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Fix bugs in _cairo_traps_tessellate_convex_quad

Browse source 
The previous code was not handling all cases correctly, (yes,
even something as simple as a quadrilateral can exhibit a
remarkably large number of different cases when tessellation
is attempted).

This fix now introduces slope comparison which handles several
cases that were mis-handled with the previous implementation which
only used independent sorting of the X and Y values of the
coordinates.

This fixes the skew-extreme test case and the bug reported here:

	Skew transforms were broken by the cairo update in December
	https://bugzilla.mozilla.org/show_bug.cgi?id=373632
This commit is contained in:
Carl Worth 2007-03-13 17:42:39 -07:00
parent 0a6ae06c35
commit 1f3a5b4e12
1 changed files with 59 additions and 42 deletions
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101
src/cairo-traps.c
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@ -380,6 +380,8 @@ _cairo_traps_tessellate_convex_quad (cairo_traps_t *traps, cairo_point_t q[4])
{
int a, b, c, d;
int i;
cairo_slope_t ab, ad;
cairo_bool_t b_left_of_d;
/* Choose a as a point with minimal y */
a = 0;
@ -399,24 +401,39 @@ _cairo_traps_tessellate_convex_quad (cairo_traps_t *traps, cairo_point_t q[4])
}
/* Without freedom left to choose anything else, we have four
* cases to tessellate which we can distinguish by comparing c.y
* to d.y and then by comparing b.x to d.x. And then for any of
* these cases there is a trivial way to emit three
* trapezoids. The 4 cases and their trapezoids are described and
* implemented below:
*/
if (q[c].y < q[d].y) {
if (q[b].x < q[d].x) {
/* c.y < d.y && b.x < d.x
* cases to tessellate.
*
* First, we have to determine the Y-axis sort of the four
* vertices, (either abcd or abdc). After that we need to detemine
* which edges will be "left" and which will be "right" in the
* resulting trapezoids. This can be determined by computing a
* slope comparison of ab and ad to determine if b is left of d or
* not.
*
* Note that "left of" here is in the sense of which edges should
* be the left vs. right edges of the trapezoid. In particular, b
* left of d does *not* mean that b.x is less than d.x.
*
* This should hopefully be made clear in the lame ASCII art
* below. Since the same slope comparison is used in all cases, we
* compute it before testing for the Y-value sort. */
_cairo_slope_init (&ab, &q[a], &q[b]);
_cairo_slope_init (&ad, &q[a], &q[d]);
b_left_of_d = (_cairo_slope_compare (&ab, &ad) > 0);
if (q[c].y <= q[d].y) {
if (b_left_of_d) {
/* Y-sort is abcd and b is left of d, (slope(ab) > slope (ad))
*
* top bot left right
* a
* / | a.y b.y ab ad
* b |
* | | b.y c.y bc ad
* c |
* \ | c.y d.y cd ad
* d
* top bot left right
* _a a a
* / / /| |\ a.y b.y ab ad
* b / b | b \
* / / | | \ \ b.y c.y bc ad
* c / c | c \
* | / \| \ \ c.y d.y cd ad
* d d d
*/
_cairo_traps_add_trap_from_points (traps,
q[a].y, q[b].y,
@ -428,15 +445,15 @@ _cairo_traps_tessellate_convex_quad (cairo_traps_t *traps, cairo_point_t q[4])
q[c].y, q[d].y,
q[c], q[d], q[a], q[d]);
} else {
/* c.y < d.y && b.x >= d.x
/* Y-sort is abcd and b is right of d, (slope(ab) <= slope (ad))
*
* a
* | \ a.y b.y ad ab
* | b
* | | b.y c.y ad bc
* | c
* | / c.y d.y ad cd
* d
* a a a_
* /| |\ \ \ a.y b.y ad ab
* / b | b \ b
* / / | | \ \ b.y c.y ad bc
* / c | c \ c
* / / |/ \ | c.y d.y ad cd
* d d d
*/
_cairo_traps_add_trap_from_points (traps,
q[a].y, q[b].y,
@ -449,16 +466,16 @@ _cairo_traps_tessellate_convex_quad (cairo_traps_t *traps, cairo_point_t q[4])
q[a], q[d], q[c], q[d]);
}
} else {
if (q[b].x < q[d].x) {
/* c.y >= d.y && b.x < d.x
if (b_left_of_d) {
/* Y-sort is abdc and b is left of d, (slope (ab) > slope (ad))
*
* a
* / \ a.y b.y ab ad
* b \
* \ \ b.y d.y bc ad
* \ d
* \ / d.y c.y bc dc
* c
* a a a
* // / \ |\ a.y b.y ab ad
* /b/ b \ b \
* / / \ \ \ \ b.y d.y bc ad
* /d/ \ d \ d
* // \ / \| d.y c.y bc dc
* c c c
*/
_cairo_traps_add_trap_from_points (traps,
q[a].y, q[b].y,
@ -470,15 +487,15 @@ _cairo_traps_tessellate_convex_quad (cairo_traps_t *traps, cairo_point_t q[4])
q[d].y, q[c].y,
q[b], q[c], q[d], q[c]);
} else {
/* c.y >= d.y && b.x >= d.x
/* Y-sort is abdc and b is right of d, (slope (ab) <= slope (ad))
*
* a
* / \ a.y b.y ad ab
* / b
* / / b.y d.y ad bc
* d /
* \ / d.y c.y dc bc
* c
* a a a
* /| / \ \\ a.y b.y ad ab
* / b / b \b\
* / / / / \ \ b.y d.y ad bc
* d / d / \d\
* |/ \ / \\ d.y c.y dc bc
* c c c
*/
_cairo_traps_add_trap_from_points (traps,
q[a].y, q[b].y,