hpgs/lib/hpgsbezier.c

41     at point \c i of \c path at curve parameter \c t.
43 void hpgs_bezier_path_delta(const hpgs_paint_path *path, int i,
51   p->x = 3.0* ((path->points[i+1].p.x-path->points[i].p.x)*tm*tm+
52 	       2.0 * (path->points[i+2].p.x-path->points[i+1].p.x) * tm*tp+
53 	       (path->points[i+3].p.x-path->points[i+2].p.x) * tp*tp);
55   p->y = 3.0 * ((path->points[i+1].p.y-path->points[i].p.y)*tm*tm+
56 		2.0 * (path->points[i+2].p.y-path->points[i+1].p.y) * tm*tp+
57 		(path->points[i+3].p.y-path->points[i+2].p.y) * tp*tp);
61     at point \c i of \c path at curve parameter \c t.
63 double hpgs_bezier_path_delta_x(const hpgs_paint_path *path, int i, double t)
70   return 3.0* ((path->points[i+1].p.x-path->points[i].p.x)*tm*tm+
71 	       2.0 * (path->points[i+2].p.x-path->points[i+1].p.x) * tm*tp+
72 	       (path->points[i+3].p.x-path->points[i+2].p.x) * tp*tp);
76     at point \c i of \c path at curve parameter \c t.
78 double hpgs_bezier_path_delta_y(const hpgs_paint_path *path, int i, double t)
85   return 3.0* ((path->points[i+1].p.y-path->points[i].p.y)*tm*tm+
86 	       2.0 * (path->points[i+2].p.y-path->points[i+1].p.y) * tm*tp+
87 	       (path->points[i+3].p.y-path->points[i+2].p.y) * tp*tp);
91     at point \c i of \c path at curve parameter \c t.
103 void hpgs_bezier_path_tangent(const hpgs_paint_path *path, int i,
107   hpgs_bezier_path_delta(path,i,t,p);
116         hpgs_bezier_path_point(path,i,t-1.0e-4,&p1);
118         hpgs_bezier_path_point(path,i,t,&p1);
121         hpgs_bezier_path_point(path,i,t+1.0e-4,p);
123         hpgs_bezier_path_point(path,i,t,p);
199 void hpgs_bezier_path_singularities(const hpgs_paint_path *path, int i,
205     (path->points[i+1].p.x-path->points[i].p.x)*(path->points[i+2].p.y-path->points[i+1].p.y) -
206     (path->points[i+1].p.y-path->points[i].p.y)*(path->points[i+2].p.x-path->points[i+1].p.x);
209     (path->points[i+1].p.x-path->points[i].p.x)*(path->points[i+3].p.y-path->points[i+2].p.y) -
210     (path->points[i+1].p.y-path->points[i].p.y)*(path->points[i+3].p.x-path->points[i+2].p.x);
213     (path->points[i+2].p.x-path->points[i+1].p.x)*(path->points[i+3].p.y-path->points[i+2].p.y) -
214     (path->points[i+2].p.y-path->points[i+1].p.y)*(path->points[i+3].p.x-path->points[i+2].p.x);
268 void hpgs_bezier_path_to_quadratic(const hpgs_paint_path *path, int i,
274     (path->points[i+1].p.x-path->points[i].p.x)*(path->points[i+2].p.y-path->points[i+1].p.y) -
275     (path->points[i+1].p.y-path->points[i].p.y)*(path->points[i+2].p.x-path->points[i+1].p.x);
278     (path->points[i+1].p.x-path->points[i].p.x)*(path->points[i+3].p.y-path->points[i+2].p.y) -
279     (path->points[i+1].p.y-path->points[i].p.y)*(path->points[i+3].p.x-path->points[i+2].p.x);
282     (path->points[i+2].p.x-path->points[i+1].p.x)*(path->points[i+3].p.y-path->points[i+2].p.y) -
283     (path->points[i+2].p.y-path->points[i+1].p.y)*(path->points[i+3].p.x-path->points[i+2].p.x);
331   xmax = xmin = path->points[i].p.x;
332   if (path->points[i+1].p.x > xmax) xmax = path->points[i+1].p.x;
333   if (path->points[i+2].p.x > xmax) xmax = path->points[i+2].p.x;
334   if (path->points[i+3].p.x > xmax) xmax = path->points[i+3].p.x;
335   if (path->points[i+1].p.x < xmin) xmin = path->points[i+1].p.x;
336   if (path->points[i+2].p.x < xmin) xmin = path->points[i+2].p.x;
337   if (path->points[i+3].p.x < xmin) xmin = path->points[i+3].p.x;
339   ymax = ymin = path->points[i].p.y;
340   if (path->points[i+1].p.y > ymax) ymax = path->points[i+1].p.y;
341   if (path->points[i+2].p.y > ymax) ymax = path->points[i+2].p.y;
342   if (path->points[i+3].p.y > ymax) ymax = path->points[i+3].p.y;
343   if (path->points[i+1].p.y < ymin) ymin = path->points[i+1].p.y;
344   if (path->points[i+2].p.y < ymin) ymin = path->points[i+2].p.y;
345   if (path->points[i+3].p.y < ymin) ymin = path->points[i+3].p.y;
374       hpgs_bezier_path_point(path,i,tpart[ipart],&p1);
375       hpgs_bezier_path_tangent(path,i,tpart[ipart],1,1.0e-3,&d1);
384           hpgs_bezier_path_point(path,i,t,&p2);
385           hpgs_bezier_path_tangent(path,i,t,j<n_splines ? 0 : -1,1.0e-3,&d2);
400 static double bezier_dl(const hpgs_paint_path *path, int i, double t)
407   return 3.0*hypot((path->points[i+1].p.x-path->points[i].p.x)*tm*tm+
408 		   2.0 * (path->points[i+2].p.x-path->points[i+1].p.x) * tm*tp+
409 		   (path->points[i+3].p.x-path->points[i+2].p.x) * tp*tp,
411 		   (path->points[i+1].p.y-path->points[i].p.y)*tm*tm+
412 		   2.0 * (path->points[i+2].p.y-path->points[i+1].p.y) * tm*tp+
413 		   (path->points[i+3].p.y-path->points[i+2].p.y) * tp*tp
424                              const hpgs_paint_path *path, int i)
428   b->dl[0] = bezier_dl(path,i,-0.5);
437       b->dl[ip] = bezier_dl(path,i,(ip-8.0)*0.0625);
439       dlm0 = bezier_dl(path,i,(ip-(8.5+0.22360679774997896964))*0.0625);
440       dlm1 = bezier_dl(path,i,(ip-(8.5-0.22360679774997896964))*0.0625);
474 double hpgs_bezier_path_xmin (const hpgs_paint_path *path, int i)
477     path->points[i].p.x < path->points[i+1].p.x ?
478     path->points[i].p.x : path->points[i+1].p.x;
481     path->points[i+2].p.x < path->points[i+3].p.x ?
482     path->points[i+2].p.x : path->points[i+3].p.x;
489 double hpgs_bezier_path_xmax (const hpgs_paint_path *path, int i)
492     path->points[i].p.x > path->points[i+1].p.x ?
493     path->points[i].p.x : path->points[i+1].p.x;
496     path->points[i+2].p.x > path->points[i+3].p.x ?
497     path->points[i+2].p.x : path->points[i+3].p.x;
504 double hpgs_bezier_path_ymin (const hpgs_paint_path *path, int i)
507     path->points[i].p.y < path->points[i+1].p.y ?
508     path->points[i].p.y : path->points[i+1].p.y;
511     path->points[i+2].p.y < path->points[i+3].p.y ?
512     path->points[i+2].p.y : path->points[i+3].p.y;
519 double hpgs_bezier_path_ymax (const hpgs_paint_path *path, int i)
522     path->points[i].p.y > path->points[i+1].p.y ?
523     path->points[i].p.y : path->points[i+1].p.y;
526     path->points[i+2].p.y > path->points[i+3].p.y ?
527     path->points[i+2].p.y : path->points[i+3].p.y;
533 double hpgs_bezier_path_x (const hpgs_paint_path *path, int i, double t)
541     path->points[i].p.x *tm*tm*tm +
542     3.0 * tm*tp * (path->points[i+1].p.x * tm + path->points[i+2].p.x * tp) +
543     path->points[i+3].p.x * tp*tp*tp;
547 double hpgs_bezier_path_y (const hpgs_paint_path *path, int i, double t)
555     path->points[i].p.y *tm*tm*tm +
556     3.0 * tm*tp * (path->points[i+1].p.y * tm + path->points[i+2].p.y * tp) +
557     path->points[i+3].p.y * tp*tp*tp;
561     at point \c i of \c path at curve parameter \c t.
563 void hpgs_bezier_path_point(const hpgs_paint_path *path, int i,
572     path->points[i].p.x *tm*tm*tm +
573     3.0 * tm*tp * (path->points[i+1].p.x * tm + path->points[i+2].p.x * tp) +
574     path->points[i+3].p.x * tp*tp*tp;
577     path->points[i].p.y *tm*tm*tm +
578     3.0 * tm*tp * (path->points[i+1].p.y * tm + path->points[i+2].p.y * tp) +
579     path->points[i+3].p.y * tp*tp*tp;