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Efficient calculation of tmax, tmin

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hkrish 2013-05-14 22:34:06 +02:00
parent ebbe2d7569
commit 0a9a0bdb9b
1 changed files with 13 additions and 35 deletions
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48
fatline/Intersect.js
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@ -196,14 +196,18 @@ function _clipBezierFatLine( v1, v2, v2t ){
if( dmin > maxdist || dmax < mindist ){ if( dmin > maxdist || dmax < mindist ){
return 0; return 0;
} }
if( dq3 < dq0 ){
var tmp = dmin;
dmin = dmax;
dmax = tmp;
}
// Calculate the convex hull for non-parametric bezier curve D(ti, di(t)) // Calculate the convex hull for non-parametric bezier curve D(ti, di(t))
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
// for the coorresponding t values (tmin, tmax): // for the coorresponding t values (tmin, tmax):
// Portions of curve v2 before tmin and after tmax can safely be clipped away // Portions of curve v2 before tmin and after tmax can safely be clipped away
// TODO: try to calculate tmin and tmax directly here var tmaxdmin = -Infinity, ixd, ixdx, i, len;
var tmindmin = Infinity, tmaxdmin = -Infinity, var tmin = Infinity, tmax = -Infinity;
tmindmax = Infinity, tmaxdmax = -Infinity, ixd, ixdx, i, len;
// var dmina = [0, dmin, 2, dmin]; // var dmina = [0, dmin, 2, dmin];
// var dmaxa = [0, dmax, 2, dmax]; // var dmaxa = [0, dmax, 2, dmax];
for (i = 0, len = Dt.length; i < len; i++) { for (i = 0, len = Dt.length; i < len; i++) {
@ -213,49 +217,23 @@ function _clipBezierFatLine( v1, v2, v2t ){
ixd = Line.intersectRaw( Dtl[0], Dtl[1], Dtl[2], Dtl[3], 0, dmin, 2, dmin, false); ixd = Line.intersectRaw( Dtl[0], Dtl[1], Dtl[2], Dtl[3], 0, dmin, 2, dmin, false);
if( ixd ){ if( ixd ){
ixdx = ixd[0]; ixdx = ixd[0];
tmindmin = ( ixdx < tmindmin )? ixdx : tmindmin; if ( ixdx < tmin ) tmin = ixdx;
tmaxdmin = ( ixdx > tmaxdmin )? ixdx : tmaxdmin; if ( ixdx > tmaxdmin ) tmaxdmin = ixdx;
} }
// ixd = _intersectLines( Dtl, dmaxa); // ixd = _intersectLines( Dtl, dmaxa);
ixd = Line.intersectRaw( Dtl[0], Dtl[1], Dtl[2], Dtl[3], 0, dmax, 2, dmax, false); ixd = Line.intersectRaw( Dtl[0], Dtl[1], Dtl[2], Dtl[3], 0, dmax, 2, dmax, false);
if( ixd ){ if( ixd ){
ixdx = ixd[0]; ixdx = ixd[0];
tmindmax = ( ixdx < tmindmax )? ixdx : tmindmax; if( ixdx > tmax ) tmax = ixdx;
tmaxdmax = ( ixdx > tmaxdmax )? ixdx : tmaxdmax; if( ixdx < tmin ) tmin = 0;
} }
} }
// Return the parameter values for v2 for which we can be sure that the // Return the parameter values for v2 for which we can be sure that the
// intersection with v1 lies within. // intersection with v1 lies within.
var tmin, tmax; if(tmin === Infinity || tmax === -Infinity){
if(tmindmin === Infinity || tmaxdmin === -Infinity || tmindmax === Infinity || tmaxdmax === -Infinity){
return -1; return -1;
} }
if( tmaxdmin > tmax ) tmax = 1;
if( dq3 > dq0 ){
// if dmin or dmax doesnot intersect with the convexhull, reset the parameter limits
// if( tmindmin === Infinity ) tmindmin = 0;
// if( tmaxdmin === -Infinity ) tmaxdmin = 0;
// if( tmindmax === Infinity ) tmindmax = 1;
// if( tmaxdmax === -Infinity ) tmaxdmax =1;
tmin = Math.min( tmindmin, tmaxdmin );
tmax = Math.max( tmindmax, tmaxdmax );
if( Math.min( tmindmax, tmaxdmax ) < tmin )
tmin = 0;
if( Math.max( tmindmin, tmaxdmin ) > tmax )
tmax = 1;
}else{
// if dmin or dmax doesnot intersect with the convexhull, reset the parameter limits
// if( tmindmin === Infinity ) tmindmin =1;
// if( tmaxdmin === -Infinity ) tmaxdmin =1;
// if( tmindmax === Infinity ) tmindmax = 0;
// if( tmaxdmax === -Infinity ) tmaxdmax = 0;
tmax = Math.max( tmindmin, tmaxdmin );
tmin = Math.min( tmindmax, tmaxdmax );
if( Math.min( tmindmin, tmaxdmin ) < tmin )
tmin = 0;
if( Math.max( tmindmax, tmaxdmax ) > tmax )
tmax = 1;
}
// Debug: Plot the non-parametric graph and hull // Debug: Plot the non-parametric graph and hull
// plotD_vs_t( 500, 110, Dt, [dq0, dq1, dq2, dq3], v1, dmin, dmax, tmin, tmax, 1.0 / ( tmax - tmin + 0.3 ) ) // plotD_vs_t( 500, 110, Dt, [dq0, dq1, dq2, dq3], v1, dmin, dmax, tmin, tmax, 1.0 / ( tmax - tmin + 0.3 ) )
// tmin and tmax are within the range (0, 1). We need to project it to the original // tmin and tmax are within the range (0, 1). We need to project it to the original