optimized spline conversion.

diff --git a/lib/drawer.c b/lib/drawer.c
index f0d3d34..d371657 100644 (file)
--- a/lib/drawer.c
+++ b/lib/drawer.c
@@ -43,7 +43,7 @@ static char* getToken(const char**p)
     return result;
 }
 
-void draw_conicto(drawer_t*draw, FPOINT*  c, FPOINT*  to)
+void draw_conicTo(drawer_t*draw, FPOINT*  c, FPOINT*  to)
 {
     FPOINT* pos = &draw->pos;
     FPOINT c1,c2;
@@ -51,7 +51,7 @@ void draw_conicto(drawer_t*draw, FPOINT*  c, FPOINT*  to)
     c1.y = (pos->y + 2 * c->y) / 3;
     c2.x = (2 * c->x + to->x) / 3;
     c2.y = (2 * c->y + to->y) / 3;
-    draw_cubicto(draw, &c1,&c2,to);
+    draw_cubicTo(draw, &c1,&c2,to);
 
     draw->pos = *to;
 }
@@ -61,6 +61,8 @@ void draw_string(drawer_t*draw, const char*string)
     const char*p = string;
     while(*p) {
        char*token = getToken(&p);
+       if(!token || !*token) 
+           break;
        if(!strncmp(token, "moveTo", 6)) {
            FPOINT to;
            to.x = atoi(getToken(&p));
@@ -81,6 +83,18 @@ void draw_string(drawer_t*draw, const char*string)
            to.y = atoi(getToken(&p));
            draw->splineTo(draw, &mid, &to);
        }
+       else if(!strncmp(token, "cubicTo", 5)) {
+           FPOINT mid1,mid2,to;
+           mid1.x = atoi(getToken(&p));
+           mid1.y = atoi(getToken(&p));
+           mid2.x = atoi(getToken(&p));
+           mid2.y = atoi(getToken(&p));
+           to.x = atoi(getToken(&p));
+           to.y = atoi(getToken(&p));
+           draw_cubicTo(draw, &mid1, &mid2, &to);
+       }
+       else fprintf(stderr, "drawer: Warning: unknown primitive '%s'", token);
+       
        free(token);
     }
 }
@@ -105,29 +119,21 @@ struct cspline
     struct SPLINEPOINT end;
 };
 
-/* move the control point so that the spline runs through the original
-   control point */
-static void fixcp(struct qspline*s)
-{
-    struct SPLINEPOINT mid,dir;
-    mid.x = (s->end.x + s->start.x)/2;
-    mid.y = (s->end.y + s->start.y)/2;
-    dir.x = s->control.x - mid.x;
-    dir.y = s->control.y - mid.y;
-    s->control.x = mid.x + 2*dir.x;
-    s->control.y = mid.y + 2*dir.y;
-}
-
-static inline struct SPLINEPOINT cspline_getpoint(struct cspline*s, double t)
+static inline struct SPLINEPOINT cspline_getpoint(const struct cspline*s, double t)
 {
     struct SPLINEPOINT p;
-    p.x= s->end.x*t*t*t + 3*s->control2.x*t*t*(1-t) 
-           + 3*s->control1.x*t*(1-t)*(1-t) + s->start.x*(1-t)*(1-t)*(1-t);
-    p.y= s->end.y*t*t*t + 3*s->control2.y*t*t*(1-t) 
-           + 3*s->control1.y*t*(1-t)*(1-t) + s->start.y*(1-t)*(1-t)*(1-t);
+    double tt = t*t;
+    double ttt = tt*t;
+    double mt = (1-t);
+    double mtmt = mt*(1-t);
+    double mtmtmt = mtmt*(1-t);
+    p.x= s->end.x*ttt + 3*s->control2.x*tt*mt
+           + 3*s->control1.x*t*mtmt + s->start.x*mtmtmt;
+    p.y= s->end.y*ttt + 3*s->control2.y*tt*mt
+           + 3*s->control1.y*t*mtmt + s->start.y*mtmtmt;
     return p;
 }
-static struct SPLINEPOINT qspline_getpoint(struct qspline*s, double t)
+static struct SPLINEPOINT qspline_getpoint(const struct qspline*s, double t)
 {
     struct SPLINEPOINT p;
     p.x= s->end.x*t*t + 2*s->control.x*t*(1-t) + s->start.x*(1-t)*(1-t);
@@ -135,85 +141,104 @@ static struct SPLINEPOINT qspline_getpoint(struct qspline*s, double t)
     return p;
 }
 
-static struct SPLINEPOINT cspline_getderivative(struct cspline*s, double t)
+static int approximate3(const struct cspline*s, struct qspline*q, int size, double quality2)
 {
-    struct SPLINEPOINT d;
-    d.x = s->end.x*(3*t*t) + 3*s->control2.x*(2*t-3*t*t) + 
-               3*s->control1.x*(1-4*t+3*t*t) + s->start.x*(-3+6*t-3*t*t);
-    d.y = s->end.y*(3*t*t) + 3*s->control2.y*(2*t-3*t*t) + 
-               3*s->control1.y*(1-4*t+3*t*t) + s->start.y*(-3+6*t-3*t*t);
-    return d;
-}
+    unsigned int gran = 0;
+    unsigned int istep = 0x80000000;
+    unsigned int istart = 0;
+    int num = 0;
+    int level = 0;
+    
+    while(istart<0x80000000)
+    {
+       unsigned int iend = istart + istep;
+       double start = istart/(double)0x80000000;
+       double end = iend/(double)0x80000000;
+       struct qspline test;
+       double pos,qpos;
+       char left = 0,recurse=0;
+       int t;
+       int probes = 15;
 
-static int approximate2(struct cspline*s, struct qspline*q, double quality, double start, double end, int max, int depth)
-{
-    int num=0;
-    struct SPLINEPOINT qr1,qr2,cr1,cr2;
-    double dist1,dist2;
-    double qquality = quality*quality;
-    int t;
-    int recurse = 0;
-    int probes = 15;
-    struct qspline test;
-    char left = 0;
-    test.start = cspline_getpoint(s, start);
-    test.control = cspline_getpoint(s, (start+end)/2);
-    test.end = cspline_getpoint(s, end);
-    fixcp(&test);
-
-    if(start< 0.5) {
-       test.control = cspline_getderivative(s, start);
-       test.control.x *= (end-start)/2;
-       test.control.y *= (end-start)/2;
-       test.control.x += test.start.x;
-       test.control.y += test.start.y;
-    } else {
-       test.control = cspline_getderivative(s, end);
-       test.control.x *= -(end-start)/2;
-       test.control.y *= -(end-start)/2;
-       test.control.x += test.end.x;
-       test.control.y += test.end.y;
-    }
+       /* create simple approximation: a qspline which run's through the
+          qspline point at 0.5 */
+       test.start = cspline_getpoint(s, start);
+       test.control = cspline_getpoint(s, (start+end)/2);
+       test.end = cspline_getpoint(s, end);
+       /* fix the control point:
+          move it so that the new spline does runs through it */
+       test.control.x = -(test.end.x + test.start.x)/2 + 2*(test.control.x);
+       test.control.y = -(test.end.y + test.start.y)/2 + 2*(test.control.y);
 
-    for(t=0;t<probes;t++) {
-       double pos = 0.5/(probes*2)*(t*2+1);
-       double dx,dy;
-       qr1 = qspline_getpoint(&test, pos);
-       cr1 = cspline_getpoint(s, start+pos*(end-start));
+       /* depending on where we are in the spline, we either try to match
+          the left or right tangent */
+       if(start<0.5) 
+           left=1;
+       /* get derivative */
+       pos = left?start:end;
+       qpos = pos*pos;
+       test.control.x = s->end.x*(3*qpos) + 3*s->control2.x*(2*pos-3*qpos) + 
+                   3*s->control1.x*(1-4*pos+3*qpos) + s->start.x*(-3+6*pos-3*qpos);
+       test.control.y = s->end.y*(3*qpos) + 3*s->control2.y*(2*pos-3*qpos) + 
+                   3*s->control1.y*(1-4*pos+3*qpos) + s->start.y*(-3+6*pos-3*qpos);
+       if(left) {
+           test.control.x *= (end-start)/2;
+           test.control.y *= (end-start)/2;
+           test.control.x += test.start.x;
+           test.control.y += test.start.y;
+       } else {
+           test.control.x *= -(end-start)/2;
+           test.control.y *= -(end-start)/2;
+           test.control.x += test.end.x;
+           test.control.y += test.end.y;
+       }
 
-       dx = qr1.x - cr1.x;
-       dy = qr1.y - cr1.y;
-       dist1 = dx*dx+dy*dy;
+       /* measure the spline's accurancy, by taking a number of probes */
 
-       if(dist1>qquality) {
-           recurse=1;break;
-       }
-       qr2 = qspline_getpoint(&test, (1-pos));
-       cr2 = cspline_getpoint(s, start+(1-pos)*(end-start));
+       for(t=0;t<probes;t++) {
+           struct SPLINEPOINT qr1,qr2,cr1,cr2;
+           double pos = 0.5/(probes*2)*(t*2+1);
+           double dx,dy;
+           double dist1,dist2;
+           qr1 = qspline_getpoint(&test, pos);
+           cr1 = cspline_getpoint(s, start+pos*(end-start));
 
-       dx = qr2.x - cr2.x;
-       dy = qr2.y - cr2.y;
-       dist2 = dx*dx+dy*dy;
+           dx = qr1.x - cr1.x;
+           dy = qr1.y - cr1.y;
+           dist1 = dx*dx+dy*dy;
 
-       if(dist2>qquality) {
-           recurse=1;break;
+           if(dist1>quality2) {
+               recurse=1;break;
+           }
+           qr2 = qspline_getpoint(&test, (1-pos));
+           cr2 = cspline_getpoint(s, start+(1-pos)*(end-start));
+
+           dx = qr2.x - cr2.x;
+           dy = qr2.y - cr2.y;
+           dist2 = dx*dx+dy*dy;
+
+           if(dist2>quality2) {
+               recurse=1;break;
+           }
        }
-    }
 
-    if(recurse && (end-start)>1.0/120 && max-depth > 0) {
-       /* quality is too bad, split it up recursively */
-       num += approximate2(s, q, quality, start, (start+end)/2, max, depth+1);
-       q+=num;
-       max-=num;
-       num += approximate2(s, q, quality, (start+end)/2, end, max, depth+1);
-       return num;
-    } else {
-       *q = test;
-       return 1;
+       if(recurse && istep>1 && size-level > num) {
+           istep >>= 1;
+           level++;
+       } else {
+           *q++ = test;
+           num++;
+           istart += istep;
+           while(!(istart & istep)) {
+               level--;
+               istep <<= 1;
+           }
+       }
     }
+    return num;
 }
 
-void draw_cubicto(drawer_t*draw, FPOINT*  control1, FPOINT* control2, FPOINT*  to)
+void draw_cubicTo(drawer_t*draw, FPOINT*  control1, FPOINT* control2, FPOINT*  to)
 {
     struct qspline q[128];
     struct cspline c;
@@ -225,10 +250,10 @@ void draw_cubicto(drawer_t*draw, FPOINT*  control1, FPOINT* control2, FPOINT*  t
     c.control2.y = control2->y;
     c.end.x = to->x;
     c.end.y = to->y;
-    double quality = 0.8;
+    double quality = 80;
     double maxerror = (500-(quality*5)>1?500-(quality*5):1)/20.0;
 
-    int num = approximate2(&c, q, maxerror, 0.0, 1.0, 128, 0);
+    int num = approximate3(&c, q, 128, maxerror*maxerror);
     int t;
     for(t=0;t<num;t++) {
        FPOINT mid;

diff --git a/lib/drawer.h b/lib/drawer.h
index f79e6b5..7c88df5 100644 (file)
--- a/lib/drawer.h
+++ b/lib/drawer.h
@@ -45,8 +45,8 @@ typedef struct _drawer_t
 
 } drawer_t;
 
-void draw_cubicto(drawer_t*drawer, FPOINT*  control1, FPOINT* control2, FPOINT*  to);
-void draw_conicto(drawer_t*drawer, FPOINT*  control, FPOINT*  to);
+void draw_cubicTo(drawer_t*drawer, FPOINT*  control1, FPOINT* control2, FPOINT*  to);
+void draw_conicTo(drawer_t*drawer, FPOINT*  control, FPOINT*  to);
 void draw_string(drawer_t*drawer, const char*code);
 
 #endif