scratchfoundation/paper.js
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Fat-line clipping. Needs more tests.

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hkrish 2013-05-05 17:45:06 +02:00
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fatline/Intersect.js
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@ -3,7 +3,7 @@
var EPSILON = 10e-12; var EPSILON = 10e-12;
var TOLERANCE = 10e-6; var TOLERANCE = 10e-6;
var _tolerence = TOLERANCE; var _tolerence = EPSILON;
function getIntersections2( path1, path2 ){ function getIntersections2( path1, path2 ){
var locations = []; var locations = [];
@ -11,11 +11,15 @@ function getIntersections2( path1, path2 ){
} }
paper.Curve.getIntersections2 = function( v1, v2, curve1, curve2, locations, _t1, _t2, _u1, _u2, tstart ) { paper.Curve.getIntersections2 = function( v1, v2, curve1, curve2, locations, _t1, _t2, _u1, _u2 ) {
_t1 = _t1 || 0; _t2 = _t2 || 1; _t1 = _t1 || 0; _t2 = _t2 || 1;
_u1 = _u1 || 0; _u2 = _u2 || 1; _u1 = _u1 || 0; _u2 = _u2 || 1;
var ret = _clipFatLine( v1, v2, _t1, _t2, _u1, _u2, (_t2 - _t1), (_u2 - _u1), true, curve1, curve2, locations, tstart ); var loc = { parameter: null };
if( ret > 1) { var ret = _clipFatLine( v1, v2, 0, 1, 0, 1, true, curve1, curve2, loc );
if( ret === 1 ){
var parameter = _t1 + loc.parameter * ( _t2 - _t1 );
locations.push( new CurveLocation( curve1, parameter, curve1.getPoint(parameter), curve2 ) );
} else if( ret < 0) {
// We need to subdivide one of the curves // We need to subdivide one of the curves
// Better if we can subdivide the longest curve // Better if we can subdivide the longest curve
var v1lx = v1[6] - v1[0]; var v1lx = v1[6] - v1[0];
@ -25,31 +29,24 @@ paper.Curve.getIntersections2 = function( v1, v2, curve1, curve2, locations, _t1
var sqrDist1 = v1lx * v1lx + v1ly * v1ly; var sqrDist1 = v1lx * v1lx + v1ly * v1ly;
var sqrDist2 = v2lx * v2lx + v2ly * v2ly; var sqrDist2 = v2lx * v2lx + v2ly * v2ly;
var parts; var parts;
// This is a quick but dirty way to determine which curve to subdivide // A quick and dirty way to determine which curve to subdivide
if( sqrDist1 > sqrDist2 ){ if( sqrDist1 > sqrDist2 ){
parts = Curve.subdivide( v1 ); parts = Curve.subdivide( v1 );
nuT = ( _t1 + _t2 ) / 2; nuT = ( _t1 + _t2 ) / 2;
Curve.getIntersections2( parts[0], v2, curve1, curve2, locations, _t1, nuT, _u1, _u2, -0.5 ); Curve.getIntersections2( parts[0], v2, curve1, curve2, locations, _t1, nuT, _u1, _u2 );
Curve.getIntersections2( parts[1], v2, curve1, curve2, locations, nuT, _t2, _u1, _u2, 0.5 ); Curve.getIntersections2( parts[1], v2, curve1, curve2, locations, nuT, _t2, _u1, _u2 );
} else { } else {
parts = Curve.subdivide( v2 ); parts = Curve.subdivide( v2 );
nuU = ( _u1 + _u2 ) / 2; nuU = ( _u1 + _u2 ) / 2;
Curve.getIntersections2( v1, parts[0], curve1, curve2, locations, _t1, _t2, _u1, nuU, -0.5 ); Curve.getIntersections2( v1, parts[0], curve1, curve2, locations, _t1, _t2, _u1, nuU );
Curve.getIntersections2( v1, parts[1], curve1, curve2, locations, _t1, _t2, nuU, _u2, 0.5 ); Curve.getIntersections2( v1, parts[1], curve1, curve2, locations, _t1, _t2, nuU, _u2 );
} }
} }
}; };
function _clipFatLine( v1, v2, t1, t2, u1, u2, tdiff, udiff, tvalue, curve1, curve2, locations, count ){ function _clipFatLine( v1, v2, t1, t2, u1, u2, tvalue, curve1, curve2, location ){
// DEBUG: count the iterations
if( count === undefined ) { count = 0; }
else { ++count; }
if( t1 >= t2 - _tolerence && t1 <= t2 + _tolerence && u1 >= u2 - _tolerence && u1 <= u2 + _tolerence ){ if( t1 >= t2 - _tolerence && t1 <= t2 + _tolerence && u1 >= u2 - _tolerence && u1 <= u2 + _tolerence ){
loc = new CurveLocation( curve2, Math.abs( t1 ), null, curve1 ); location.parameter = u1;
// var loc = tvalue ? new CurveLocation( curve2, Math.abs( tstart - t1 ), null, curve1 ) :
// new CurveLocation( curve1, Math.abs( ustart - u1 ), null, curve2 );
// console.log( t1, t2, u1, u2 )
locations.push( loc );
return 1; return 1;
} else { } else {
var p0x = v1[0], p0y = v1[1]; var p0x = v1[0], p0y = v1[1];
@ -85,9 +82,7 @@ function _clipFatLine( v1, v2, t1, t2, u1, u2, tdiff, udiff, tvalue, curve1, cur
if( dmin > maxdist || dmax < mindist ){ if( dmin > maxdist || dmax < mindist ){
return 0; return 0;
} }
// Ideally we need to calculate the convex hull for D(ti, di(t)) // Calculate the convex hull for non-parametric bezier curve D(ti, di(t))
// here we are just checking against all possibilities and sorting them
// TODO: implement simple polygon convexhull method.
var Dt = _convexhull( dq0, dq1, dq2, dq3 ); var Dt = _convexhull( dq0, dq1, dq2, dq3 );
// Now we clip the convex hulls for D(ti, di(t)) with dmin and dmax // Now we clip the convex hulls for D(ti, di(t)) with dmin and dmax
@ -121,15 +116,6 @@ function _clipFatLine( v1, v2, t1, t2, u1, u2, tdiff, udiff, tvalue, curve1, cur
tmaxdmax = ( tmaxdmax === -Infinity )? 1 : tmaxdmax; tmaxdmax = ( tmaxdmax === -Infinity )? 1 : tmaxdmax;
var tmin = Math.min( tmindmin, tmaxdmin, tmindmax, tmaxdmax ); var tmin = Math.min( tmindmin, tmaxdmin, tmindmax, tmaxdmax );
var tmax = Math.max( tmindmin, tmaxdmin, tmindmax, tmaxdmax); var tmax = Math.max( tmindmin, tmaxdmin, tmindmax, tmaxdmax);
// if( count === 1 ){
// console.log( Dt )
// // console.log( dmin, dmax, tmin, tmax, " - ", tmindmin, tmaxdmin, tmindmax, tmaxdmax )
// plotD_vs_t( 250, 110, Dt, dmin, dmax, tmin, tmax, 1, tvalue );
// // return;
// }
// We need to toggle clipping both curves alternatively // We need to toggle clipping both curves alternatively
// tvalue indicates whether to compare t or u for testing for convergence // tvalue indicates whether to compare t or u for testing for convergence
var nuV2 = Curve.getPart( v2, tmin, tmax ); var nuV2 = Curve.getPart( v2, tmin, tmax );
@ -140,24 +126,26 @@ function _clipFatLine( v1, v2, t1, t2, u1, u2, tdiff, udiff, tvalue, curve1, cur
// Test the convergence rate // Test the convergence rate
// if the clipping fails to converge by atleast 20%, // if the clipping fails to converge by atleast 20%,
// we need to subdivide the longest curve and try again. // we need to subdivide the longest curve and try again.
convRate = (tdiff - tmax + tmin ) / tdiff; var td = ( t2 - t1 );
convRate = ( td - ( nuT2 - nuT1 ) ) / td;
// console.log( 'convergence rate for t = ' + convRate + "%" ); // console.log( 'convergence rate for t = ' + convRate + "%" );
if( convRate <= 0.2) { if( convRate <= 0.2) {
// subdivide the curve and try again // subdivide the curve and try again
return 2; return -1;
} else { } else {
return _clipFatLine( nuV2, v1, nuT1, nuT2, u1, u2, (tmax - tmin), udiff, !tvalue, curve1, curve2, locations, count ); return _clipFatLine( nuV2, v1, nuT1, nuT2, u1, u2, !tvalue, curve1, curve2, location );
} }
} else { } else {
nuU1 = u1 + tmin * ( u2 - u1 ); nuU1 = u1 + tmin * ( u2 - u1 );
nuU2 = u1 + tmax * ( u2 - u1 ); nuU2 = u1 + tmax * ( u2 - u1 );
convRate = ( udiff - tmax + tmin ) / udiff; var ud = ( u2 - u1 );
convRate = ( ud - ( nuU2 - nuU1 ) ) / ud;
// console.log( 'convergence rate for u = ' + convRate + "%" ); // console.log( 'convergence rate for u = ' + convRate + "%" );
if( convRate <= 0.2) { if( convRate <= 0.2) {
// subdivide the curve and try again // subdivide the curve and try again
return 2; return -1;
} else { } else {
return _clipFatLine( nuV2, v1, t1, t2, nuU1, nuU2 , tdiff, (tmax - tmin), !tvalue, curve1, curve2, locations, count ); return _clipFatLine( nuV2, v1, t1, t2, nuU1, nuU2 , !tvalue, curve1, curve2, location );
} }
} }
} }
@ -165,18 +153,18 @@ function _clipFatLine( v1, v2, t1, t2, u1, u2, tdiff, udiff, tvalue, curve1, cur
/** /**
* Clip curve values V2 with fatline of v * Clip curve values V2 with fat-line of v1 and vice versa
* @param {Array} v - Section of the first curve, for which we will make a fatline * @param {Array} v - Section of the first curve, for which we will make a fat-line
* @param {Number} t1 - start parameter for v in vOrg * @param {Number} t1 - start parameter for v in vOrg
* @param {Number} t2 - end parameter for v in vOrg * @param {Number} t2 - end parameter for v in vOrg
* @param {Array} v2 - Section of the second curve; we will clip this curve with the fatline of v * @param {Array} v2 - Section of the second curve; we will clip this curve with the fat-line of v
* @param {Number} u1 - start parameter for v2 in v2Org * @param {Number} u1 - start parameter for v2 in v2Org
* @param {Number} u2 - end parameter for v2 in v2Org * @param {Number} u2 - end parameter for v2 in v2Org
* @param {Array} vOrg - The original curve values for v * @param {Array} vOrg - The original curve values for v
* @param {Array} v2Org - The original curve values for v2 * @param {Array} v2Org - The original curve values for v2
* @return {[type]} * @return {[type]}
*/ */
function _clipWithFatline( v, t1, t2, v2, u1, u2, vOrg, v2Org ){ function _clipBezFatLine( v1, t1, t2, v2, u1, u2, vOrg, v2Org ){
} }
@ -187,7 +175,8 @@ function _convexhull( dq0, dq1, dq2, dq3 ){
// Check if [1/3, dq1] and [2/3, dq2] are on the same side of line [0,dq0, 1,dq3] // Check if [1/3, dq1] and [2/3, dq2] are on the same side of line [0,dq0, 1,dq3]
if( distq1 * distq2 < 0 ) { if( distq1 * distq2 < 0 ) {
// dq1 and dq2 lie on different sides on [0, q0, 1, q3] // dq1 and dq2 lie on different sides on [0, q0, 1, q3]
// Convexhull is a quadrilatteral and line [0, q0, 1, q3] is not part of the convexhull // Convexhull is a quadrilatteral and line [0, q0, 1, q3] is NOT part of the convexhull
// so we are pretty much done here.
Dt = [ Dt = [
[ 0.0, dq0, 0.3333333333333333, dq1 ], [ 0.0, dq0, 0.3333333333333333, dq1 ],
[ 0.3333333333333333, dq1, 1.0, dq3 ], [ 0.3333333333333333, dq1, 1.0, dq3 ],
@ -195,48 +184,56 @@ function _convexhull( dq0, dq1, dq2, dq3 ){
[ 1.0, dq3, 0.6666666666666666, dq2 ] [ 1.0, dq3, 0.6666666666666666, dq2 ]
]; ];
} else { } else {
// dq1 and dq2 lie on the same sides on [0, q0, 1, q3]
// Convexhull can be a triangle or a quadrilatteral and
// line [0, q0, 1, q3] is part of the convexhull.
// Check if the hull is a triangle or a quadrilatteral // Check if the hull is a triangle or a quadrilatteral
var dqmin, dqmax, dqapex1, dqapex2; var dqmin, dqmax, dqapex1, dqapex2;
distq1 = Math.abs(distq1); distq1 = Math.abs(distq1);
distq2 = Math.abs(distq2); distq2 = Math.abs(distq2);
var vqa1a2x, vqa1a2y, vqa1Maxx, vqa1Maxy, vqa1Minx, vqa1Miny;
if( distq1 > distq2 ){ if( distq1 > distq2 ){
dqapex1 = [ 1.0, dq3 ]; dqmin = [ 0.6666666666666666, dq2 ];
dqapex2 = [ 0.0, dq0 ]; dqmax = [ 0.3333333333333333, dq1 ];
dqmin = [ 0.6666666666666666, dq2 ]; // apex is dq3 and the other apex point is dq0
dqmax = [ 0.3333333333333333, dq1 ]; // vector dqapex->dqapex2 or the base vector which is already part of c-hull
vqa1a2x = 1.0, vqa1a2y = dq3 - dq0;
// vector dqapex->dqmax
vqa1Maxx = 0.6666666666666666, vqa1Maxy = dq3 - dq1;
// vector dqapex->dqmin
vqa1Minx = 0.3333333333333333, vqa1Miny = dq3 - dq2;
} else { } else {
dqapex1 = [ 0.0, dq0 ]; dqmin = [ 0.3333333333333333, dq1 ];
dqapex2 = [ 1.0, dq3 ]; dqmax = [ 0.6666666666666666, dq2 ];
dqmin = [ 0.3333333333333333, dq1 ]; // apex is dq0 in this case, and the other apex point is dq3
dqmax = [ 0.6666666666666666, dq2 ]; // vector dqapex->dqapex2 or the base vector which is already part of c-hull
vqa1a2x = -1.0, vqa1a2y = dq0 - dq3;
// vector dqapex->dqmax
vqa1Maxx = -0.6666666666666666, vqa1Maxy = dq0 - dq2;
// vector dqapex->dqmin
vqa1Minx = -0.3333333333333333, vqa1Miny = dq0 - dq1;
} }
// vector dqapex1->dqapex2
var vqa1a2x = dqapex1[0] - dqapex2[0], vqa1a2y = dqapex1[1] - dqapex2[1];
// vector dqapex1->dqmax
var vqa1Maxx = dqapex1[0] - dqmax[0], vqa1Maxy = dqapex1[1] - dqmax[1];
// vector dqapex1->dqmin
var vqa1Minx = dqapex1[0] - dqmin[0], vqa1Miny = dqapex1[1] - dqmin[1];
// compare cross products of these vectors to determine, if // compare cross products of these vectors to determine, if
// point is in triangles [ dq3, dqMax, dq0 ] or [ dq0, dqMax, dq3 ] // point is in triangles [ dq3, dqMax, dq0 ] or [ dq0, dqMax, dq3 ]
var vcrossa1a2_a1Max = vqa1a2x * vqa1Maxy - vqa1a2y * vqa1Maxx; var vcrossa1a2_a1Max = vqa1a2x * vqa1Maxy - vqa1a2y * vqa1Maxx;
var vcrossa1a2_a1Min = vqa1a2x * vqa1Miny - vqa1a2y * vqa1Minx; var vcrossa1a2_a1Min = vqa1a2x * vqa1Miny - vqa1a2y * vqa1Minx;
var vcrossa1Max_a1Min = vqa1Maxx * vqa1Miny - vqa1Maxy * vqa1Minx; var vcrossa1Max_a1Min = vqa1Maxx * vqa1Miny - vqa1Maxy * vqa1Minx;
if( vcrossa1Max_a1Min * vcrossa1a2_a1Min < 0 ){ if( vcrossa1Max_a1Min * vcrossa1a2_a1Min < 0 ){
// Point [2/3, dq2] is inside the triangle and the convex hull is a triangle // Point [2/3, dq2] is inside the triangle and the convex hull is a triangle
Dt = [ Dt = [
[ 0.0, dq0, dqmax[0], dqmax[1] ], [ 0.0, dq0, dqmax[0], dqmax[1] ],
[ dqmax[0], dqmax[1], 1.0, dq3 ], [ dqmax[0], dqmax[1], 1.0, dq3 ],
[ 1.0, dq3, 0.0, dq0 ] [ 1.0, dq3, 0.0, dq0 ]
]; ];
} else { } else {
// Convexhull is a quadrilatteral and we need all lines in the correct order where // Convexhull is a quadrilatteral and we need all lines in the correct order where
// line [0, q0, 1, q3] is part of the convex hull // line [0, q0, 1, q3] is part of the convex hull
Dt = [ Dt = [
[ 0.0, dq0, 0.3333333333333333, dq1 ], [ 0.0, dq0, 0.3333333333333333, dq1 ],
[ 0.3333333333333333, dq1, 0.6666666666666666, dq2 ], [ 0.3333333333333333, dq1, 0.6666666666666666, dq2 ],
[ 0.6666666666666666, dq2, 1.0, dq3 ], [ 0.6666666666666666, dq2, 1.0, dq3 ],
[ 1.0, dq3, 0.0, dq0 ] [ 1.0, dq3, 0.0, dq0 ]
]; ];
} }
} }
return Dt; return Dt;