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#define __Geom_PATH_C__
#include "path.h"
static void
nr_curve_bbox(Geom::Point const p000, Geom::Point const p001,
Geom::Point const p011, Geom::Point const p111,
Geom::Rect r)
{
using Geom::X;
using Geom::Y;
for(unsigned dim = 0; dim < 2; dim++)
nr_curve_bbox(p000[dim], p001[dim],
p011[dim], p111[dim],
bbox.x0, bbox.x1);
}
/* Fast bbox calculation */
/* Thanks to Nathan Hurst for suggesting it */
static void
nr_curve_bbox (Geom::Coord x000, Geom::Coord x001, Geom::Coord x011, Geom::Coord x111, Geom::Coord lo, Geom::Coord hi)
{
Geom::Coord a, b, c, D;
lo = (Geom::Coord) MIN (lo, x111);
hi = (Geom::Coord) MAX (hi, x111);
/*
* xttt = s * (s * (s * x000 + t * x001) + t * (s * x001 + t * x011)) + t * (s * (s * x001 + t * x011) + t * (s * x011 + t * x111))
* xttt = s * (s2 * x000 + s * t * x001 + t * s * x001 + t2 * x011) + t * (s2 * x001 + s * t * x011 + t * s * x011 + t2 * x111)
* xttt = s * (s2 * x000 + 2 * st * x001 + t2 * x011) + t * (s2 * x001 + 2 * st * x011 + t2 * x111)
* xttt = s3 * x000 + 2 * s2t * x001 + st2 * x011 + s2t * x001 + 2st2 * x011 + t3 * x111
* xttt = s3 * x000 + 3s2t * x001 + 3st2 * x011 + t3 * x111
* xttt = s3 * x000 + (1 - s) 3s2 * x001 + (1 - s) * (1 - s) * 3s * x011 + (1 - s) * (1 - s) * (1 - s) * x111
* xttt = s3 * x000 + (3s2 - 3s3) * x001 + (3s - 6s2 + 3s3) * x011 + (1 - 2s + s2 - s + 2s2 - s3) * x111
* xttt = (x000 - 3 * x001 + 3 * x011 - x111) * s3 +
* ( 3 * x001 - 6 * x011 + 3 * x111) * s2 +
* ( 3 * x011 - 3 * x111) * s +
* ( x111)
* xttt' = (3 * x000 - 9 * x001 + 9 * x011 - 3 * x111) * s2 +
* ( 6 * x001 - 12 * x011 + 6 * x111) * s +
* ( 3 * x011 - 3 * x111)
*/
a = 3 * x000 - 9 * x001 + 9 * x011 - 3 * x111;
b = 6 * x001 - 12 * x011 + 6 * x111;
c = 3 * x011 - 3 * x111;
/*
* s = (-b +/- sqrt (b * b - 4 * a * c)) / 2 * a;
*/
if (fabs (a) < Geom_EPSILON) {
/* s = -c / b */
if (fabs (b) > Geom_EPSILON) {
double s, t, xttt;
s = -c / b;
if ((s > 0.0) && (s < 1.0)) {
t = 1.0 - s;
xttt = s * s * s * x000 + 3 * s * s * t * x001 + 3 * s * t * t * x011 + t * t * t * x111;
lo = (float) MIN (lo, xttt);
hi = (float) MAX (hi, xttt);
}
}
} else {
/* s = (-b +/- sqrt (b * b - 4 * a * c)) / 2 * a; */
D = b * b - 4 * a * c;
if (D >= 0.0) {
Geom::Coord d, s, t, xttt;
/* Have solution */
d = sqrt (D);
s = (-b + d) / (2 * a);
if ((s > 0.0) && (s < 1.0)) {
t = 1.0 - s;
xttt = s * s * s * x000 + 3 * s * s * t * x001 + 3 * s * t * t * x011 + t * t * t * x111;
lo = (Geom::Coord) MIN (lo, xttt);
hi = (Geom::Coord) MAX (hi, xttt);
}
s = (-b - d) / (2 * a);
if ((s > 0.0) && (s < 1.0)) {
t = 1.0 - s;
xttt = s * s * s * x000 + 3 * s * s * t * x001 + 3 * s * t * t * x011 + t * t * t * x111;
lo = (Geom::Coord) MIN (lo, xttt);
hi = (Geom::Coord) MAX (hi, xttt);
}
}
}
}
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