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cssease: Optimize with Newton's method

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Idea stolen from Webkit's implementation.
This commit is contained in:
Benjamin Otte
2016-04-04 14:53:46 +02:00
parent 3659741414
commit 7ca4ef7b0c
1 changed files with 25 additions and 0 deletions
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25
gtk/gtkcsseasevalue.c
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@@ -452,6 +452,12 @@ cubic (double a, double b, double c, double t)
return ((a * t + b) * t + c) * t;
}
static inline double
cubic_deriv (double a, double b, double c, double t)
{
return (3 * a * t + 2 * b) * t + c;
}
double
_gtk_css_ease_value_transform (const GtkCssValue *ease,
double progress)
@@ -471,6 +477,7 @@ _gtk_css_ease_value_transform (const GtkCssValue *ease,
double ax, bx, cx;
double ay, by, cy;
double tmin, t, tmax;
guint i;
cx = 3.0 * ease->u.cubic.x1;
bx = 3.0 * (ease->u.cubic.x2 - ease->u.cubic.x1) - cx;
@@ -479,6 +486,24 @@ _gtk_css_ease_value_transform (const GtkCssValue *ease,
by = 3.0 * (ease->u.cubic.y2 - ease->u.cubic.y1) - cy;
ay = 1.0 - cy - by;
/* Try with Newton's method first */
t = progress;
for (i = 0; i < 8; i++)
{
double sample, deriv;
sample = cubic (ax, bx, cx, t);
if (fabs (sample - t) < epsilon)
return cubic (ay, by, cy, t);
deriv = cubic_deriv (ax, bx, cx, t);
if (deriv < epsilon)
return cubic (ay, by, cy, t);
t = t - (sample - t) / deriv;
}
/* Fallback if Newton doesn't converge */
tmin = 0.0;
tmax = 1.0;
t = progress;