[cairo] arc_to again
Behdad Esfahbod
behdad at cs.toronto.edu
Tue Aug 9 20:29:18 PDT 2005
Hi,
I reworked the arc_to patch, added comments, overly commented
actually. As per cworth's principle that "small changes in the
input should result in small changes in the visual output", I
decided to reduce the radius when the arc doesn't fit.
The problem with not doing this is that as the angle that the arc
has got to fit in approaches zero, the arc would go farther and
farther from the scene, and when finally the angle becomes zero,
the arc should be placed at infinity, so a decision should be
made, which most probably is to not draw the arc at all and the
visual appearance changes drastically. So I went for reducing
the radius, that looks pretty smooth.
I'm attaching both the old and new patchesh, and the arclock test
code. Run arclock with both patches and decide which one you
prefer to get in. The patches include the sincos stuff too.
Cheers,
--behdad
http://behdad.org/
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Index: configure.in
===================================================================
RCS file: /cvs/cairo/cairo/configure.in,v
retrieving revision 1.111
diff -u -p -r1.111 configure.in
--- configure.in 18 Jul 2005 18:51:42 -0000 1.111
+++ configure.in 27 Jul 2005 06:07:24 -0000
@@ -31,20 +31,19 @@ AM_CONFIG_HEADER(config.h)
AM_MAINTAINER_MODE
+AC_GNU_SOURCE
AC_PROG_CC
AC_PROG_CPP
AM_PROG_LIBTOOL
AC_STDC_HEADERS
AC_C_BIGENDIAN
-AC_CHECK_FUNCS(vasnprintf)
-
+AC_CHECK_FUNCS(vasnprintf, sincos)
+
AC_CHECK_LIBM
LIBS="$LIBS $LIBM"
-AC_CHECK_FUNCS(sincos)
-
dnl ===========================================================================
AC_ARG_ENABLE(xlib,
Index: src/cairo-arc-private.h
===================================================================
RCS file: /cvs/cairo/cairo/src/cairo-arc-private.h,v
retrieving revision 1.1
diff -u -p -r1.1 cairo-arc-private.h
--- src/cairo-arc-private.h 26 Apr 2005 19:38:06 -0000 1.1
+++ src/cairo-arc-private.h 27 Jul 2005 06:07:24 -0000
@@ -54,4 +54,11 @@ _cairo_arc_path_negative (cairo_t *cr,
double angle1,
double angle2);
+void
+_cairo_arc_with_handle (cairo_t *cr,
+ double x0, double y0,
+ double x1, double y1,
+ double x2, double y2,
+ double radius);
+
#endif /* CAIRO_ARC_PRIVATE_H */
Index: src/cairo-arc.c
===================================================================
RCS file: /cvs/cairo/cairo/src/cairo-arc.c,v
retrieving revision 1.3
diff -u -p -r1.3 cairo-arc.c
--- src/cairo-arc.c 11 Jul 2005 20:29:46 -0000 1.3
+++ src/cairo-arc.c 27 Jul 2005 06:07:24 -0000
@@ -61,7 +61,10 @@
static double
_arc_error_normalized (double angle)
{
- return 2.0/27.0 * pow (sin (angle / 4), 6) / pow (cos (angle / 4), 2);
+ double sin_, cos_;
+
+ _cairo_sincos (angle / 4, &sin_, &cos_);
+ return 2.0/27.0 * pow (sin_, 6) / pow (cos_, 2);
}
static double
@@ -164,10 +167,12 @@ _cairo_arc_segment (cairo_t *cr,
double r_sin_B, r_cos_B;
double h;
- r_sin_A = radius * sin (angle_A);
- r_cos_A = radius * cos (angle_A);
- r_sin_B = radius * sin (angle_B);
- r_cos_B = radius * cos (angle_B);
+ _cairo_sincos (angle_A, &r_sin_A, &r_cos_A);
+ _cairo_sincos (angle_B, &r_sin_B, &r_cos_B);
+ r_sin_A *= radius;
+ r_cos_A *= radius;
+ r_sin_B *= radius;
+ r_cos_B *= radius;
h = 4.0/3.0 * tan ((angle_B - angle_A) / 4.0);
@@ -296,3 +301,49 @@ _cairo_arc_path_negative (cairo_t *cr,
angle2, angle1,
CAIRO_DIRECTION_REVERSE);
}
+
+void
+_cairo_arc_with_handle (cairo_t *cr,
+ double x0, double y0,
+ double x1, double y1,
+ double x2, double y2,
+ double radius)
+{
+ double angle0, angle1, angle2, angled;
+ double xc, yc, dc;
+ cairo_direction_t dir;
+
+ angle0 = atan2 (y0 - y1, x0 - x1);
+ angle2 = atan2 (y2 - y1, x2 - x1);
+ angle1 = (angle0 + angle2) / 2;
+
+ angled = angle2 - angle0;
+
+ if (angled > M_PI || (angled < 0 && angled > -M_PI)) {
+ angle1 += M_PI;
+ angled = 2 * M_PI - angled;
+ angle0 += M_PI_2;
+ angle2 -= M_PI_2;
+ dir = CAIRO_DIRECTION_FORWARD;
+ } else {
+ angle0 -= M_PI_2;
+ angle2 += M_PI_2;
+ dir = CAIRO_DIRECTION_REVERSE;
+ }
+
+ /* distance of center from (x1,y1) */
+ dc = radius / sin (angled / 2);
+
+ _cairo_sincos (angle1, &yc, &xc);
+ xc = x1 + xc * dc;
+ yc = y1 + yc * dc;
+ /* (cx,cy) is the center of arc now */
+
+ if (dir == CAIRO_DIRECTION_FORWARD)
+ cairo_arc (cr, xc, yc, radius, angle0, angle2);
+ else
+ cairo_arc_negative (cr, xc, yc, radius, angle0, angle2);
+
+ cairo_line_to (cr, x2, y2);
+}
+
Index: src/cairo-matrix.c
===================================================================
RCS file: /cvs/cairo/cairo/src/cairo-matrix.c,v
retrieving revision 1.29
diff -u -p -r1.29 cairo-matrix.c
--- src/cairo-matrix.c 20 Jun 2005 19:54:15 -0000 1.29
+++ src/cairo-matrix.c 27 Jul 2005 06:07:24 -0000
@@ -227,17 +227,12 @@ void
cairo_matrix_init_rotate (cairo_matrix_t *matrix,
double radians)
{
- double s;
- double c;
-#if HAVE_SINCOS
- sincos (radians, &s, &c);
-#else
- s = sin (radians);
- c = cos (radians);
-#endif
+ double sin_, cos_;
+
+ _cairo_sincos (radians, &sin_, &cos_);
cairo_matrix_init (matrix,
- c, s,
- -s, c,
+ cos_, sin_,
+ -sin_, cos_,
0, 0);
}
slim_hidden_def(cairo_matrix_init_rotate);
Index: src/cairo-pattern.c
===================================================================
RCS file: /cvs/cairo/cairo/src/cairo-pattern.c,v
retrieving revision 1.50
diff -u -p -r1.50 cairo-pattern.c
--- src/cairo-pattern.c 14 Jul 2005 22:47:18 -0000 1.50
+++ src/cairo-pattern.c 27 Jul 2005 06:07:25 -0000
@@ -1100,6 +1100,8 @@ _cairo_image_data_set_radial (cairo_radi
denumerator = -2.0 * c0_e * c0_c1;
if (denumerator != 0.0) {
+ double sin_, cos_;
+
fraction = (c1_e * c1_e - c0_e * c0_e - c0_c1 * c0_c1) /
denumerator;
@@ -1110,8 +1112,9 @@ _cairo_image_data_set_radial (cairo_radi
angle_c0 = acos (fraction);
- c0_y = cos (angle_c0) * c0_c1;
- c1_y = sin (angle_c0) * c0_c1;
+ _cairo_sincos (angle_c0, &sin_, &cos_);
+ c0_y = cos_ * c0_c1;
+ c1_y = sin_ * c0_c1;
y_x = sqrt (r1_2 - c1_y * c1_y);
c0_x = y_x + c0_y;
Index: src/cairo-pen.c
===================================================================
RCS file: /cvs/cairo/cairo/src/cairo-pen.c,v
retrieving revision 1.23
diff -u -p -r1.23 cairo-pen.c
--- src/cairo-pen.c 7 Apr 2005 17:01:49 -0000 1.23
+++ src/cairo-pen.c 27 Jul 2005 06:07:25 -0000
@@ -102,8 +102,11 @@ _cairo_pen_init (cairo_pen_t *pen, doubl
*/
for (i=0; i < pen->num_vertices; i++) {
double theta = 2 * M_PI * i / (double) pen->num_vertices;
- double dx = radius * cos (reflect ? -theta : theta);
- double dy = radius * sin (reflect ? -theta : theta);
+ double dx, dy;
+
+ _cairo_sincos (reflect ? -theta : theta, &dx, &dy);
+ dx *= radius;
+ dy *= radius;
cairo_pen_vertex_t *v = &pen->vertices[i];
cairo_matrix_transform_distance (&gstate->ctm, &dx, &dy);
v->point.x = _cairo_fixed_from_double (dx);
Index: src/cairo.c
===================================================================
RCS file: /cvs/cairo/cairo/src/cairo.c,v
retrieving revision 1.114
diff -u -p -r1.114 cairo.c
--- src/cairo.c 25 Jul 2005 19:29:24 -0000 1.114
+++ src/cairo.c 27 Jul 2005 06:07:25 -0000
@@ -1013,6 +1013,8 @@ cairo_arc (cairo_t *cr,
double radius,
double angle1, double angle2)
{
+ double sin_, cos_;
+
if (cr->status) {
_cairo_error (cr, cr->status);
return;
@@ -1025,9 +1027,11 @@ cairo_arc (cairo_t *cr,
while (angle2 < angle1)
angle2 += 2 * M_PI;
+ _cairo_sincos (angle1, &sin_, &cos_);
+
cairo_line_to (cr,
- xc + radius * cos (angle1),
- yc + radius * sin (angle1));
+ xc + radius * cos_,
+ yc + radius * sin_);
_cairo_arc_path (cr, xc, yc, radius,
angle1, angle2);
@@ -1053,6 +1057,8 @@ cairo_arc_negative (cairo_t *cr,
double radius,
double angle1, double angle2)
{
+ double sin_, cos_;
+
if (cr->status) {
_cairo_error (cr, cr->status);
return;
@@ -1065,30 +1071,37 @@ cairo_arc_negative (cairo_t *cr,
while (angle2 > angle1)
angle2 -= 2 * M_PI;
+ _cairo_sincos (angle1, &sin_, &cos_);
+
cairo_line_to (cr,
- xc + radius * cos (angle1),
- yc + radius * sin (angle1));
+ xc + radius * cos_,
+ yc + radius * sin_);
- _cairo_arc_path_negative (cr, xc, yc, radius,
- angle1, angle2);
+ _cairo_arc_path_negative (cr, xc, yc, radius,
+ angle1, angle2);
}
-/* XXX: NYI
void
cairo_arc_to (cairo_t *cr,
double x1, double y1,
double x2, double y2,
double radius)
{
+ double x0, y0;
+
if (cr->status)
return;
- cr->status = _cairo_gstate_arc_to (cr->gstate,
- x1, y1,
- x2, y2,
- radius);
+ cairo_get_current_point (cr, &x0, &y0);
+
+
+
+ _cairo_arc_with_handle (cr,
+ x0, y0,
+ x1, y1,
+ x2, y2,
+ radius);
}
-*/
void
cairo_rel_move_to (cairo_t *cr, double dx, double dy)
Index: src/cairo.h
===================================================================
RCS file: /cvs/cairo/cairo/src/cairo.h,v
retrieving revision 1.139
diff -u -p -r1.139 cairo.h
--- src/cairo.h 25 Jul 2005 19:29:24 -0000 1.139
+++ src/cairo.h 27 Jul 2005 06:07:26 -0000
@@ -412,13 +412,11 @@ cairo_arc_negative (cairo_t *cr,
double radius,
double angle1, double angle2);
-/* XXX: NYI
void
cairo_arc_to (cairo_t *cr,
double x1, double y1,
double x2, double y2,
double radius);
-*/
void
cairo_rel_move_to (cairo_t *cr, double dx, double dy);
Index: src/cairoint.h
===================================================================
RCS file: /cvs/cairo/cairo/src/cairoint.h,v
retrieving revision 1.169
diff -u -p -r1.169 cairoint.h
--- src/cairoint.h 25 Jul 2005 23:23:05 -0000 1.169
+++ src/cairoint.h 27 Jul 2005 06:07:26 -0000
@@ -65,6 +65,16 @@
#include "cairo.h"
#include <pixman.h>
+#if HAVE_SINCOS
+# define _cairo_sincos(angle,s,c) sincos((angle), (s), (c))
+#else
+# define _cairo_sincos(angle,s,c) do { \
+ double _sincos_angle = (angle); \
+ *(s) = sin(_sincos_angle); \
+ *(c) = cos(_sincos_angle); \
+ } while (0)
+#endif
+
#if __GNUC__ >= 3 && defined(__ELF__)
# define slim_hidden_proto(name) slim_hidden_proto1(name, INT_##name)
# define slim_hidden_def(name) slim_hidden_def1(name, INT_##name)
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