diff options
Diffstat (limited to 'Build/source/texk/dvisvgm/dvisvgm-1.0.1/potracelib/trace.c')
-rw-r--r-- | Build/source/texk/dvisvgm/dvisvgm-1.0.1/potracelib/trace.c | 1230 |
1 files changed, 0 insertions, 1230 deletions
diff --git a/Build/source/texk/dvisvgm/dvisvgm-1.0.1/potracelib/trace.c b/Build/source/texk/dvisvgm/dvisvgm-1.0.1/potracelib/trace.c deleted file mode 100644 index bd193f57218..00000000000 --- a/Build/source/texk/dvisvgm/dvisvgm-1.0.1/potracelib/trace.c +++ /dev/null @@ -1,1230 +0,0 @@ -/* Copyright (C) 2001-2007 Peter Selinger. - This file is part of Potrace. It is free software and it is covered - by the GNU General Public License. See the file COPYING for details. */ - -/* $Id: trace.c 147 2007-04-09 00:44:09Z selinger $ */ -/* transform jaggy paths into smooth curves */ - -#include <stdio.h> -#include <math.h> -#include <stdlib.h> -#include <string.h> - -#include "potracelib.h" -#include "curve.h" -#include "lists.h" -#include "auxiliary.h" -#include "trace.h" -#include "progress.h" - -#define INFTY 10000000 /* it suffices that this is longer than any - path; it need not be really infinite */ -#define COS179 -0.999847695156 /* the cosine of 179 degrees */ - -/* ---------------------------------------------------------------------- */ -#define SAFE_MALLOC(var, n, typ) \ - if ((var = (typ *)malloc((n)*sizeof(typ))) == NULL) goto malloc_error - -/* ---------------------------------------------------------------------- */ -/* auxiliary functions */ - -/* return a direction that is 90 degrees counterclockwise from p2-p0, - but then restricted to one of the major wind directions (n, nw, w, etc) */ -static inline point_t dorth_infty(dpoint_t p0, dpoint_t p2) { - point_t r; - - r.y = sign(p2.x-p0.x); - r.x = -sign(p2.y-p0.y); - - return r; -} - -/* return (p1-p0)x(p2-p0), the area of the parallelogram */ -static inline double dpara(dpoint_t p0, dpoint_t p1, dpoint_t p2) { - double x1, y1, x2, y2; - - x1 = p1.x-p0.x; - y1 = p1.y-p0.y; - x2 = p2.x-p0.x; - y2 = p2.y-p0.y; - - return x1*y2 - x2*y1; -} - -/* ddenom/dpara have the property that the square of radius 1 centered - at p1 intersects the line p0p2 iff |dpara(p0,p1,p2)| <= ddenom(p0,p2) */ -static inline double ddenom(dpoint_t p0, dpoint_t p2) { - point_t r = dorth_infty(p0, p2); - - return r.y*(p2.x-p0.x) - r.x*(p2.y-p0.y); -} - -/* return 1 if a <= b < c < a, in a cyclic sense (mod n) */ -static inline int cyclic(int a, int b, int c) { - if (a<=c) { - return (a<=b && b<c); - } else { - return (a<=b || b<c); - } -} - -/* determine the center and slope of the line i..j. Assume i<j. Needs - "sum" components of p to be set. */ -static void pointslope(privpath_t *pp, int i, int j, dpoint_t *ctr, dpoint_t *dir) { - /* assume i<j */ - - int n = pp->len; - sums_t *sums = pp->sums; - - double x, y, x2, xy, y2; - double k; - double a, b, c, lambda2, l; - int r=0; /* rotations from i to j */ - - while (j>=n) { - j-=n; - r+=1; - } - while (i>=n) { - i-=n; - r-=1; - } - while (j<0) { - j+=n; - r-=1; - } - while (i<0) { - i+=n; - r+=1; - } - - x = sums[j+1].x-sums[i].x+r*sums[n].x; - y = sums[j+1].y-sums[i].y+r*sums[n].y; - x2 = sums[j+1].x2-sums[i].x2+r*sums[n].x2; - xy = sums[j+1].xy-sums[i].xy+r*sums[n].xy; - y2 = sums[j+1].y2-sums[i].y2+r*sums[n].y2; - k = j+1-i+r*n; - - ctr->x = x/k; - ctr->y = y/k; - - a = (x2-(double)x*x/k)/k; - b = (xy-(double)x*y/k)/k; - c = (y2-(double)y*y/k)/k; - - lambda2 = (a+c+sqrt((a-c)*(a-c)+4*b*b))/2; /* larger e.value */ - - /* now find e.vector for lambda2 */ - a -= lambda2; - c -= lambda2; - - if (fabs(a) >= fabs(c)) { - l = sqrt(a*a+b*b); - if (l!=0) { - dir->x = -b/l; - dir->y = a/l; - } - } else { - l = sqrt(c*c+b*b); - if (l!=0) { - dir->x = -c/l; - dir->y = b/l; - } - } - if (l==0) { - dir->x = dir->y = 0; /* sometimes this can happen when k=4: - the two eigenvalues coincide */ - } -} - -/* the type of (affine) quadratic forms, represented as symmetric 3x3 - matrices. The value of the quadratic form at a vector (x,y) is v^t - Q v, where v = (x,y,1)^t. */ -typedef double quadform_t[3][3]; - -/* Apply quadratic form Q to vector w = (w.x,w.y) */ -static inline double quadform(quadform_t Q, dpoint_t w) { - double v[3]; - int i, j; - double sum; - - v[0] = w.x; - v[1] = w.y; - v[2] = 1; - sum = 0.0; - - for (i=0; i<3; i++) { - for (j=0; j<3; j++) { - sum += v[i] * Q[i][j] * v[j]; - } - } - return sum; -} - -/* calculate p1 x p2 */ -static inline int xprod(point_t p1, point_t p2) { - return p1.x*p2.y - p1.y*p2.x; -} - -/* calculate (p1-p0)x(p3-p2) */ -static inline double cprod(dpoint_t p0, dpoint_t p1, dpoint_t p2, dpoint_t p3) { - double x1, y1, x2, y2; - - x1 = p1.x - p0.x; - y1 = p1.y - p0.y; - x2 = p3.x - p2.x; - y2 = p3.y - p2.y; - - return x1*y2 - x2*y1; -} - -/* calculate (p1-p0)*(p2-p0) */ -static inline double iprod(dpoint_t p0, dpoint_t p1, dpoint_t p2) { - double x1, y1, x2, y2; - - x1 = p1.x - p0.x; - y1 = p1.y - p0.y; - x2 = p2.x - p0.x; - y2 = p2.y - p0.y; - - return x1*x2 + y1*y2; -} - -/* calculate (p1-p0)*(p3-p2) */ -static inline double iprod1(dpoint_t p0, dpoint_t p1, dpoint_t p2, dpoint_t p3) { - double x1, y1, x2, y2; - - x1 = p1.x - p0.x; - y1 = p1.y - p0.y; - x2 = p3.x - p2.x; - y2 = p3.y - p2.y; - - return x1*x2 + y1*y2; -} - -/* calculate distance between two points */ -static inline double ddist(dpoint_t p, dpoint_t q) { - return sqrt(sq(p.x-q.x)+sq(p.y-q.y)); -} - -/* calculate point of a bezier curve */ -static inline dpoint_t bezier(double t, dpoint_t p0, dpoint_t p1, dpoint_t p2, dpoint_t p3) { - double s = 1-t; - dpoint_t res; - - /* Note: a good optimizing compiler (such as gcc-3) reduces the - following to 16 multiplications, using common subexpression - elimination. */ - - res.x = s*s*s*p0.x + 3*(s*s*t)*p1.x + 3*(t*t*s)*p2.x + t*t*t*p3.x; - res.y = s*s*s*p0.y + 3*(s*s*t)*p1.y + 3*(t*t*s)*p2.y + t*t*t*p3.y; - - return res; -} - -/* calculate the point t in [0..1] on the (convex) bezier curve - (p0,p1,p2,p3) which is tangent to q1-q0. Return -1.0 if there is no - solution in [0..1]. */ -static double tangent(dpoint_t p0, dpoint_t p1, dpoint_t p2, dpoint_t p3, dpoint_t q0, dpoint_t q1) { - double A, B, C; /* (1-t)^2 A + 2(1-t)t B + t^2 C = 0 */ - double a, b, c; /* a t^2 + b t + c = 0 */ - double d, s, r1, r2; - - A = cprod(p0, p1, q0, q1); - B = cprod(p1, p2, q0, q1); - C = cprod(p2, p3, q0, q1); - - a = A - 2*B + C; - b = -2*A + 2*B; - c = A; - - d = b*b - 4*a*c; - - if (a==0 || d<0) { - return -1.0; - } - - s = sqrt(d); - - r1 = (-b + s) / (2 * a); - r2 = (-b - s) / (2 * a); - - if (r1 >= 0 && r1 <= 1) { - return r1; - } else if (r2 >= 0 && r2 <= 1) { - return r2; - } else { - return -1.0; - } -} - -/* ---------------------------------------------------------------------- */ -/* Preparation: fill in the sum* fields of a path (used for later - rapid summing). Return 0 on success, 1 with errno set on - failure. */ -static int calc_sums(privpath_t *pp) { - int i, x, y; - int n = pp->len; - - SAFE_MALLOC(pp->sums, pp->len+1, sums_t); - - /* origin */ - pp->x0 = pp->pt[0].x; - pp->y0 = pp->pt[0].y; - - /* preparatory computation for later fast summing */ - pp->sums[0].x2 = pp->sums[0].xy = pp->sums[0].y2 = pp->sums[0].x = pp->sums[0].y = 0; - for (i=0; i<n; i++) { - x = pp->pt[i].x - pp->x0; - y = pp->pt[i].y - pp->y0; - pp->sums[i+1].x = pp->sums[i].x + x; - pp->sums[i+1].y = pp->sums[i].y + y; - pp->sums[i+1].x2 = pp->sums[i].x2 + x*x; - pp->sums[i+1].xy = pp->sums[i].xy + x*y; - pp->sums[i+1].y2 = pp->sums[i].y2 + y*y; - } - return 0; - - malloc_error: - return 1; -} - -/* ---------------------------------------------------------------------- */ -/* Stage 1: determine the straight subpaths (Sec. 2.2.1). Fill in the - "lon" component of a path object (based on pt/len). For each i, - lon[i] is the furthest index such that a straight line can be drawn - from i to lon[i]. Return 1 on error with errno set, else 0. */ - -/* this algorithm depends on the fact that the existence of straight - subpaths is a triplewise property. I.e., there exists a straight - line through squares i0,...,in iff there exists a straight line - through i,j,k, for all i0<=i<j<k<=in. (Proof?) */ - -/* this implementation of calc_lon is O(n^2). It replaces an older - O(n^3) version. A "constraint" means that future points must - satisfy xprod(constraint[0], cur) >= 0 and xprod(constraint[1], - cur) <= 0. */ - -/* Remark for Potrace 1.1: the current implementation of calc_lon is - more complex than the implementation found in Potrace 1.0, but it - is considerably faster. The introduction of the "nc" data structure - means that we only have to test the constraints for "corner" - points. On a typical input file, this speeds up the calc_lon - function by a factor of 31.2, thereby decreasing its time share - within the overall Potrace algorithm from 72.6% to 7.82%, and - speeding up the overall algorithm by a factor of 3.36. On another - input file, calc_lon was sped up by a factor of 6.7, decreasing its - time share from 51.4% to 13.61%, and speeding up the overall - algorithm by a factor of 1.78. In any case, the savings are - substantial. */ - -/* returns 0 on success, 1 on error with errno set */ -static int calc_lon(privpath_t *pp) { - point_t *pt = pp->pt; - int n = pp->len; - int i, j, k, k1; - int ct[4], dir; - point_t constraint[2]; - point_t cur; - point_t off; - int *pivk = NULL; /* pivk[n] */ - int *nc = NULL; /* nc[n]: next corner */ - point_t dk; /* direction of k-k1 */ - int a, b, c, d; - - SAFE_MALLOC(pivk, n, int); - SAFE_MALLOC(nc, n, int); - - /* initialize the nc data structure. Point from each point to the - furthest future point to which it is connected by a vertical or - horizontal segment. We take advantage of the fact that there is - always a direction change at 0 (due to the path decomposition - algorithm). But even if this were not so, there is no harm, as - in practice, correctness does not depend on the word "furthest" - above. */ - k = 0; - for (i=n-1; i>=0; i--) { - if (pt[i].x != pt[k].x && pt[i].y != pt[k].y) { - k = i+1; /* necessarily i<n-1 in this case */ - } - nc[i] = k; - } - - SAFE_MALLOC(pp->lon, n, int); - - /* determine pivot points: for each i, let pivk[i] be the furthest k - such that all j with i<j<k lie on a line connecting i,k. */ - - for (i=n-1; i>=0; i--) { - ct[0] = ct[1] = ct[2] = ct[3] = 0; - - /* keep track of "directions" that have occurred */ - dir = (3+3*(pt[mod(i+1,n)].x-pt[i].x)+(pt[mod(i+1,n)].y-pt[i].y))/2; - ct[dir]++; - - constraint[0].x = 0; - constraint[0].y = 0; - constraint[1].x = 0; - constraint[1].y = 0; - - /* find the next k such that no straight line from i to k */ - k = nc[i]; - k1 = i; - while (1) { - - dir = (3+3*sign(pt[k].x-pt[k1].x)+sign(pt[k].y-pt[k1].y))/2; - ct[dir]++; - - /* if all four "directions" have occurred, cut this path */ - if (ct[0] && ct[1] && ct[2] && ct[3]) { - pivk[i] = k1; - goto foundk; - } - - cur.x = pt[k].x - pt[i].x; - cur.y = pt[k].y - pt[i].y; - - /* see if current constraint is violated */ - if (xprod(constraint[0], cur) < 0 || xprod(constraint[1], cur) > 0) { - goto constraint_viol; - } - - /* else, update constraint */ - if (abs(cur.x) <= 1 && abs(cur.y) <= 1) { - /* no constraint */ - } else { - off.x = cur.x + ((cur.y>=0 && (cur.y>0 || cur.x<0)) ? 1 : -1); - off.y = cur.y + ((cur.x<=0 && (cur.x<0 || cur.y<0)) ? 1 : -1); - if (xprod(constraint[0], off) >= 0) { - constraint[0] = off; - } - off.x = cur.x + ((cur.y<=0 && (cur.y<0 || cur.x<0)) ? 1 : -1); - off.y = cur.y + ((cur.x>=0 && (cur.x>0 || cur.y<0)) ? 1 : -1); - if (xprod(constraint[1], off) <= 0) { - constraint[1] = off; - } - } - k1 = k; - k = nc[k1]; - if (!cyclic(k,i,k1)) { - break; - } - } - constraint_viol: - /* k1 was the last "corner" satisfying the current constraint, and - k is the first one violating it. We now need to find the last - point along k1..k which satisfied the constraint. */ - dk.x = sign(pt[k].x-pt[k1].x); - dk.y = sign(pt[k].y-pt[k1].y); - cur.x = pt[k1].x - pt[i].x; - cur.y = pt[k1].y - pt[i].y; - /* find largest integer j such that xprod(constraint[0], cur+j*dk) - >= 0 and xprod(constraint[1], cur+j*dk) <= 0. Use bilinearity - of xprod. */ - a = xprod(constraint[0], cur); - b = xprod(constraint[0], dk); - c = xprod(constraint[1], cur); - d = xprod(constraint[1], dk); - /* find largest integer j such that a+j*b>=0 and c+j*d<=0. This - can be solved with integer arithmetic. */ - j = INFTY; - if (b<0) { - j = floordiv(a,-b); - } - if (d>0) { - j = min(j, floordiv(-c,d)); - } - pivk[i] = mod(k1+j,n); - foundk: - ; - } /* for i */ - - /* clean up: for each i, let lon[i] be the largest k such that for - all i' with i<=i'<k, i'<k<=pivk[i']. */ - - j=pivk[n-1]; - pp->lon[n-1]=j; - for (i=n-2; i>=0; i--) { - if (cyclic(i+1,pivk[i],j)) { - j=pivk[i]; - } - pp->lon[i]=j; - } - - for (i=n-1; cyclic(mod(i+1,n),j,pp->lon[i]); i--) { - pp->lon[i] = j; - } - - free(pivk); - free(nc); - return 0; - - malloc_error: - free(pivk); - free(nc); - return 1; -} - - -/* ---------------------------------------------------------------------- */ -/* Stage 2: calculate the optimal polygon (Sec. 2.2.2-2.2.4). */ - -/* Auxiliary function: calculate the penalty of an edge from i to j in - the given path. This needs the "lon" and "sum*" data. */ - -static double penalty3(privpath_t *pp, int i, int j) { - int n = pp->len; - point_t *pt = pp->pt; - sums_t *sums = pp->sums; - - /* assume 0<=i<j<=n */ - double x, y, x2, xy, y2; - double k; - double a, b, c, s; - double px, py, ex, ey; - - int r=0; /* rotations from i to j */ - - if (j>=n) { - j-=n; - r+=1; - } - - x = sums[j+1].x-sums[i].x+r*sums[n].x; - y = sums[j+1].y-sums[i].y+r*sums[n].y; - x2 = sums[j+1].x2-sums[i].x2+r*sums[n].x2; - xy = sums[j+1].xy-sums[i].xy+r*sums[n].xy; - y2 = sums[j+1].y2-sums[i].y2+r*sums[n].y2; - k = j+1-i+r*n; - - px = (pt[i].x+pt[j].x)/2.0-pt[0].x; - py = (pt[i].y+pt[j].y)/2.0-pt[0].y; - ey = (pt[j].x-pt[i].x); - ex = -(pt[j].y-pt[i].y); - - a = ((x2-2*x*px)/k+px*px); - b = ((xy-x*py-y*px)/k+px*py); - c = ((y2-2*y*py)/k+py*py); - - s = ex*ex*a + 2*ex*ey*b + ey*ey*c; - - return sqrt(s); -} - -/* find the optimal polygon. Fill in the m and po components. Return 1 - on failure with errno set, else 0. Non-cyclic version: assumes i=0 - is in the polygon. Fixme: ### implement cyclic version. */ -static int bestpolygon(privpath_t *pp) -{ - int i, j, m, k; - int n = pp->len; - double *pen = NULL; /* pen[n+1]: penalty vector */ - int *prev = NULL; /* prev[n+1]: best path pointer vector */ - int *clip0 = NULL; /* clip0[n]: longest segment pointer, non-cyclic */ - int *clip1 = NULL; /* clip1[n+1]: backwards segment pointer, non-cyclic */ - int *seg0 = NULL; /* seg0[m+1]: forward segment bounds, m<=n */ - int *seg1 = NULL; /* seg1[m+1]: backward segment bounds, m<=n */ - double thispen; - double best; - int c; - - SAFE_MALLOC(pen, n+1, double); - SAFE_MALLOC(prev, n+1, int); - SAFE_MALLOC(clip0, n, int); - SAFE_MALLOC(clip1, n+1, int); - SAFE_MALLOC(seg0, n+1, int); - SAFE_MALLOC(seg1, n+1, int); - - /* calculate clipped paths */ - for (i=0; i<n; i++) { - c = mod(pp->lon[mod(i-1,n)]-1,n); - if (c == i) { - c = mod(i+1,n); - } - if (c < i) { - clip0[i] = n; - } else { - clip0[i] = c; - } - } - - /* calculate backwards path clipping, non-cyclic. j <= clip0[i] iff - clip1[j] <= i, for i,j=0..n. */ - j = 1; - for (i=0; i<n; i++) { - while (j <= clip0[i]) { - clip1[j] = i; - j++; - } - } - - /* calculate seg0[j] = longest path from 0 with j segments */ - i = 0; - for (j=0; i<n; j++) { - seg0[j] = i; - i = clip0[i]; - } - seg0[j] = n; - m = j; - - /* calculate seg1[j] = longest path to n with m-j segments */ - i = n; - for (j=m; j>0; j--) { - seg1[j] = i; - i = clip1[i]; - } - seg1[0] = 0; - - /* now find the shortest path with m segments, based on penalty3 */ - /* note: the outer 2 loops jointly have at most n interations, thus - the worst-case behavior here is quadratic. In practice, it is - close to linear since the inner loop tends to be short. */ - pen[0]=0; - for (j=1; j<=m; j++) { - for (i=seg1[j]; i<=seg0[j]; i++) { - best = -1; - for (k=seg0[j-1]; k>=clip1[i]; k--) { - thispen = penalty3(pp, k, i) + pen[k]; - if (best < 0 || thispen < best) { - prev[i] = k; - best = thispen; - } - } - pen[i] = best; - } - } - - pp->m = m; - SAFE_MALLOC(pp->po, m, int); - - /* read off shortest path */ - for (i=n, j=m-1; i>0; j--) { - i = prev[i]; - pp->po[j] = i; - } - - free(pen); - free(prev); - free(clip0); - free(clip1); - free(seg0); - free(seg1); - return 0; - - malloc_error: - free(pen); - free(prev); - free(clip0); - free(clip1); - free(seg0); - free(seg1); - return 1; -} - -/* ---------------------------------------------------------------------- */ -/* Stage 3: vertex adjustment (Sec. 2.3.1). */ - -/* Adjust vertices of optimal polygon: calculate the intersection of - the two "optimal" line segments, then move it into the unit square - if it lies outside. Return 1 with errno set on error; 0 on - success. */ - -static int adjust_vertices(privpath_t *pp) { - int m = pp->m; - int *po = pp->po; - int n = pp->len; - point_t *pt = pp->pt; - int x0 = pp->x0; - int y0 = pp->y0; - - dpoint_t *ctr = NULL; /* ctr[m] */ - dpoint_t *dir = NULL; /* dir[m] */ - quadform_t *q = NULL; /* q[m] */ - double v[3]; - double d; - int i, j, k, l; - dpoint_t s; - int r; - - SAFE_MALLOC(ctr, m, dpoint_t); - SAFE_MALLOC(dir, m, dpoint_t); - SAFE_MALLOC(q, m, quadform_t); - - r = privcurve_init(&pp->curve, m); - if (r) { - goto malloc_error; - } - - /* calculate "optimal" point-slope representation for each line - segment */ - for (i=0; i<m; i++) { - j = po[mod(i+1,m)]; - j = mod(j-po[i],n)+po[i]; - pointslope(pp, po[i], j, &ctr[i], &dir[i]); - } - - /* represent each line segment as a singular quadratic form; the - distance of a point (x,y) from the line segment will be - (x,y,1)Q(x,y,1)^t, where Q=q[i]. */ - for (i=0; i<m; i++) { - d = sq(dir[i].x) + sq(dir[i].y); - if (d == 0.0) { - for (j=0; j<3; j++) { - for (k=0; k<3; k++) { - q[i][j][k] = 0; - } - } - } else { - v[0] = dir[i].y; - v[1] = -dir[i].x; - v[2] = - v[1] * ctr[i].y - v[0] * ctr[i].x; - for (l=0; l<3; l++) { - for (k=0; k<3; k++) { - q[i][l][k] = v[l] * v[k] / d; - } - } - } - } - - /* now calculate the "intersections" of consecutive segments. - Instead of using the actual intersection, we find the point - within a given unit square which minimizes the square distance to - the two lines. */ - for (i=0; i<m; i++) { - quadform_t Q; - dpoint_t w; - double dx, dy; - double det; - double min, cand; /* minimum and candidate for minimum of quad. form */ - double xmin, ymin; /* coordinates of minimum */ - int z; - - /* let s be the vertex, in coordinates relative to x0/y0 */ - s.x = pt[po[i]].x-x0; - s.y = pt[po[i]].y-y0; - - /* intersect segments i-1 and i */ - - j = mod(i-1,m); - - /* add quadratic forms */ - for (l=0; l<3; l++) { - for (k=0; k<3; k++) { - Q[l][k] = q[j][l][k] + q[i][l][k]; - } - } - - while(1) { - /* minimize the quadratic form Q on the unit square */ - /* find intersection */ - -#ifdef HAVE_GCC_LOOP_BUG - /* work around gcc bug #12243 */ - free(NULL); -#endif - - det = Q[0][0]*Q[1][1] - Q[0][1]*Q[1][0]; - if (det != 0.0) { - w.x = (-Q[0][2]*Q[1][1] + Q[1][2]*Q[0][1]) / det; - w.y = ( Q[0][2]*Q[1][0] - Q[1][2]*Q[0][0]) / det; - break; - } - - /* matrix is singular - lines are parallel. Add another, - orthogonal axis, through the center of the unit square */ - if (Q[0][0]>Q[1][1]) { - v[0] = -Q[0][1]; - v[1] = Q[0][0]; - } else if (Q[1][1]) { - v[0] = -Q[1][1]; - v[1] = Q[1][0]; - } else { - v[0] = 1; - v[1] = 0; - } - d = sq(v[0]) + sq(v[1]); - v[2] = - v[1] * s.y - v[0] * s.x; - for (l=0; l<3; l++) { - for (k=0; k<3; k++) { - Q[l][k] += v[l] * v[k] / d; - } - } - } - dx = fabs(w.x-s.x); - dy = fabs(w.y-s.y); - if (dx <= .5 && dy <= .5) { - pp->curve.vertex[i].x = w.x+x0; - pp->curve.vertex[i].y = w.y+y0; - continue; - } - - /* the minimum was not in the unit square; now minimize quadratic - on boundary of square */ - min = quadform(Q, s); - xmin = s.x; - ymin = s.y; - - if (Q[0][0] == 0.0) { - goto fixx; - } - for (z=0; z<2; z++) { /* value of the y-coordinate */ - w.y = s.y-0.5+z; - w.x = - (Q[0][1] * w.y + Q[0][2]) / Q[0][0]; - dx = fabs(w.x-s.x); - cand = quadform(Q, w); - if (dx <= .5 && cand < min) { - min = cand; - xmin = w.x; - ymin = w.y; - } - } - fixx: - if (Q[1][1] == 0.0) { - goto corners; - } - for (z=0; z<2; z++) { /* value of the x-coordinate */ - w.x = s.x-0.5+z; - w.y = - (Q[1][0] * w.x + Q[1][2]) / Q[1][1]; - dy = fabs(w.y-s.y); - cand = quadform(Q, w); - if (dy <= .5 && cand < min) { - min = cand; - xmin = w.x; - ymin = w.y; - } - } - corners: - /* check four corners */ - for (l=0; l<2; l++) { - for (k=0; k<2; k++) { - w.x = s.x-0.5+l; - w.y = s.y-0.5+k; - cand = quadform(Q, w); - if (cand < min) { - min = cand; - xmin = w.x; - ymin = w.y; - } - } - } - - pp->curve.vertex[i].x = xmin + x0; - pp->curve.vertex[i].y = ymin + y0; - continue; - } - - free(ctr); - free(dir); - free(q); - return 0; - - malloc_error: - free(ctr); - free(dir); - free(q); - return 1; -} - -/* ---------------------------------------------------------------------- */ -/* Stage 4: smoothing and corner analysis (Sec. 2.3.3) */ - -/* Always succeeds and returns 0 */ -static int smooth(privcurve_t *curve, int sign, double alphamax) { - int m = curve->n; - - int i, j, k; - double dd, denom, alpha; - dpoint_t p2, p3, p4; - - if (sign == '-') { - /* reverse orientation of negative paths */ - for (i=0, j=m-1; i<j; i++, j--) { - dpoint_t tmp; - tmp = curve->vertex[i]; - curve->vertex[i] = curve->vertex[j]; - curve->vertex[j] = tmp; - } - } - - /* examine each vertex and find its best fit */ - for (i=0; i<m; i++) { - j = mod(i+1, m); - k = mod(i+2, m); - p4 = interval(1/2.0, curve->vertex[k], curve->vertex[j]); - - denom = ddenom(curve->vertex[i], curve->vertex[k]); - if (denom != 0.0) { - dd = dpara(curve->vertex[i], curve->vertex[j], curve->vertex[k]) / denom; - dd = fabs(dd); - alpha = dd>1 ? (1 - 1.0/dd) : 0; - alpha = alpha / 0.75; - } else { - alpha = 4/3.0; - } - curve->alpha0[j] = alpha; /* remember "original" value of alpha */ - - if (alpha > alphamax) { /* pointed corner */ - curve->tag[j] = POTRACE_CORNER; - curve->c[j][1] = curve->vertex[j]; - curve->c[j][2] = p4; - } else { - if (alpha < 0.55) { - alpha = 0.55; - } else if (alpha > 1) { - alpha = 1; - } - p2 = interval(.5+.5*alpha, curve->vertex[i], curve->vertex[j]); - p3 = interval(.5+.5*alpha, curve->vertex[k], curve->vertex[j]); - curve->tag[j] = POTRACE_CURVETO; - curve->c[j][0] = p2; - curve->c[j][1] = p3; - curve->c[j][2] = p4; - } - curve->alpha[j] = alpha; /* store the "cropped" value of alpha */ - curve->beta[j] = 0.5; - } - curve->alphacurve = 1; - - return 0; -} - -/* ---------------------------------------------------------------------- */ -/* Stage 5: Curve optimization (Sec. 2.4) */ - -/* a private type for the result of opti_penalty */ -struct opti_s { - double pen; /* penalty */ - dpoint_t c[2]; /* curve parameters */ - double t, s; /* curve parameters */ - double alpha; /* curve parameter */ -}; -typedef struct opti_s opti_t; - -/* 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(privpath_t *pp, int i, int j, opti_t *res, double opttolerance, int *convc, double *areac) { - int m = pp->curve.n; - int k, k1, k2, conv, i1; - double area, alpha, d, d1, d2; - dpoint_t 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 1; - } - - k = i; - i1 = mod(i+1, m); - k1 = mod(k+1, m); - conv = convc[k1]; - if (conv == 0) { - return 1; - } - d = ddist(pp->curve.vertex[i], pp->curve.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(pp->curve.vertex[i], pp->curve.vertex[i1], pp->curve.vertex[k1], pp->curve.vertex[k2])) != conv) { - return 1; - } - if (iprod1(pp->curve.vertex[i], pp->curve.vertex[i1], pp->curve.vertex[k1], pp->curve.vertex[k2]) < d * ddist(pp->curve.vertex[k1], pp->curve.vertex[k2]) * COS179) { - return 1; - } - } - - /* the curve we're working in: */ - p0 = pp->curve.c[mod(i,m)][2]; - p1 = pp->curve.vertex[mod(i+1,m)]; - p2 = pp->curve.vertex[mod(j,m)]; - p3 = pp->curve.c[mod(j,m)][2]; - - /* determine its area */ - area = areac[j] - areac[i]; - area -= dpara(pp->curve.vertex[0], pp->curve.c[i][2], pp->curve.c[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 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 - 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]; - 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->curve.vertex[k], pp->curve.vertex[k1]); - if (t<-.5) { - return 1; - } - pt = bezier(t, p0, p1, p2, p3); - d = ddist(pp->curve.vertex[k], pp->curve.vertex[k1]); - if (d == 0.0) { /* this should never happen */ - return 1; - } - d1 = dpara(pp->curve.vertex[k], pp->curve.vertex[k1], pt) / d; - if (fabs(d1) > opttolerance) { - return 1; - } - if (iprod(pp->curve.vertex[k], pp->curve.vertex[k1], pt) < 0 || iprod(pp->curve.vertex[k1], pp->curve.vertex[k], pt) < 0) { - return 1; - } - res->pen += sq(d1); - } - - /* check corners */ - for (k=i; k!=j; k=k1) { - k1 = mod(k+1,m); - t = tangent(p0, p1, p2, p3, pp->curve.c[k][2], pp->curve.c[k1][2]); - if (t<-.5) { - return 1; - } - pt = bezier(t, p0, p1, p2, p3); - d = ddist(pp->curve.c[k][2], pp->curve.c[k1][2]); - if (d == 0.0) { /* this should never happen */ - return 1; - } - d1 = dpara(pp->curve.c[k][2], pp->curve.c[k1][2], pt) / d; - d2 = dpara(pp->curve.c[k][2], pp->curve.c[k1][2], pp->curve.vertex[k1]) / d; - d2 *= 0.75 * pp->curve.alpha[k1]; - if (d2 < 0) { - d1 = -d1; - d2 = -d2; - } - if (d1 < d2 - opttolerance) { - return 1; - } - if (d1 < d2) { - res->pen += sq(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 int opticurve(privpath_t *pp, double opttolerance) { - int m = pp->curve.n; - int *pt = NULL; /* pt[m+1] */ - double *pen = NULL; /* pen[m+1] */ - int *len = NULL; /* len[m+1] */ - opti_t *opt = NULL; /* opt[m+1] */ - int om; - int i,j,r; - opti_t o; - dpoint_t p0; - int i1; - double area; - double alpha; - double *s = NULL; - double *t = NULL; - - int *convc = NULL; /* conv[m]: pre-computed convexities */ - double *areac = NULL; /* cumarea[m+1]: cache for fast area computation */ - - SAFE_MALLOC(pt, m+1, int); - SAFE_MALLOC(pen, m+1, double); - SAFE_MALLOC(len, m+1, int); - SAFE_MALLOC(opt, m+1, opti_t); - SAFE_MALLOC(convc, m, int); - SAFE_MALLOC(areac, m+1, double); - - /* pre-calculate convexity: +1 = right turn, -1 = left turn, 0 = corner */ - for (i=0; i<m; i++) { - if (pp->curve.tag[i] == POTRACE_CURVETO) { - convc[i] = sign(dpara(pp->curve.vertex[mod(i-1,m)], pp->curve.vertex[i], pp->curve.vertex[mod(i+1,m)])); - } else { - convc[i] = 0; - } - } - - /* pre-calculate areas */ - area = 0.0; - areac[0] = 0.0; - p0 = pp->curve.vertex[0]; - for (i=0; i<m; i++) { - i1 = mod(i+1, m); - if (pp->curve.tag[i1] == POTRACE_CURVETO) { - alpha = pp->curve.alpha[i1]; - area += 0.3*alpha*(4-alpha)*dpara(pp->curve.c[i][2], pp->curve.vertex[i1], pp->curve.c[i1][2])/2; - area += dpara(p0, pp->curve.c[i][2], pp->curve.c[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), &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]; - r = privcurve_init(&pp->ocurve, om); - if (r) { - goto malloc_error; - } - SAFE_MALLOC(s, om, double); - SAFE_MALLOC(t, om, double); - - j = m; - for (i=om-1; i>=0; i--) { - if (pt[j]==j-1) { - pp->ocurve.tag[i] = pp->curve.tag[mod(j,m)]; - pp->ocurve.c[i][0] = pp->curve.c[mod(j,m)][0]; - pp->ocurve.c[i][1] = pp->curve.c[mod(j,m)][1]; - pp->ocurve.c[i][2] = pp->curve.c[mod(j,m)][2]; - pp->ocurve.vertex[i] = pp->curve.vertex[mod(j,m)]; - pp->ocurve.alpha[i] = pp->curve.alpha[mod(j,m)]; - pp->ocurve.alpha0[i] = pp->curve.alpha0[mod(j,m)]; - pp->ocurve.beta[i] = pp->curve.beta[mod(j,m)]; - s[i] = t[i] = 1.0; - } else { - pp->ocurve.tag[i] = POTRACE_CURVETO; - pp->ocurve.c[i][0] = opt[j].c[0]; - pp->ocurve.c[i][1] = opt[j].c[1]; - pp->ocurve.c[i][2] = pp->curve.c[mod(j,m)][2]; - pp->ocurve.vertex[i] = interval(opt[j].s, pp->curve.c[mod(j,m)][2], pp->curve.vertex[mod(j,m)]); - pp->ocurve.alpha[i] = opt[j].alpha; - pp->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); - pp->ocurve.beta[i] = s[i] / (s[i] + t[i1]); - } - pp->ocurve.alphacurve = 1; - - free(pt); - free(pen); - free(len); - free(opt); - free(s); - free(t); - free(convc); - free(areac); - return 0; - - malloc_error: - free(pt); - free(pen); - free(len); - free(opt); - free(s); - free(t); - free(convc); - free(areac); - return 1; -} - -/* ---------------------------------------------------------------------- */ - -#define TRY(x) if (x) goto try_error - -/* return 0 on success, 1 on error with errno set. */ -int process_path(path_t *plist, const potrace_param_t *param, progress_t *progress) { - path_t *p; - double nn = 0, cn = 0; - - if (progress->callback) { - /* precompute task size for progress estimates */ - nn = 0; - list_forall (p, plist) { - nn += p->priv->len; - } - cn = 0; - } - - /* call downstream function with each path */ - list_forall (p, plist) { - TRY(calc_sums(p->priv)); - TRY(calc_lon(p->priv)); - TRY(bestpolygon(p->priv)); - TRY(adjust_vertices(p->priv)); - TRY(smooth(&p->priv->curve, p->sign, param->alphamax)); - if (param->opticurve) { - TRY(opticurve(p->priv, param->opttolerance)); - p->priv->fcurve = &p->priv->ocurve; - } else { - p->priv->fcurve = &p->priv->curve; - } - privcurve_to_curve(p->priv->fcurve, &p->curve); - - if (progress->callback) { - cn += p->priv->len; - progress_update(cn/nn, progress); - } - } - - progress_update(1.0, progress); - - return 0; - - try_error: - return 1; -} |