/* ---------------------------------------------------------------------- */
/* Stage 5: Curve optimization (Sec. 2.4) */
/* 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 int opti_penalty(Path path, int i, int j, Opti res, double opttolerance,
int[] convc, double[] areac)
{
int m = path.curve.n;
privcurve curve = path.curve;
dPoint[] vertex = curve.vertex;
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,
s, t;
/* check convexity, corner-freeness, and maximum bend < 179 degrees */
if (i == j)
{ /* sanity - a full loop can never be an opticurve */
return(1);
}
k = i;
i1 = mod(i + 1, m);
k1 = mod(k + 1, m);
conv = convc[k1];
if (conv == 0)
{
return(1);
}
d = ddist(vertex[i], vertex[i1]);
for (k = k1; k != j; k = k1)
{
k1 = mod(k + 1, m);
k2 = mod(k + 2, m);
if (convc[k1] != conv)
{
return(1);
}
if (sign(cprod(vertex[i], vertex[i1], vertex[k1], vertex[k2])) !=
conv)
{
return(1);
}
if (iprod1(vertex[i], vertex[i1], vertex[k1], vertex[k2]) <
d * ddist(vertex[k1], vertex[k2]) * -0.999847695156)
{
return(1);
}
}
/* the curve we're working in: */
p0 = curve.c[mod(i, m) * 3 + 2].copy();
p1 = vertex[mod(i + 1, m)].copy();
p2 = vertex[mod(j, m)].copy();
p3 = curve.c[mod(j, m) * 3 + 2].copy();
/* determine its area */
area = areac[j] - areac[i];
area -= dpara(vertex[0], curve.c[i * 3 + 2], curve.c[j * 3 + 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 = A1 + A3 - A2;
if (A2 == A1)
{ /* this should never happen */
return(1);
}
t = A3 / (A3 - A4);
s = A2 / (A2 - A1);
A = A2 * t / 2.0;
if (A == 0.0)
{
/* this should never happen */
return(1);
}
R = area / A; /* relative area */
alpha = 2 - Math.Sqrt(4 - R / 0.3); /* overall alpha for p0-o-p3 curve */
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].copy();
p2 = res.c[1].copy(); /* 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, vertex[k], vertex[k1]);
if (t < -0.5)
{
return(1);
}
pt = bezier(t, p0, p1, p2, p3);
d = ddist(vertex[k], vertex[k1]);
if (d == 0.0)
{
/* this should never happen */
return(1);
}
d1 = dpara(vertex[k], vertex[k1], pt) / d;
if (Math.Abs(d1) > opttolerance)
{
return(1);
}
if (iprod(vertex[k], vertex[k1], pt) < 0 ||
iprod(vertex[k1], vertex[k], pt) < 0)
{
return(1);
}
res.pen += d1 * d1;
}
/* check corners */
for (k = i; k != j; k = k1)
{
k1 = mod(k + 1, m);
t = tangent(p0, p1, p2, p3, curve.c[k * 3 + 2], curve.c[k1 * 3 + 2]);
if (t < -0.5)
{
return(1);
}
pt = bezier(t, p0, p1, p2, p3);
d = ddist(curve.c[k * 3 + 2], curve.c[k1 * 3 + 2]);
if (d == 0.0)
{
/* this should never happen */
return(1);
}
d1 = dpara(curve.c[k * 3 + 2], curve.c[k1 * 3 + 2], pt) / d;
d2 = dpara(curve.c[k * 3 + 2], curve.c[k1 * 3 + 2], vertex[k1]) / d;
d2 *= 0.75 * curve.alpha[k1];
if (d2 < 0)
{
d1 = -d1;
d2 = -d2;
}
if (d1 < d2 - opttolerance)
{
return(1);
}
if (d1 < d2)
{
res.pen += (d1 - d2) * (d1 - d2);
}
}
return(0);
}
/* 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 path, double opttolerance)
{
privcurve curve = path.curve;
int m = curve.n;
dPoint[] vert = curve.vertex;
int[] pt = new int[m + 1];
double[] pen = new double[m + 1];
int[] len = new int[m + 1];
Opti[] opt = new Opti[m + 1];
Opti o = new Opti();
int om, i, j, r;
dPoint p0;
int i1;
double area, alpha;
privcurve ocurve;
int[] convc = new int[m]; /* conv[m]: pre-computed convexities */
double[] areac = new double[m + 1];
/* pre-calculate convexity: +1 = right turn, -1 = left turn, 0 = corner */
for (i = 0; i < m; i++)
{
if (curve.tag[i] == POTRACE_CURVETO)
{
convc[i] = sign(dpara(vert[mod(i - 1, m)], vert[i], vert[mod(i + 1, m)]));
}
else
{
convc[i] = 0;
}
}
/* pre-calculate areas */
area = 0.0;
areac[0] = 0.0;
p0 = curve.vertex[0];
for (i = 0; i < m; i++)
{
i1 = mod(i + 1, m);
if (curve.tag[i1] == POTRACE_CURVETO)
{
alpha = curve.alpha[i1];
area += 0.3 * alpha * (4 - alpha) *
dpara(curve.c[i * 3 + 2], vert[i1], curve.c[i1 * 3 + 2]) / 2;
area += dpara(p0, curve.c[i * 3 + 2], curve.c[i1 * 3 + 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(path, i, mod(j, m), o, opttolerance, convc,
areac);
if (r == 1)
{
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;
o = new Opti();
}
}
}
om = len[m];
ocurve = new privcurve(om);
double[] s = new double[om];
double[] t = new double[om];
j = m;
for (i = om - 1; i >= 0; i--)
{
if (pt[j] == j - 1)
{
ocurve.tag[i] = curve.tag[mod(j, m)];
ocurve.c[i * 3 + 0] = curve.c[mod(j, m) * 3 + 0];
ocurve.c[i * 3 + 1] = curve.c[mod(j, m) * 3 + 1];
ocurve.c[i * 3 + 2] = curve.c[mod(j, m) * 3 + 2];
ocurve.vertex[i] = curve.vertex[mod(j, m)];
ocurve.alpha[i] = curve.alpha[mod(j, m)];
ocurve.alpha0[i] = curve.alpha0[mod(j, m)];
ocurve.beta[i] = curve.beta[mod(j, m)];
s[i] = t[i] = 1.0;
}
else
{
ocurve.tag[i] = POTRACE_CURVETO;
ocurve.c[i * 3 + 0] = opt[j].c[0];
ocurve.c[i * 3 + 1] = opt[j].c[1];
ocurve.c[i * 3 + 2] = curve.c[mod(j, m) * 3 + 2];
ocurve.vertex[i] = interval(opt[j].s, curve.c[mod(j, m) * 3 + 2],
vert[mod(j, m)]);
ocurve.alpha[i] = opt[j].alpha;
ocurve.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);
ocurve.beta[i] = s[i] / (s[i] + t[i1]);
}
ocurve.alphacurve = 1;
path.curve = ocurve;
}
