist1 > sqrDist2 ){
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parts = Curve.subdivide( v1 );
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nuT = ( _t1 + _t2 ) / 2;
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Curve.getIntersections2( parts[0], v2, curve1, curve2, locations, _t1, nuT, _u1, _u2, -0.5 );
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Curve.getIntersections2( parts[1], v2, curve1, curve2, locations, nuT, _t2, _u1, _u2, 0.5 );
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Curve.getIntersections2( parts[0], v2, curve1, curve2, locations, _t1, nuT, _u1, _u2 );
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Curve.getIntersections2( parts[1], v2, curve1, curve2, locations, nuT, _t2, _u1, _u2 );
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} else {
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parts = Curve.subdivide( v2 );
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nuU = ( _u1 + _u2 ) / 2;
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Curve.getIntersections2( v1, parts[0], curve1, curve2, locations, _t1, _t2, _u1, nuU, -0.5 );
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Curve.getIntersections2( v1, parts[1], curve1, curve2, locations, _t1, _t2, nuU, _u2, 0.5 );
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Curve.getIntersections2( v1, parts[0], curve1, curve2, locations, _t1, _t2, _u1, nuU );
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Curve.getIntersections2( v1, parts[1], curve1, curve2, locations, _t1, _t2, nuU, _u2 );
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}
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}
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};
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function _clipFatLine( v1, v2, t1, t2, u1, u2, tdiff, udiff, tvalue, curve1, curve2, locations, count ){
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// DEBUG: count the iterations
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if( count === undefined ) { count = 0; }
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else { ++count; }
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function _clipFatLine( v1, v2, t1, t2, u1, u2, tvalue, curve1, curve2, location ){
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if( t1 >= t2 - _tolerence && t1 <= t2 + _tolerence && u1 >= u2 - _tolerence && u1 <= u2 + _tolerence ){
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loc = new CurveLocation( curve2, Math.abs( t1 ), null, curve1 );
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// var loc = tvalue ? new CurveLocation( curve2, Math.abs( tstart - t1 ), null, curve1 ) :
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// new CurveLocation( curve1, Math.abs( ustart - u1 ), null, curve2 );
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// console.log( t1, t2, u1, u2 )
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locations.push( loc );
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location.parameter = u1;
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return 1;
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} else {
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var p0x = v1[0], p0y = v1[1];
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@ -85,9 +82,7 @@ function _clipFatLine( v1, v2, t1, t2, u1, u2, tdiff, udiff, tvalue, curve1, cur
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if( dmin > maxdist || dmax < mindist ){
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return 0;
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}
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// Ideally we need to calculate the convex hull for D(ti, di(t))
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// here we are just checking against all possibilities and sorting them
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// TODO: implement simple polygon convexhull method.
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// Calculate the convex hull for non-parametric bezier curve D(ti, di(t))
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var Dt = _convexhull( dq0, dq1, dq2, dq3 );
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// Now we clip the convex hulls for D(ti, di(t)) with dmin and dmax
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@ -121,15 +116,6 @@ function _clipFatLine( v1, v2, t1, t2, u1, u2, tdiff, udiff, tvalue, curve1, cur
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tmaxdmax = ( tmaxdmax === -Infinity )? 1 : tmaxdmax;
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var tmin = Math.min( tmindmin, tmaxdmin, tmindmax, tmaxdmax );
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var tmax = Math.max( tmindmin, tmaxdmin, tmindmax, tmaxdmax);
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// if( count === 1 ){
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// console.log( Dt )
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// // console.log( dmin, dmax, tmin, tmax, " - ", tmindmin, tmaxdmin, tmindmax, tmaxdmax )
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// plotD_vs_t( 250, 110, Dt, dmin, dmax, tmin, tmax, 1, tvalue );
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// // return;
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// }
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// We need to toggle clipping both curves alternatively
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// tvalue indicates whether to compare t or u for testing for convergence
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var nuV2 = Curve.getPart( v2, tmin, tmax );
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@ -140,24 +126,26 @@ function _clipFatLine( v1, v2, t1, t2, u1, u2, tdiff, udiff, tvalue, curve1, cur
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// Test the convergence rate
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// if the clipping fails to converge by atleast 20%,
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// we need to subdivide the longest curve and try again.
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convRate = (tdiff - tmax + tmin ) / tdiff;
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var td = ( t2 - t1 );
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convRate = ( td - ( nuT2 - nuT1 ) ) / td;
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// console.log( 'convergence rate for t = ' + convRate + "%" );
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if( convRate <= 0.2) {
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// subdivide the curve and try again
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return 2;
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return -1;
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} else {
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return _clipFatLine( nuV2, v1, nuT1, nuT2, u1, u2, (tmax - tmin), udiff, !tvalue, curve1, curve2, locations, count );
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return _clipFatLine( nuV2, v1, nuT1, nuT2, u1, u2, !tvalue, curve1, curve2, location );
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}
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} else {
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nuU1 = u1 + tmin * ( u2 - u1 );
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nuU2 = u1 + tmax * ( u2 - u1 );
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convRate = ( udiff - tmax + tmin ) / udiff;
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var ud = ( u2 - u1 );
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convRate = ( ud - ( nuU2 - nuU1 ) ) / ud;
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// console.log( 'convergence rate for u = ' + convRate + "%" );
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if( convRate <= 0.2) {
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// subdivide the curve and try again
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return 2;
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return -1;
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} else {
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return _clipFatLine( nuV2, v1, t1, t2, nuU1, nuU2 , tdiff, (tmax - tmin), !tvalue, curve1, curve2, locations, count );
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return _clipFatLine( nuV2, v1, t1, t2, nuU1, nuU2 , !tvalue, curve1, curve2, location );
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}
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}
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}
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@ -165,18 +153,18 @@ function _clipFatLine( v1, v2, t1, t2, u1, u2, tdiff, udiff, tvalue, curve1, cur
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/**
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* Clip curve values V2 with fatline of v
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* @param {Array} v - Section of the first curve, for which we will make a fatline
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* Clip curve values V2 with fat-line of v1 and vice versa
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* @param {Array} v - Section of the first curve, for which we will make a fat-line
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* @param {Number} t1 - start parameter for v in vOrg
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* @param {Number} t2 - end parameter for v in vOrg
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* @param {Array} v2 - Section of the second curve; we will clip this curve with the fatline of v
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* @param {Array} v2 - Section of the second curve; we will clip this curve with the fat-line of v
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* @param {Number} u1 - start parameter for v2 in v2Org
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* @param {Number} u2 - end parameter for v2 in v2Org
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* @param {Array} vOrg - The original curve values for v
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* @param {Array} v2Org - The original curve values for v2
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* @return {[type]}
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*/
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function _clipWithFatline( v, t1, t2, v2, u1, u2, vOrg, v2Org ){
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function _clipBezFatLine( v1, t1, t2, v2, u1, u2, vOrg, v2Org ){
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}
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@ -187,7 +175,8 @@ function _convexhull( dq0, dq1, dq2, dq3 ){
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// Check if [1/3, dq1] and [2/3, dq2] are on the same side of line [0,dq0, 1,dq3]
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if( distq1 * distq2 < 0 ) {
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// dq1 and dq2 lie on different sides on [0, q0, 1, q3]
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// Convexhull is a quadrilatteral and line [0, q0, 1, q3] is not part of the convexhull
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// Convexhull is a quadrilatteral and line [0, q0, 1, q3] is NOT part of the convexhull
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// so we are pretty much done here.
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Dt = [
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[ 0.0, dq0, 0.3333333333333333, dq1 ],
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[ 0.3333333333333333, dq1, 1.0, dq3 ],
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@ -195,48 +184,56 @@ function _convexhull( dq0, dq1, dq2, dq3 ){
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[ 1.0, dq3, 0.6666666666666666, dq2 ]
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];
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} else {
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// dq1 and dq2 lie on the same sides on [0, q0, 1, q3]
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// Convexhull can be a triangle or a quadrilatteral and
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// line [0, q0, 1, q3] is part of the convexhull.
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// Check if the hull is a triangle or a quadrilatteral
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var dqmin, dqmax, dqapex1, dqapex2;
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distq1 = Math.abs(distq1);
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distq2 = Math.abs(distq2);
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var vqa1a2x, vqa1a2y, vqa1Maxx, vqa1Maxy, vqa1Minx, vqa1Miny;
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if( distq1 > distq2 ){
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dqapex1 = [ 1.0, dq3 ];
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dqapex2 = [ 0.0, dq0 ];
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dqmin = [ 0.6666666666666666, dq2 ];
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dqmax = [ 0.3333333333333333, dq1 ];
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dqmin = [ 0.6666666666666666, dq2 ];
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dqmax = [ 0.3333333333333333, dq1 ];
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// apex is dq3 and the other apex point is dq0
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// vector dqapex->dqapex2 or the base vector which is already part of c-hull
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vqa1a2x = 1.0, vqa1a2y = dq3 - dq0;
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// vector dqapex->dqmax
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vqa1Maxx = 0.6666666666666666, vqa1Maxy = dq3 - dq1;
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// vector dqapex->dqmin
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vqa1Minx = 0.3333333333333333, vqa1Miny = dq3 - dq2;
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} else {
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dqapex1 = [ 0.0, dq0 ];
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dqapex2 = [ 1.0, dq3 ];
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dqmin = [ 0.3333333333333333, dq1 ];
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dqmax = [ 0.6666666666666666, dq2 ];
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dqmin = [ 0.3333333333333333, dq1 ];
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dqmax = [ 0.6666666666666666, dq2 ];
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// apex is dq0 in this case, and the other apex point is dq3
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// vector dqapex->dqapex2 or the base vector which is already part of c-hull
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vqa1a2x = -1.0, vqa1a2y = dq0 - dq3;
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// vector dqapex->dqmax
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vqa1Maxx = -0.6666666666666666, vqa1Maxy = dq0 - dq2;
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// vector dqapex->dqmin
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vqa1Minx = -0.3333333333333333, vqa1Miny = dq0 - dq1;
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}
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// vector dqapex1->dqapex2
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var vqa1a2x = dqapex1[0] - dqapex2[0], vqa1a2y = dqapex1[1] - dqapex2[1];
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// vector dqapex1->dqmax
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var vqa1Maxx = dqapex1[0] - dqmax[0], vqa1Maxy = dqapex1[1] - dqmax[1];
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// vector dqapex1->dqmin
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var vqa1Minx = dqapex1[0] - dqmin[0], vqa1Miny = dqapex1[1] - dqmin[1];
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// compare cross products of these vectors to determine, if
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// point is in triangles [ dq3, dqMax, dq0 ] or [ dq0, dqMax, dq3 ]
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var vcrossa1a2_a1Max = vqa1a2x * vqa1Maxy - vqa1a2y * vqa1Maxx;
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var vcrossa1a2_a1Min = vqa1a2x * vqa1Miny - vqa1a2y * vqa1Minx;
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var vcrossa1Max_a1Min = vqa1Maxx * vqa1Miny - vqa1Maxy * vqa1Minx;
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if( vcrossa1Max_a1Min * vcrossa1a2_a1Min < 0 ){
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// Point [2/3, dq2] is inside the triangle and the convex hull is a triangle
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Dt = [
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[ 0.0, dq0, dqmax[0], dqmax[1] ],
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[ dqmax[0], dqmax[1], 1.0, dq3 ],
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[ 1.0, dq3, 0.0, dq0 ]
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];
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// Point [2/3, dq2] is inside the triangle and the convex hull is a triangle
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Dt = [
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[ 0.0, dq0, dqmax[0], dqmax[1] ],
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[ dqmax[0], dqmax[1], 1.0, dq3 ],
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[ 1.0, dq3, 0.0, dq0 ]
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];
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} else {
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// Convexhull is a quadrilatteral and we need all lines in the correct order where
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// line [0, q0, 1, q3] is part of the convex hull
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Dt = [
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[ 0.0, dq0, 0.3333333333333333, dq1 ],
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[ 0.3333333333333333, dq1, 0.6666666666666666, dq2 ],
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[ 0.6666666666666666, dq2, 1.0, dq3 ],
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[ 1.0, dq3, 0.0, dq0 ]
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];
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// Convexhull is a quadrilatteral and we need all lines in the correct order where
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// line [0, q0, 1, q3] is part of the convex hull
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Dt = [
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[ 0.0, dq0, 0.3333333333333333, dq1 ],
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[ 0.3333333333333333, dq1, 0.6666666666666666, dq2 ],
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[ 0.6666666666666666, dq2, 1.0, dq3 ],
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[ 1.0, dq3, 0.0, dq0 ]
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];
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}
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}
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return Dt;
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