/* calculate best fit from i+.5 to j+.5. Assume i<j (cyclically).
Return 0 and set badness and parameters (alpha, beta), if
possible. Return 1 if impossible. */
static bool opti_penalty(Path pp, int i, int j, ref opti res, double opttolerance, int[] convc, double[] areac)
{
int m = pp.Curves.n;
int k, k1, k2, conv, i1;
double area, alpha, d, d1, d2;
dPoint p0, p1, p2, p3, pt;
double A, R, A1, A2, A3, A4;
double s, t;
/* check convexity, corner-freeness, and maximum bend < 179 degrees */
if (i == j)
{ /* sanity - a full loop can never be an opticurve */
return true;
}
k = i;
i1 = mod(i + 1, m);
k1 = mod(k + 1, m);
conv = convc[k1];
if (conv == 0)
{
return true;
}
d = ddist(pp.Curves.vertex[i], pp.Curves.vertex[i1]);
for (k = k1; k != j; k = k1)
{
k1 = mod(k + 1, m);
k2 = mod(k + 2, m);
if (convc[k1] != conv)
{
return true;
}
if (sign(cprod(pp.Curves.vertex[i], pp.Curves.vertex[i1], pp.Curves.vertex[k1], pp.Curves.vertex[k2])) != conv)
{
return true;
}
if (iprod1(pp.Curves.vertex[i], pp.Curves.vertex[i1], pp.Curves.vertex[k1], pp.Curves.vertex[k2]) < d * ddist(pp.Curves.vertex[k1], pp.Curves.vertex[k2]) * COS179)
{
return true;
}
}
/* the curve we're working in: */
p0 = pp.Curves.ControlPoints[mod(i, m), 2];
p1 = pp.Curves.vertex[mod(i + 1, m)];
p2 = pp.Curves.vertex[mod(j, m)];
p3 = pp.Curves.ControlPoints[mod(j, m), 2];
/* determine its area */
area = areac[j] - areac[i];
area -= dpara(pp.Curves.vertex[0], pp.Curves.ControlPoints[i, 2], pp.Curves.ControlPoints[j, 2]) / 2;
if (i >= j)
{
area += areac[m];
}
/* find intersection o of p0p1 and p2p3. Let t,s such that o =
interval(t,p0,p1) = interval(s,p3,p2). Let A be the area of the
triangle (p0,o,p3). */
A1 = dpara(p0, p1, p2);
A2 = dpara(p0, p1, p3);
A3 = dpara(p0, p2, p3);
/* A4 = dpara(p1, p2, p3); */
A4 = A1 + A3 - A2;
if (A2 == A1)
{ /* this should never happen */
return true;
}
t = A3 / (A3 - A4);
s = A2 / (A2 - A1);
A = A2 * t / 2.0;
if (A == 0.0)
{ /* this should never happen */
return true;
}
R = area / A; /* relative area */
alpha = 2 - Math.Sqrt(4 - R / 0.3); /* overall alpha for p0-o-p3 curve */
res.c = new dPoint[2];
res.c[0] = interval(t * alpha, p0, p1);
res.c[1] = interval(s * alpha, p3, p2);
res.alpha = alpha;
res.t = t;
res.s = s;
p1 = res.c[0];
p2 = res.c[1]; /* the proposed curve is now (p0,p1,p2,p3) */
res.pen = 0;
/* calculate penalty */
/* check tangency with edges */
for (k = mod(i + 1, m); k != j; k = k1)
{
k1 = mod(k + 1, m);
t = tangent(p0, p1, p2, p3, pp.Curves.vertex[k], pp.Curves.vertex[k1]);
if (t < -.5)
{
return true;
}
pt = bezier(t, p0, p1, p2, p3);
d = ddist(pp.Curves.vertex[k], pp.Curves.vertex[k1]);
if (d == 0.0)
{ /* this should never happen */
return true;
}
d1 = dpara(pp.Curves.vertex[k], pp.Curves.vertex[k1], pt) / d;
if (Math.Abs(d1) > opttolerance)
{
return true;
}
if (iprod(pp.Curves.vertex[k], pp.Curves.vertex[k1], pt) < 0 || iprod(pp.Curves.vertex[k1], pp.Curves.vertex[k], pt) < 0)
{
return true;
}
res.pen += d1 * d1;
}
/* check corners */
for (k = i; k != j; k = k1)
{
k1 = mod(k + 1, m);
t = tangent(p0, p1, p2, p3, pp.Curves.ControlPoints[k, 2], pp.Curves.ControlPoints[k1, 2]);
if (t < -.5)
{
return true;
}
pt = bezier(t, p0, p1, p2, p3);
d = ddist(pp.Curves.ControlPoints[k, 2], pp.Curves.ControlPoints[k1, 2]);
if (d == 0.0)
{ /* this should never happen */
return true;
}
d1 = dpara(pp.Curves.ControlPoints[k, 2], pp.Curves.ControlPoints[k1, 2], pt) / d;
d2 = dpara(pp.Curves.ControlPoints[k, 2], pp.Curves.ControlPoints[k1, 2], pp.Curves.vertex[k1]) / d;
d2 *= 0.75 * pp.Curves.alpha[k1];
if (d2 < 0)
{
d1 = -d1;
d2 = -d2;
}
if (d1 < d2 - opttolerance)
{
return true;
}
if (d1 < d2)
{
res.pen += (d1 - d2) * (d1 - d2);
}
}
return false;
}
/* optimize the path p, replacing sequences of Bezier segments by a
single segment when possible. Return 0 on success, 1 with errno set
on failure. */
static void opticurve(Path pp, double opttolerance)
{
int m = pp.Curves.n;
int[] pt = new int[m + 1]; /* pt[m+1] */
double[] pen = new double[m + 1]; /* pen[m+1] */
int[] len = new int[m + 1]; /* len[m+1] */
opti[] opt = new opti[m + 1]; /* opt[m+1] */
int[] convc = new int[m]; /* conv[m]: pre-computed convexities */
double[] areac = new double[m + 1]; /* cumarea[m+1]: cache for fast area computation */
int om;
int i, j;
bool r;
opti o = new opti();
dPoint p0;
int i1;
double area;
double alpha;
double[] s;
double[] t;
/* pre-calculate convexity: +1 = right turn, -1 = left turn, 0 = corner */
for (i = 0; i < m; i++)
{
if (pp.Curves.tag[i] == POTRACE_CURVETO)
{
convc[i] = sign(dpara(pp.Curves.vertex[mod(i - 1, m)], pp.Curves.vertex[i], pp.Curves.vertex[mod(i + 1, m)]));
}
else
{
convc[i] = 0;
}
}
/* pre-calculate areas */
area = 0.0;
areac[0] = 0.0;
p0 = pp.Curves.vertex[0];
for (i = 0; i < m; i++)
{
i1 = mod(i + 1, m);
if (pp.Curves.tag[i1] == POTRACE_CURVETO)
{
alpha = pp.Curves.alpha[i1];
area += 0.3 * alpha * (4 - alpha) * dpara(pp.Curves.ControlPoints[i, 2], pp.Curves.vertex[i1], pp.Curves.ControlPoints[i1, 2]) / 2;
area += dpara(p0, pp.Curves.ControlPoints[i, 2], pp.Curves.ControlPoints[i1, 2]) / 2;
}
areac[i + 1] = area;
}
pt[0] = -1;
pen[0] = 0;
len[0] = 0;
/* Fixme: we always start from a fixed point -- should find the best
curve cyclically ### */
for (j = 1; j <= m; j++)
{
/* calculate best path from 0 to j */
pt[j] = j - 1;
pen[j] = pen[j - 1];
len[j] = len[j - 1] + 1;
for (i = j - 2; i >= 0; i--)
{
r = opti_penalty(pp, i, mod(j, m), ref o, opttolerance, convc, areac);
if (r)
{
break;
}
if (len[j] > len[i] + 1 || (len[j] == len[i] + 1 && pen[j] > pen[i] + o.pen))
{
pt[j] = i;
pen[j] = pen[i] + o.pen;
len[j] = len[i] + 1;
opt[j] = o;
}
}
}
om = len[m];
pp.OptimizedCurves = new privcurve(om);
s = new double[om];
t = new double[om];
j = m;
for (i = om - 1; i >= 0; i--)
{
if (pt[j] == j - 1)
{
pp.OptimizedCurves.tag[i] = pp.Curves.tag[mod(j, m)];
pp.OptimizedCurves.ControlPoints[i, 0] = pp.Curves.ControlPoints[mod(j, m), 0];
pp.OptimizedCurves.ControlPoints[i, 1] = pp.Curves.ControlPoints[mod(j, m), 1];
pp.OptimizedCurves.ControlPoints[i, 2] = pp.Curves.ControlPoints[mod(j, m), 2];
pp.OptimizedCurves.vertex[i] = pp.Curves.vertex[mod(j, m)];
pp.OptimizedCurves.alpha[i] = pp.Curves.alpha[mod(j, m)];
pp.OptimizedCurves.alpha0[i] = pp.Curves.alpha0[mod(j, m)];
pp.OptimizedCurves.beta[i] = pp.Curves.beta[mod(j, m)];
s[i] = t[i] = 1.0;
}
else
{
pp.OptimizedCurves.tag[i] = POTRACE_CURVETO;
pp.OptimizedCurves.ControlPoints[i, 0] = opt[j].c[0];
pp.OptimizedCurves.ControlPoints[i, 1] = opt[j].c[1];
pp.OptimizedCurves.ControlPoints[i, 2] = pp.Curves.ControlPoints[mod(j, m), 2];
pp.OptimizedCurves.vertex[i] = interval(opt[j].s, pp.Curves.ControlPoints[mod(j, m), 2], pp.Curves.vertex[mod(j, m)]);
pp.OptimizedCurves.alpha[i] = opt[j].alpha;
pp.OptimizedCurves.alpha0[i] = opt[j].alpha;
s[i] = opt[j].s;
t[i] = opt[j].t;
}
j = pt[j];
}
/* calculate beta parameters */
for (i = 0; i < om; i++)
{
i1 = mod(i + 1, om);
pp.OptimizedCurves.beta[i] = s[i] / (s[i] + t[i1]);
}
}