Fixed spline error calculation. New effort to compute spline initial/final slopes even for degenerate splines, (degenerate splines are still broken somewhere though).

Imakefile

@@ -26,6 +26,7 @@ SRCS =	xr.c \
 	xrcolor.c \
 	xrfiller.c \
 	xrgstate.c \
+	xrmisc.c \
 	xrpath.c \
 	xrpen.c \
 	xrpolygon.c \
@@ -40,6 +41,7 @@ OBJS =	xr.o \
 	xrcolor.o \
 	xrfiller.o \
 	xrgstate.o \
+	xrmisc.o \
 	xrpath.o \
 	xrpen.o \
 	xrpolygon.o \

src/xrgstate.c

@@ -95,12 +95,21 @@ XrGStateInitCopy(XrGState *gstate, XrGState *other)
     XrSurfaceSetSolidColor(&gstate->src, &gstate->color, gstate->solidFormat);
 
     err = XrPathInitCopy(&gstate->path, &other->path);
-    if (err) {
-	if (gstate->dashes) {    
-	    free (gstate->dashes);
-	    gstate->dashes = 0;
-	}
-    }
+    if (err)
+	goto CLEANUP_DASHES;
+
+    err = XrPenInitCopy(&gstate->pen_regular, &other->pen_regular);
+    if (err)
+	goto CLEANUP_PATH;
+
+    return err;
+
+  CLEANUP_PATH:
+    XrPathDeinit(&gstate->path);
+  CLEANUP_DASHES:
+    free (gstate->dashes);
+    gstate->dashes = NULL;
+
     return err;
 }
 
@@ -117,8 +126,10 @@ XrGStateDeinit(XrGState *gstate)
 
     XrPenDeinit(&gstate->pen_regular);
 
-    if (gstate->dashes)
+    if (gstate->dashes) {
 	free (gstate->dashes);
+	gstate->dashes = NULL;
+    }
 }
 
 void

src/xrint.h

@@ -122,20 +122,23 @@ typedef struct _XrPolygon {
     int closed;
 } XrPolygon;
 
-typedef struct _XrSpline {
-    XPointFixed a, b, c, d;
-
-    int num_pts;
-    int pts_size;
-    XPointFixed *pts;
-} XrSpline;
-
 typedef struct _XrSlopeFixed
 {
     XFixed dx;
     XFixed dy;
 } XrSlopeFixed;
 
+typedef struct _XrSpline {
+    XPointFixed a, b, c, d;
+
+    XrSlopeFixed initial_slope;
+    XrSlopeFixed final_slope;
+
+    int num_pts;
+    int pts_size;
+    XPointFixed *pts;
+} XrSpline;
+
 typedef enum _XrPenVertexTag {
     XrPenVertexTagNone,
     XrPenVertexTagForward,
@@ -580,5 +583,10 @@ XrTrapsTessellateRectangle (XrTraps *traps, XPointFixed q[4]);
 XrError
 XrTrapsTessellatePolygon (XrTraps *traps, XrPolygon *poly, int winding);
 
+/* xrmisc.c */
+
+void
+ComputeSlope(XPointFixed *a, XPointFixed *b, XrSlopeFixed *slope);
+
 #endif
 

src/xrmisc.c

@@ -0,0 +1,34 @@
+/*
+ * $XFree86: $
+ *
+ * Copyright © 2002 Carl D. Worth
+ *
+ * Permission to use, copy, modify, distribute, and sell this software
+ * and its documentation for any purpose is hereby granted without
+ * fee, provided that the above copyright notice appear in all copies
+ * and that both that copyright notice and this permission notice
+ * appear in supporting documentation, and that the name of Carl
+ * D. Worth not be used in advertising or publicity pertaining to
+ * distribution of the software without specific, written prior
+ * permission.  Carl D. Worth makes no representations about the
+ * suitability of this software for any purpose.  It is provided "as
+ * is" without express or implied warranty.
+ *
+ * CARL D. WORTH DISCLAIMS ALL WARRANTIES WITH REGARD TO THIS
+ * SOFTWARE, INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY AND
+ * FITNESS, IN NO EVENT SHALL CARL D. WORTH BE LIABLE FOR ANY SPECIAL,
+ * INDIRECT OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES WHATSOEVER
+ * RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN ACTION
+ * OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR
+ * IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
+ */
+
+#include "xrint.h"
+
+void
+ComputeSlope(XPointFixed *a, XPointFixed *b, XrSlopeFixed *slope)
+{
+    slope->dx = b->x - a->x;
+    slope->dy = b->y - a->y;
+}
+

src/xrpath.c

@@ -221,7 +221,6 @@ _XrPathOpBufCreate(void)
 static void
 _XrPathOpBufDestroy(XrPathOpBuf *op)
 {
-    op->num_ops = 0;
     free(op);
 }
 
@@ -249,7 +248,6 @@ _XrPathArgBufCreate(void)
 static void
 _XrPathArgBufDestroy(XrPathArgBuf *arg)
 {
-    arg->num_pts = 0;
     free(arg);
 }
 

src/xrpen.c

@@ -31,9 +31,6 @@ _XrPenVerticesNeeded(double radius, double tolerance, XrTransform *matrix);
 static void
 _XrPenComputeSlopes(XrPen *pen);
 
-static void
-_FindSlope(XPointFixed *a, XPointFixed *b, XrSlopeFixed *slope);
-
 static int
 _SlopeClockwise(XrSlopeFixed *a, XrSlopeFixed *b);
 
@@ -231,18 +228,11 @@ _XrPenComputeSlopes(XrPen *pen)
 	v = &pen->vertex[i];
 	next = &pen->vertex[(i + 1) % pen->num_vertices];
 
-	_FindSlope(&prev->pt, &v->pt, &v->slope_cw);
-	_FindSlope(&v->pt, &next->pt, &v->slope_ccw);
+	ComputeSlope(&prev->pt, &v->pt, &v->slope_cw);
+	ComputeSlope(&v->pt, &next->pt, &v->slope_ccw);
     }
 }
 
-static void
-_FindSlope(XPointFixed *a, XPointFixed *b, XrSlopeFixed *slope)
-{
-    slope->dx = b->x - a->x;
-    slope->dy = b->y - a->y;
-}
-
 static int
 _SlopeClockwise(XrSlopeFixed *a, XrSlopeFixed *b)
 {
@@ -283,12 +273,14 @@ _XrPenStrokeSplineHalf(XrPen *pen, XrSpline *spline, XrPenVertexTag dir, XrPolyg
 	start = 0;
 	stop = num_pts;
 	step = 1;
-	_FindSlope(&spline->c, &spline->d, &final_slope);
+	final_slope = spline->final_slope;
     } else {
 	start = num_pts - 1;
 	stop = -1;
 	step = -1;
-	_FindSlope(&spline->b, &spline->a, &final_slope);
+	final_slope = spline->initial_slope;
+	final_slope.dx = -final_slope.dx; 
+	final_slope.dy = -final_slope.dy; 
     }
 
     i = start;
@@ -302,7 +294,7 @@ _XrPenStrokeSplineHalf(XrPen *pen, XrSpline *spline, XrPenVertexTag dir, XrPolyg
 	if (i + step == stop)
 	    slope = final_slope;
 	else
-	    _FindSlope(&pt[i], &pt[i+step], &slope);
+	    ComputeSlope(&pt[i], &pt[i+step], &slope);
 	if (_SlopeCounterClockwise(&slope, &pen->vertex[active].slope_ccw)) {
 	    if (++active == pen->num_vertices)
 		active = 0;

src/xrpolygon.c

@@ -56,6 +56,7 @@ XrPolygonDeinit(XrPolygon *polygon)
 {
     if (polygon->edges_size) {
 	free(polygon->edges);
+	polygon->edges = NULL;
 	polygon->edges_size = 0;
 	polygon->num_edges = 0;
     }

src/xrspline.c

@@ -38,7 +38,7 @@ static void
 _DeCastlejau(XrSpline *spline, XrSpline *s1, XrSpline *s2);
 
 static double
-_XrSplineErrorSquared(XrSpline *spline, XPointFixed *p);
+_XrSplineErrorSquared(XrSpline *spline);
 
 static XrError
 _XrSplineDecomposeInto(XrSpline *spline, double tolerance_squared, XrSpline *result);
@@ -53,6 +53,30 @@ XrSplineInit(XrSpline *spline, XPointFixed *a,  XPointFixed *b,  XPointFixed *c,
     spline->c = *c;
     spline->d = *d;
 
+    if (a->x != b->x || a->y != b->y) {
+	ComputeSlope(&spline->a, &spline->b, &spline->initial_slope);
+    } else if (a->x != c->x || a->y != c->y) {
+	ComputeSlope(&spline->a, &spline->c, &spline->initial_slope);
+    } else if (a->x != d->x || a->y != d->y) {
+	ComputeSlope(&spline->a, &spline->d, &spline->initial_slope);
+    } else {
+	/* XXX: Completely degenerate spline (single point). I'm still
+           not sure what the fallout from this is. */
+	spline->initial_slope.dx = 0;
+	spline->initial_slope.dy = 0;
+    }
+
+    if (c->x != d->x || c->y != d->y) {
+	ComputeSlope(&spline->c, &spline->d, &spline->final_slope);
+    } else if (b->x != d->x || b->y != d->y) {
+	ComputeSlope(&spline->b, &spline->b, &spline->final_slope);
+    } else if (a->x != d->x || a->y != d->y) {
+	ComputeSlope(&spline->a, &spline->d, &spline->final_slope);
+    } else {
+	spline->final_slope.dx = 0;
+	spline->final_slope.dy = 0;
+    }
+
     spline->num_pts = 0;
     spline->pts_size = 0;
     spline->pts = NULL;
@@ -64,6 +88,7 @@ XrSplineDeinit(XrSpline *spline)
     spline->num_pts = 0;
     spline->pts_size = 0;
     free(spline->pts);
+    spline->pts = NULL;
 }
 
 static XrError
@@ -139,44 +164,89 @@ _DeCastlejau(XrSpline *spline, XrSpline *s1, XrSpline *s2)
 }
 
 static double
-_XrSplineErrorSquared(XrSpline *spline, XPointFixed *p)
+_PointDistanceSquaredToPoint(XPointFixed *a, XPointFixed *b)
 {
-    XPointFixed mid;
-    double dx, dy;
-
-    _LerpHalf(&spline->a, &spline->d, &mid);
-
-    dx = XFixedToDouble(mid.x - p->x);
-    dy = XFixedToDouble(mid.y - p->y);
+    double dx = XFixedToDouble(b->x - a->x);
+    double dy = XFixedToDouble(b->y - a->y);
 
     return dx*dx + dy*dy;
 }
 
+static double
+_PointDistanceSquaredToSegment(XPointFixed *p, XPointFixed *p1, XPointFixed *p2)
+{
+    double u;
+    double dx, dy;
+    double pdx, pdy;
+    XPointFixed px;
+
+    /* intersection point (px):
+
+       px = p1 + u(p2 - p1)
+       (p - px) . (p2 - p1) = 0
+
+       Thus:
+
+       u = ((p - p1) . (p2 - p1)) / (||(p2 - p1)|| ^ 2);
+    */
+
+    dx = XFixedToDouble(p2->x - p1->x);
+    dy = XFixedToDouble(p2->y - p1->y);
+
+    if (dx == 0 && dy == 0)
+	return _PointDistanceSquaredToPoint(p, p1);
+
+    pdx = XFixedToDouble(p->x - p1->x);
+    pdy = XFixedToDouble(p->y - p1->y);
+
+    u = (pdx * dx + pdy * dy) / (dx*dx + dy*dy);
+
+    if (u <= 0)
+	return _PointDistanceSquaredToPoint(p, p1);
+    else if (u >= 1)
+	return _PointDistanceSquaredToPoint(p, p2);
+
+    px.x = p1->x + u * (p2->x - p1->x);
+    px.y = p1->y + u * (p2->y - p1->y);
+
+    return _PointDistanceSquaredToPoint(p, &px);
+}
+
+/* Return an upper bound on the error (squared) that could result from approximating
+   a spline as a line segment connecting the two endpoints */
+static double
+_XrSplineErrorSquared(XrSpline *spline)
+{
+    double berr, cerr;
+
+    berr = _PointDistanceSquaredToSegment(&spline->b, &spline->a, &spline->d);
+    cerr = _PointDistanceSquaredToSegment(&spline->c, &spline->a, &spline->d);
+
+    if (berr > cerr)
+	return berr;
+    else
+	return cerr;
+}
+
 static XrError
 _XrSplineDecomposeInto(XrSpline *spline, double tolerance_squared, XrSpline *result)
 {
     XrError err;
     XrSpline s1, s2;
 
+    if (_XrSplineErrorSquared(spline) < tolerance_squared) {
+	return _XrSplineAddPoint(result, &spline->a);
+    }
+
     _DeCastlejau(spline, &s1, &s2);
 
-    if (_XrSplineErrorSquared(spline, &s1.d) < tolerance_squared) {
-	err = _XrSplineAddPoint(result, &s1.a);
-	if (err)
-	    return err;
-
-	err = _XrSplineAddPoint(result, &s1.d);
-	if (err)
-	    return err;
-    } else {
-	err = _XrSplineDecomposeInto(&s1, tolerance_squared, result);
-	if (err)
-	    return err;
-
-	err = _XrSplineDecomposeInto(&s2, tolerance_squared, result);
-	if (err)
-	    return err;
-    }
+    err = _XrSplineDecomposeInto(&s1, tolerance_squared, result);
+    if (err)
+	return err;
+    
+    err = _XrSplineDecomposeInto(&s2, tolerance_squared, result);
+    if (err)
+	return err;
 
     return XrErrorSuccess;
 }

src/xrtraps.c

@@ -74,6 +74,7 @@ XrTrapsDeinit(XrTraps *traps)
 {
     if (traps->xtraps_size) {
 	free(traps->xtraps);
+	traps->xtraps = NULL;
 	traps->xtraps_size = 0;
 	traps->num_xtraps = 0;
     }

xrgstate.c

@@ -95,12 +95,21 @@ XrGStateInitCopy(XrGState *gstate, XrGState *other)
     XrSurfaceSetSolidColor(&gstate->src, &gstate->color, gstate->solidFormat);
 
     err = XrPathInitCopy(&gstate->path, &other->path);
-    if (err) {
-	if (gstate->dashes) {    
-	    free (gstate->dashes);
-	    gstate->dashes = 0;
-	}
-    }
+    if (err)
+	goto CLEANUP_DASHES;
+
+    err = XrPenInitCopy(&gstate->pen_regular, &other->pen_regular);
+    if (err)
+	goto CLEANUP_PATH;
+
+    return err;
+
+  CLEANUP_PATH:
+    XrPathDeinit(&gstate->path);
+  CLEANUP_DASHES:
+    free (gstate->dashes);
+    gstate->dashes = NULL;
+
     return err;
 }
 
@@ -117,8 +126,10 @@ XrGStateDeinit(XrGState *gstate)
 
     XrPenDeinit(&gstate->pen_regular);
 
-    if (gstate->dashes)
+    if (gstate->dashes) {
 	free (gstate->dashes);
+	gstate->dashes = NULL;
+    }
 }
 
 void

xrint.h

@@ -122,20 +122,23 @@ typedef struct _XrPolygon {
     int closed;
 } XrPolygon;
 
-typedef struct _XrSpline {
-    XPointFixed a, b, c, d;
-
-    int num_pts;
-    int pts_size;
-    XPointFixed *pts;
-} XrSpline;
-
 typedef struct _XrSlopeFixed
 {
     XFixed dx;
     XFixed dy;
 } XrSlopeFixed;
 
+typedef struct _XrSpline {
+    XPointFixed a, b, c, d;
+
+    XrSlopeFixed initial_slope;
+    XrSlopeFixed final_slope;
+
+    int num_pts;
+    int pts_size;
+    XPointFixed *pts;
+} XrSpline;
+
 typedef enum _XrPenVertexTag {
     XrPenVertexTagNone,
     XrPenVertexTagForward,
@@ -580,5 +583,10 @@ XrTrapsTessellateRectangle (XrTraps *traps, XPointFixed q[4]);
 XrError
 XrTrapsTessellatePolygon (XrTraps *traps, XrPolygon *poly, int winding);
 
+/* xrmisc.c */
+
+void
+ComputeSlope(XPointFixed *a, XPointFixed *b, XrSlopeFixed *slope);
+
 #endif
 

xrmisc.c

@@ -0,0 +1,34 @@
+/*
+ * $XFree86: $
+ *
+ * Copyright © 2002 Carl D. Worth
+ *
+ * Permission to use, copy, modify, distribute, and sell this software
+ * and its documentation for any purpose is hereby granted without
+ * fee, provided that the above copyright notice appear in all copies
+ * and that both that copyright notice and this permission notice
+ * appear in supporting documentation, and that the name of Carl
+ * D. Worth not be used in advertising or publicity pertaining to
+ * distribution of the software without specific, written prior
+ * permission.  Carl D. Worth makes no representations about the
+ * suitability of this software for any purpose.  It is provided "as
+ * is" without express or implied warranty.
+ *
+ * CARL D. WORTH DISCLAIMS ALL WARRANTIES WITH REGARD TO THIS
+ * SOFTWARE, INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY AND
+ * FITNESS, IN NO EVENT SHALL CARL D. WORTH BE LIABLE FOR ANY SPECIAL,
+ * INDIRECT OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES WHATSOEVER
+ * RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN ACTION
+ * OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR
+ * IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
+ */
+
+#include "xrint.h"
+
+void
+ComputeSlope(XPointFixed *a, XPointFixed *b, XrSlopeFixed *slope)
+{
+    slope->dx = b->x - a->x;
+    slope->dy = b->y - a->y;
+}
+

xrpath.c

@@ -221,7 +221,6 @@ _XrPathOpBufCreate(void)
 static void
 _XrPathOpBufDestroy(XrPathOpBuf *op)
 {
-    op->num_ops = 0;
     free(op);
 }
 
@@ -249,7 +248,6 @@ _XrPathArgBufCreate(void)
 static void
 _XrPathArgBufDestroy(XrPathArgBuf *arg)
 {
-    arg->num_pts = 0;
     free(arg);
 }
 

xrpen.c

@@ -31,9 +31,6 @@ _XrPenVerticesNeeded(double radius, double tolerance, XrTransform *matrix);
 static void
 _XrPenComputeSlopes(XrPen *pen);
 
-static void
-_FindSlope(XPointFixed *a, XPointFixed *b, XrSlopeFixed *slope);
-
 static int
 _SlopeClockwise(XrSlopeFixed *a, XrSlopeFixed *b);
 
@@ -231,18 +228,11 @@ _XrPenComputeSlopes(XrPen *pen)
 	v = &pen->vertex[i];
 	next = &pen->vertex[(i + 1) % pen->num_vertices];
 
-	_FindSlope(&prev->pt, &v->pt, &v->slope_cw);
-	_FindSlope(&v->pt, &next->pt, &v->slope_ccw);
+	ComputeSlope(&prev->pt, &v->pt, &v->slope_cw);
+	ComputeSlope(&v->pt, &next->pt, &v->slope_ccw);
     }
 }
 
-static void
-_FindSlope(XPointFixed *a, XPointFixed *b, XrSlopeFixed *slope)
-{
-    slope->dx = b->x - a->x;
-    slope->dy = b->y - a->y;
-}
-
 static int
 _SlopeClockwise(XrSlopeFixed *a, XrSlopeFixed *b)
 {
@@ -283,12 +273,14 @@ _XrPenStrokeSplineHalf(XrPen *pen, XrSpline *spline, XrPenVertexTag dir, XrPolyg
 	start = 0;
 	stop = num_pts;
 	step = 1;
-	_FindSlope(&spline->c, &spline->d, &final_slope);
+	final_slope = spline->final_slope;
     } else {
 	start = num_pts - 1;
 	stop = -1;
 	step = -1;
-	_FindSlope(&spline->b, &spline->a, &final_slope);
+	final_slope = spline->initial_slope;
+	final_slope.dx = -final_slope.dx; 
+	final_slope.dy = -final_slope.dy; 
     }
 
     i = start;
@@ -302,7 +294,7 @@ _XrPenStrokeSplineHalf(XrPen *pen, XrSpline *spline, XrPenVertexTag dir, XrPolyg
 	if (i + step == stop)
 	    slope = final_slope;
 	else
-	    _FindSlope(&pt[i], &pt[i+step], &slope);
+	    ComputeSlope(&pt[i], &pt[i+step], &slope);
 	if (_SlopeCounterClockwise(&slope, &pen->vertex[active].slope_ccw)) {
 	    if (++active == pen->num_vertices)
 		active = 0;

xrpolygon.c

@@ -56,6 +56,7 @@ XrPolygonDeinit(XrPolygon *polygon)
 {
     if (polygon->edges_size) {
 	free(polygon->edges);
+	polygon->edges = NULL;
 	polygon->edges_size = 0;
 	polygon->num_edges = 0;
     }

xrspline.c

@@ -38,7 +38,7 @@ static void
 _DeCastlejau(XrSpline *spline, XrSpline *s1, XrSpline *s2);
 
 static double
-_XrSplineErrorSquared(XrSpline *spline, XPointFixed *p);
+_XrSplineErrorSquared(XrSpline *spline);
 
 static XrError
 _XrSplineDecomposeInto(XrSpline *spline, double tolerance_squared, XrSpline *result);
@@ -53,6 +53,30 @@ XrSplineInit(XrSpline *spline, XPointFixed *a,  XPointFixed *b,  XPointFixed *c,
     spline->c = *c;
     spline->d = *d;
 
+    if (a->x != b->x || a->y != b->y) {
+	ComputeSlope(&spline->a, &spline->b, &spline->initial_slope);
+    } else if (a->x != c->x || a->y != c->y) {
+	ComputeSlope(&spline->a, &spline->c, &spline->initial_slope);
+    } else if (a->x != d->x || a->y != d->y) {
+	ComputeSlope(&spline->a, &spline->d, &spline->initial_slope);
+    } else {
+	/* XXX: Completely degenerate spline (single point). I'm still
+           not sure what the fallout from this is. */
+	spline->initial_slope.dx = 0;
+	spline->initial_slope.dy = 0;
+    }
+
+    if (c->x != d->x || c->y != d->y) {
+	ComputeSlope(&spline->c, &spline->d, &spline->final_slope);
+    } else if (b->x != d->x || b->y != d->y) {
+	ComputeSlope(&spline->b, &spline->b, &spline->final_slope);
+    } else if (a->x != d->x || a->y != d->y) {
+	ComputeSlope(&spline->a, &spline->d, &spline->final_slope);
+    } else {
+	spline->final_slope.dx = 0;
+	spline->final_slope.dy = 0;
+    }
+
     spline->num_pts = 0;
     spline->pts_size = 0;
     spline->pts = NULL;
@@ -64,6 +88,7 @@ XrSplineDeinit(XrSpline *spline)
     spline->num_pts = 0;
     spline->pts_size = 0;
     free(spline->pts);
+    spline->pts = NULL;
 }
 
 static XrError
@@ -139,44 +164,89 @@ _DeCastlejau(XrSpline *spline, XrSpline *s1, XrSpline *s2)
 }
 
 static double
-_XrSplineErrorSquared(XrSpline *spline, XPointFixed *p)
+_PointDistanceSquaredToPoint(XPointFixed *a, XPointFixed *b)
 {
-    XPointFixed mid;
-    double dx, dy;
-
-    _LerpHalf(&spline->a, &spline->d, &mid);
-
-    dx = XFixedToDouble(mid.x - p->x);
-    dy = XFixedToDouble(mid.y - p->y);
+    double dx = XFixedToDouble(b->x - a->x);
+    double dy = XFixedToDouble(b->y - a->y);
 
     return dx*dx + dy*dy;
 }
 
+static double
+_PointDistanceSquaredToSegment(XPointFixed *p, XPointFixed *p1, XPointFixed *p2)
+{
+    double u;
+    double dx, dy;
+    double pdx, pdy;
+    XPointFixed px;
+
+    /* intersection point (px):
+
+       px = p1 + u(p2 - p1)
+       (p - px) . (p2 - p1) = 0
+
+       Thus:
+
+       u = ((p - p1) . (p2 - p1)) / (||(p2 - p1)|| ^ 2);
+    */
+
+    dx = XFixedToDouble(p2->x - p1->x);
+    dy = XFixedToDouble(p2->y - p1->y);
+
+    if (dx == 0 && dy == 0)
+	return _PointDistanceSquaredToPoint(p, p1);
+
+    pdx = XFixedToDouble(p->x - p1->x);
+    pdy = XFixedToDouble(p->y - p1->y);
+
+    u = (pdx * dx + pdy * dy) / (dx*dx + dy*dy);
+
+    if (u <= 0)
+	return _PointDistanceSquaredToPoint(p, p1);
+    else if (u >= 1)
+	return _PointDistanceSquaredToPoint(p, p2);
+
+    px.x = p1->x + u * (p2->x - p1->x);
+    px.y = p1->y + u * (p2->y - p1->y);
+
+    return _PointDistanceSquaredToPoint(p, &px);
+}
+
+/* Return an upper bound on the error (squared) that could result from approximating
+   a spline as a line segment connecting the two endpoints */
+static double
+_XrSplineErrorSquared(XrSpline *spline)
+{
+    double berr, cerr;
+
+    berr = _PointDistanceSquaredToSegment(&spline->b, &spline->a, &spline->d);
+    cerr = _PointDistanceSquaredToSegment(&spline->c, &spline->a, &spline->d);
+
+    if (berr > cerr)
+	return berr;
+    else
+	return cerr;
+}
+
 static XrError
 _XrSplineDecomposeInto(XrSpline *spline, double tolerance_squared, XrSpline *result)
 {
     XrError err;
     XrSpline s1, s2;
 
+    if (_XrSplineErrorSquared(spline) < tolerance_squared) {
+	return _XrSplineAddPoint(result, &spline->a);
+    }
+
     _DeCastlejau(spline, &s1, &s2);
 
-    if (_XrSplineErrorSquared(spline, &s1.d) < tolerance_squared) {
-	err = _XrSplineAddPoint(result, &s1.a);
-	if (err)
-	    return err;
-
-	err = _XrSplineAddPoint(result, &s1.d);
-	if (err)
-	    return err;
-    } else {
-	err = _XrSplineDecomposeInto(&s1, tolerance_squared, result);
-	if (err)
-	    return err;
-
-	err = _XrSplineDecomposeInto(&s2, tolerance_squared, result);
-	if (err)
-	    return err;
-    }
+    err = _XrSplineDecomposeInto(&s1, tolerance_squared, result);
+    if (err)
+	return err;
+    
+    err = _XrSplineDecomposeInto(&s2, tolerance_squared, result);
+    if (err)
+	return err;
 
     return XrErrorSuccess;
 }

xrtraps.c

@@ -74,6 +74,7 @@ XrTrapsDeinit(XrTraps *traps)
 {
     if (traps->xtraps_size) {
 	free(traps->xtraps);
+	traps->xtraps = NULL;
 	traps->xtraps_size = 0;
 	traps->num_xtraps = 0;
     }