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);
}
}
}
void
spiro_to_bpath(const spiro_seg *s, int n, bezctx *bc)
{
int i;
int nsegs = s[n - 1].ty == '}' ? n - 1 : n;
for (i = 0; i < nsegs; i++) {
double x0 = s[i].x;
double y0 = s[i].y;
double x1 = s[i + 1].x;
double y1 = s[i + 1].y;
if (i == 0)
bezctx_moveto(bc, x0, y0, s[0].ty == '{');
bezctx_mark_knot(bc, i);
spiro_seg_to_bpath(s[i].ks, x0, y0, x1, y1, bc, 0);
}
}
void
spiro_to_bpath(const spiro_seg *s, int n, bezctx *bc)
{
int i, nsegs;
double x0, y0, x1, y1;
if (s==NULL || n <= 0 || bc==NULL) return;
nsegs = s[n - 1].ty == '}' ? n - 1 : n;
for (i = 0; i < nsegs; i++) {
x0 = s[i].x; x1 = s[i + 1].x;
y0 = s[i].y; y1 = s[i + 1].y;
if (i == 0)
bezctx_moveto(bc, x0, y0, s[0].ty == '{');
bezctx_mark_knot(bc, i);
spiro_seg_to_bpath(s[i].ks, x0, y0, x1, y1, bc, 0);
}
}
