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[_cairo_spline_bound] Fix the check for feasible solutions

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Also make it more strict.  The only times we call sqrt now is
when a solution in (0,1) exists.
This commit is contained in:
Behdad Esfahbod 2008-12-28 02:41:39 -05:00
parent 7f840d156c
commit 3bf1b7d574
1 changed files with 6 additions and 3 deletions
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9
src/cairo-spline.c
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@ -277,15 +277,18 @@ _cairo_spline_bound (cairo_spline_add_point_func_t add_point_func,
double b2 = b * b; \
double delta = b2 - a * c; \
if (delta > 0) { \
double a2 = a * a; \
double ab = a * b; \
double a2_b2 = a * a + b2; \
double _2ab = 2 * a * b; \
double _b_a = - b / a; \
/* We are only interested in solutions t that satisfy 0<t<1 \
* here. We do some checks to avoid sqrt if the solutions \
* are not in that range. The checks can be derived from: \
* \
* 0 < (-b±√delta)/a < 1 \
*/ \
if (delta > (ab >= 0 ? b2 : a2 + b2 + 2*ab)) { \
if ((_2ab >= 0 && delta > b2 && delta < a2_b2 - _2ab) || \
(_2ab < 0 && ((_b_a>=1 && (delta < b2 && delta > a2_b2 + _2ab)) || \
(_b_a< 1 && (delta < b2 || delta < a2_b2 + _2ab))))) { \
double sqrt_delta = sqrt (delta); \
ADD ((-b - sqrt_delta) / a); \
ADD ((-b + sqrt_delta) / a); \