static void
spiro_seg_to_bpath(const double ks[4],
double x0, double y0, double x1, double y1,
bezctx *bc, int depth)
{
double bend = fabs(ks[0]) + fabs(.5 * ks[1]) + fabs(.125 * ks[2]) +
fabs((1./48) * ks[3]);
if (!bend > 1e-8) {
bezctx_lineto(bc, x1, y1);
} else {
double seg_ch = hypot(x1 - x0, y1 - y0);
double seg_th = atan2(y1 - y0, x1 - x0);
double xy[2];
double ch, th;
double scale, rot;
double th_even, th_odd;
double ul, vl;
double ur, vr;
integrate_spiro(ks, xy);
ch = hypot(xy[0], xy[1]);
th = atan2(xy[1], xy[0]);
scale = seg_ch / ch;
rot = seg_th - th;
if (depth > 5 || bend < 1.) {
th_even = (1./384) * ks[3] + (1./8) * ks[1] + rot;
th_odd = (1./48) * ks[2] + .5 * ks[0];
ul = (scale * (1./3)) * cos(th_even - th_odd);
vl = (scale * (1./3)) * sin(th_even - th_odd);
ur = (scale * (1./3)) * cos(th_even + th_odd);
vr = (scale * (1./3)) * sin(th_even + th_odd);
bezctx_curveto(bc, x0 + ul, y0 + vl, x1 - ur, y1 - vr, x1, y1);
} else {
/* subdivide */
double ksub[4];
double thsub;
double xysub[2];
double xmid, ymid;
double cth, sth;
ksub[0] = .5 * ks[0] - .125 * ks[1] + (1./64) * ks[2] - (1./768) * ks[3];
ksub[1] = .25 * ks[1] - (1./16) * ks[2] + (1./128) * ks[3];
ksub[2] = .125 * ks[2] - (1./32) * ks[3];
ksub[3] = (1./16) * ks[3];
thsub = rot - .25 * ks[0] + (1./32) * ks[1] - (1./384) * ks[2] + (1./6144) * ks[3];
cth = .5 * scale * cos(thsub);
sth = .5 * scale * sin(thsub);
integrate_spiro(ksub, xysub);
xmid = x0 + cth * xysub[0] - sth * xysub[1];
ymid = y0 + cth * xysub[1] + sth * xysub[0];
spiro_seg_to_bpath(ksub, x0, y0, xmid, ymid, bc, depth + 1);
ksub[0] += .25 * ks[1] + (1./384) * ks[3];
ksub[1] += .125 * ks[2];
ksub[2] += (1./16) * ks[3];
spiro_seg_to_bpath(ksub, xmid, ymid, x1, y1, bc, depth + 1);
}
}
}
static void
spiro_seg_to_bpath0(const double ks[4], double *dm,
double x0, double y0, double x1, double y1,
bezctx *bc, int ncq, int depth)
{
double bend, seg_ch, seg_th, ch, th, scale, rot;
double th_even, th_odd, ul, vl, ur, vr;
double thsub, xmid, ymid, cth, sth;
double ksub[4], xysub[2], xy[2];
bend = fabs(ks[0]) + fabs(.5 * ks[1]) + fabs(.125 * ks[2]) +
fabs((1./48) * ks[3]);
if (bend <= 1e-8) {
if (depth >= 0 || depth < -4) {
#ifdef VERBOSE
printf("...to next knot point...\n");
#endif
bezctx_lineto(bc, dm[3], dm[4]);
} else {
bezctx_lineto(bc, (x1 * dm[0] + dm[1]), (y1 * dm[0] + dm[2]));
}
} else {
seg_ch = hypot(x1 - x0, y1 - y0);
seg_th = atan2(y1 - y0, x1 - x0);
integrate_spiro(ks, xy, N_IS);
ch = hypot(xy[0], xy[1]);
th = atan2(xy[1], xy[0]);
scale = seg_ch / ch;
rot = seg_th - th;
if (abs(depth) > 5 || bend < 1.) {
th_even = (1./384) * ks[3] + (1./8) * ks[1] + rot;
th_odd = (1./48) * ks[2] + .5 * ks[0];
ul = (scale * (1./3)) * cos(th_even - th_odd);
vl = (scale * (1./3)) * sin(th_even - th_odd);
ur = (scale * (1./3)) * cos(th_even + th_odd);
vr = (scale * (1./3)) * sin(th_even + th_odd);
if (depth >= 0 || depth < -4) {
#ifdef VERBOSE
printf("...to next knot point...\n");
#endif
bezctx_curveto(bc, ((x0 + ul) * dm[0] + dm[1]), ((y0 + vl) * dm[0] + dm[2]),
((x1 - ur) * dm[0] + dm[1]), ((y1 - vr) * dm[0] + dm[2]),
dm[3], dm[4]);
} else {
bezctx_curveto(bc, ((x0 + ul) * dm[0] + dm[1]), ((y0 + vl) * dm[0] + dm[2]),
((x1 - ur) * dm[0] + dm[1]), ((y1 - vr) * dm[0] + dm[2]),
(x1 * dm[0] + dm[1]), (y1 * dm[0] + dm[2]));
}
} else {
/* subdivide */
#ifdef VERBOSE
printf("...subdivide curve...\n");
#endif
ksub[0] = .5 * ks[0] - .125 * ks[1] + (1./64) * ks[2] - (1./768) * ks[3];
ksub[1] = .25 * ks[1] - (1./16) * ks[2] + (1./128) * ks[3];
ksub[2] = .125 * ks[2] - (1./32) * ks[3];
ksub[3] = (1./16) * ks[3];
thsub = rot - .25 * ks[0] + (1./32) * ks[1] - (1./384) * ks[2] + (1./6144) * ks[3];
cth = .5 * scale * cos(thsub);
sth = .5 * scale * sin(thsub);
integrate_spiro(ksub, xysub, N_IS);
xmid = x0 + cth * xysub[0] - sth * xysub[1];
ymid = y0 + cth * xysub[1] + sth * xysub[0];
spiro_seg_to_bpath0(ksub, dm, x0, y0, xmid, ymid, bc, ncq, -(abs(depth) + 1));
ksub[0] += .25 * ks[1] + (1./384) * ks[3];
ksub[1] += .125 * ks[2];
ksub[2] += (1./16) * ks[3];
spiro_seg_to_bpath0(ksub, dm, xmid, ymid, x1, y1, bc, ncq, (depth >= 0 ? ++depth : --depth));
}
}
}