static real SplineFindMinXAtY(Spline *spline,real y,real min) {
extended t,t1,t2,tbase,val;
Spline1D *xsp;
if ( y>spline->from->me.y && y>spline->from->nextcp.y &&
y>spline->to->me.y && y>spline->to->prevcp.y )
return( min );
if ( y<spline->from->me.y && y<spline->from->nextcp.y &&
y<spline->to->me.y && y<spline->to->prevcp.y )
return( min );
if ( min!=NOTREACHED ) {
if ( min<=spline->from->me.x && min<=spline->from->nextcp.x &&
min<=spline->to->me.x && min<=spline->to->prevcp.x )
return( min );
}
xsp = &spline->splines[0];
SplineFindExtrema(&spline->splines[1], &t1, &t2 );
tbase = 0;
if ( t1!=-1 ) {
t = SplineSolve(&spline->splines[1],0,t1,y);
if ( t>=0 && t<=1 ) {
val = ((xsp->a*t+xsp->b)*t+xsp->c)*t + xsp->d;
if ( min==NOTREACHED || val<min )
min = val;
}
tbase = t1;
}
if ( t2!=-1 ) {
t = SplineSolve(&spline->splines[1],tbase,t2,y);
if ( t>=0 && t<=1 ) {
val = ((xsp->a*t+xsp->b)*t+xsp->c)*t + xsp->d;
if ( min==NOTREACHED || val<min )
min = val;
}
tbase = t2;
}
t = SplineSolve(&spline->splines[1],tbase,1.0,y);
if ( t>=0 && t<=1 ) {
val = ((xsp->a*t+xsp->b)*t+xsp->c)*t + xsp->d;
if ( min==NOTREACHED || val<min )
min = val;
}
return( min );
}
static void SplineFindEdges(Spline *spline,struct charone *ch, WidthInfo *wi) {
Spline1D *xsp, *ysp;
extended t1, t2;
double t, toff, ymin, ymax;
/* first try the end points */
PtFindEdges(spline->to->me.x,spline->to->me.y,ch,wi);
PtFindEdges(spline->from->me.x,spline->from->me.y,ch,wi);
/* then try the extrema of the spline (assuming they are between t=(0,1) */
xsp = &spline->splines[0]; ysp = &spline->splines[1];
SplineFindExtrema(xsp, &t1, &t2 );
if ( t1!=-1 )
PtFindEdges( ((xsp->a*t1+xsp->b)*t1+xsp->c)*t1+xsp->d,
((ysp->a*t1+ysp->b)*t1+ysp->c)*t1+ysp->d,
ch,wi);
if ( t2!=-1 )
PtFindEdges( ((xsp->a*t2+xsp->b)*t2+xsp->c)*t2+xsp->d,
((ysp->a*t2+ysp->b)*t2+ysp->c)*t2+ysp->d,
ch,wi);
ymin = ymax = spline->from->me.y;
if ( spline->from->nextcp.y > ymax ) ymax = spline->from->nextcp.y;
if ( spline->from->nextcp.y < ymin ) ymin = spline->from->nextcp.y;
if ( spline->to->prevcp.y > ymax ) ymax = spline->to->prevcp.y;
if ( spline->to->prevcp.y < ymin ) ymin = spline->to->prevcp.y;
if ( spline->to->me.y > ymax ) ymax = spline->to->me.y;
if ( spline->to->me.y < ymin ) ymin = spline->to->me.y;
if ( ymin!=ymax ) {
toff = wi->decimation/(2*(ymax-ymin));
for ( t=toff; t<1; t+=toff ) {
PtFindEdges( ((xsp->a*t+xsp->b)*t+xsp->c)*t+xsp->d,
((ysp->a*t+ysp->b)*t+ysp->c)*t+ysp->d,
ch,wi);
}
}
}
static void AddSpline(EdgeList *es, Spline *sp ) {
real t1=2, t2=2, t;
real b2_fourac;
real fm, tm;
Spline1D *msp = &sp->splines[es->major], *osp = &sp->splines[es->other];
/* Find the points of extrema on the curve discribing y behavior */
if ( !RealNear(msp->a,0) ) {
/* cubic, possibly 2 extrema (possibly none) */
b2_fourac = 4*msp->b*msp->b - 12*msp->a*msp->c;
if ( b2_fourac>=0 ) {
b2_fourac = sqrt(b2_fourac);
t1 = CheckExtremaForSingleBitErrors(msp,(-2*msp->b - b2_fourac) / (6*msp->a));
t2 = CheckExtremaForSingleBitErrors(msp,(-2*msp->b + b2_fourac) / (6*msp->a));
if ( t1>t2 ) { real temp = t1; t1 = t2; t2 = temp; }
else if ( t1==t2 ) t2 = 2.0;
/* check for curves which have such a small slope they might */
/* as well be horizontal */
fm = es->major==1?sp->from->me.y:sp->from->me.x;
tm = es->major==1?sp->to->me.y:sp->to->me.x;
if ( fm==tm ) {
real m1, m2, d1, d2;
m1 = m2 = fm;
if ( t1>0 && t1<1 )
m1 = ((msp->a*t1+msp->b)*t1+msp->c)*t1 + msp->d;
if ( t2>0 && t2<1 )
m2 = ((msp->a*t2+msp->b)*t2+msp->c)*t2 + msp->d;
d1 = (m1-fm)*es->scale;
d2 = (m2-fm)*es->scale;
if ( d1>-.5 && d1<.5 && d2>-.5 && d2<.5 ) {
sp->ishorvert = true;
if ( es->genmajoredges )
AddMajorEdge(es,sp);
return; /* Pretend it's horizontal, ignore it */
}
}
}
} else if ( !RealNear(msp->b,0) ) {
/* Quadratic, at most one extremum */
t1 = -msp->c/(2.0*msp->b);
} else if ( !RealNear(msp->c,0) ) {
/* linear, no points of extrema */
} else {
sp->ishorvert = true;
if ( es->genmajoredges )
AddMajorEdge(es,sp);
return; /* Horizontal line, ignore it */
}
if ( RealNear(t1,0)) t1=0;
if ( RealNear(t1,1)) t1=1;
if ( RealNear(t2,0)) t2=0;
if ( RealNear(t2,1)) t2=1;
if ( RealNear(t1,t2)) t2=2;
t=0;
if ( t1>0 && t1<1 ) {
AddEdge(es,sp,0,t1);
t = t1;
}
if ( t2>0 && t2<1 ) {
AddEdge(es,sp,t,t2);
t = t2;
}
AddEdge(es,sp,t,1.0);
if ( es->interesting ) {
/* Also store up points of extrema in X as interesting (we got the endpoints, just internals now)*/
extended ot1, ot2;
int mpos;
SplineFindExtrema(osp,&ot1,&ot2);
if ( ot1>0 && ot1<1 ) {
mpos = (int) ceil( ( ((msp->a*ot1+msp->b)*ot1+msp->c)*ot1+msp->d )*es->scale-es->mmin );
es->interesting[mpos] = 1;
}
if ( ot2>0 && ot2<1 ) {
mpos = (int) ceil( ( ((msp->a*ot2+msp->b)*ot2+msp->c)*ot2+msp->d )*es->scale-es->mmin );
es->interesting[mpos] = 1;
}
}
}
