<div dir="ltr">Well that was a pain to figure out again (it is tricky to get p and x and y cancelled out of the calculation) but does this make any sense: <div> Calculate bounding box of radius-1 circle in xy transformed to uv: Transform x,y to u,v by this matrix calculation: |u| |a c| |x| |v| = |b d|*|y| Horizontal component: u = ax+cy (1) x,y describes a radius-1 circle, p is angle to the point: p = 0..2*pi x = cos(p) y = sin(p) x^2+y^2 = 1 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) </div></div><div class="gmail_extra"> <div class="gmail_quote">On Thu, Dec 17, 2015 at 1:52 AM, Oded Gabbay <<a href="mailto:oded.gabbay@gmail.com" target="_blank">oded.gabbay@gmail.com</a>> wrote: <blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div class="HOEnZb"><div class="h5">On Sat, Dec 12, 2015 at 8:06 PM, <<a href="mailto:spitzak@gmail.com">spitzak@gmail.com</a>> wrote: > From: Bill Spitzak <<a href="mailto:spitzak@gmail.com">spitzak@gmail.com</a>> > > This is much more accurate and less blurry. In particular the filtering does > not change as the image is rotated. > --- > demos/scale.c | 43 ++----------------------------------------- > 1 file changed, 2 insertions(+), 41 deletions(-) > > diff --git a/demos/scale.c b/demos/scale.c > index d00307e..71c7791 100644 > --- a/demos/scale.c > +++ b/demos/scale.c > @@ -55,50 +55,11 @@ 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); > -} > - > 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 > -- > 1.9.1 > </div></div>> _______________________________________________ > Pixman mailing list > <a href="mailto:Pixman@lists.freedesktop.org">Pixman@lists.freedesktop.org</a> > <a href="http://lists.freedesktop.org/mailman/listinfo/pixman" rel="noreferrer" target="_blank">http://lists.freedesktop.org/mailman/listinfo/pixman</a> Could you please add some comment in the code about where this calculation comes from (reference to some mathematical equation/proof), and detail the mapping of the variables in the code to the arguments of the mathematical equation ? Otherwise, this patch is: Reviewed-by: Oded Gabbay <<a href="mailto:oded.gabbay@gmail.com">oded.gabbay@gmail.com</a>> </blockquote></div> </div>