diff options
| -rw-r--r-- | demos/scale.c | 102 |
1 files changed, 61 insertions, 41 deletions
diff --git a/demos/scale.c b/demos/scale.c index d00307e..0995ad0 100644 --- a/demos/scale.c +++ b/demos/scale.c @@ -55,50 +55,70 @@ get_widget (app_t *app, const char *name) return widget; } -static double -min4 (double a, double b, double c, double d) -{ - double m1, m2; - - m1 = MIN (a, b); - m2 = MIN (c, d); - return MIN (m1, m2); -} - -static double -max4 (double a, double b, double c, double d) -{ - double m1, m2; - - m1 = MAX (a, b); - m2 = MAX (c, d); - return MAX (m1, m2); -} - +/* Figure out the boundary of a diameter=1 circle transformed into an ellipse + * by trans. Proof that this is the correct calculation: + * + * Transform x,y to u,v by this matrix calculation: + * + * |u| |a c| |x| + * |v| = |b d|*|y| + * + * Horizontal component: + * + * u = ax+cy (1) + * + * For each x,y on a radius-1 circle (p is angle to the point): + * + * x^2+y^2 = 1 + * x = cos(p) + * y = sin(p) + * dx/dp = -sin(p) = -y + * dy/dp = cos(p) = x + * + * Figure out derivative of (1) relative to p: + * + * du/dp = a(dx/dp) + c(dy/dp) + * = -ay + cx + * + * The min and max u are when du/dp is zero: + * + * -ay + cx = 0 + * cx = ay + * c = ay/x (2) + * y = cx/a (3) + * + * Substitute (2) into (1) and simplify: + * + * u = ax + ay^2/x + * = a(x^2+y^2)/x + * = a/x (because x^2+y^2 = 1) + * x = a/u (4) + * + * Substitute (4) into (3) and simplify: + * + * y = c(a/u)/a + * y = c/u (5) + * + * Square (4) and (5) and add: + * + * x^2+y^2 = (a^2+c^2)/u^2 + * + * But x^2+y^2 is 1: + * + * 1 = (a^2+c^2)/u^2 + * u^2 = a^2+c^2 + * u = hypot(a,c) + * + * Similarily the max/min of v is at: + * + * v = hypot(b,d) + * + */ static void compute_extents (pixman_f_transform_t *trans, double *sx, double *sy) { - double min_x, max_x, min_y, max_y; - pixman_f_vector_t v[4] = - { - { { 1, 1, 1 } }, - { { -1, 1, 1 } }, - { { -1, -1, 1 } }, - { { 1, -1, 1 } }, - }; - - pixman_f_transform_point (trans, &v[0]); - pixman_f_transform_point (trans, &v[1]); - pixman_f_transform_point (trans, &v[2]); - pixman_f_transform_point (trans, &v[3]); - - min_x = min4 (v[0].v[0], v[1].v[0], v[2].v[0], v[3].v[0]); - max_x = max4 (v[0].v[0], v[1].v[0], v[2].v[0], v[3].v[0]); - min_y = min4 (v[0].v[1], v[1].v[1], v[2].v[1], v[3].v[1]); - max_y = max4 (v[0].v[1], v[1].v[1], v[2].v[1], v[3].v[1]); - - *sx = (max_x - min_x) / 2.0; - *sy = (max_y - min_y) / 2.0; + *sx = hypot (trans->m[0][0], trans->m[0][1]) / trans->m[2][2]; + *sy = hypot (trans->m[1][0], trans->m[1][1]) / trans->m[2][2]; } typedef struct |