optimized spline approximation

diff --git a/lib/gfxtools.c b/lib/gfxtools.c
index 938f6e4..ec98609 100644 (file)
--- a/lib/gfxtools.c
+++ b/lib/gfxtools.c
@@ -411,7 +411,7 @@ static int approximate3(const cspline_t*s, qspline_t*q, int size, double quality
            test.control.y += test.end.y;
        }
 
-#define PROBES
+//#define PROBES
 #ifdef PROBES
        /* measure the spline's accurancy, by taking a number of probes */
        for(t=0;t<probes;t++) {
@@ -444,16 +444,21 @@ static int approximate3(const cspline_t*s, qspline_t*q, int size, double quality
 
        /* convert control point representation to 
           d*x^3 + c*x^2 + b*x + a */
-
-       /* FIXME: we need to do this for the subspline between [start,end],
-          not [0,1] */
        dx= s->end.x  - s->control2.x*3 + s->control1.x*3 - s->start.x;
        dy= s->end.y  - s->control2.y*3 + s->control1.y*3 - s->start.y;
        
+       /* we need to do this for the subspline between [start,end], not [0,1] 
+          as a transformation of t->a*t+b does nothing to highest coefficient
+          of the spline except multiply it with a^3, we just need to modify
+          d here. */
+       {double m = end-start;
+        dx*=m*m*m;
+        dy*=m*m*m;
+       }
+       
        /* use the integral over (f(x)-g(x))^2 between 0 and 1
           to measure the approximation quality. 
-          (it boils down to const*d^2)
-        */
+          (it boils down to const*d^2) */
        recurse = (dx*dx + dy*dy > quality2);
 #endif