[Pixman] [PATCH v9 01/15] demos/scale: Compute filter size using boundary of xformed ellipse, not rectangle

[Bill Spitzak]

Okay, thanks for the info. Will try to fix them all.

On Mon, Feb 1, 2016 at 5:51 AM, Oded Gabbay <oded.gabbay at gmail.com> wrote:

> On Fri, Jan 22, 2016 at 11:41 AM, <spitzak at gmail.com> wrote:
> >
> > From: Bill Spitzak <spitzak at gmail.com>
> >
> > This is much more accurate and less blurry. In particular the filtering
> does
> > not change as the image is rotated.
> >
> > Signed-off-by: Bill Spitzak <spitzak at gmail.com>
> > ---
> >  demos/scale.c | 102
> +++++++++++++++++++++++++++++++++++-----------------------
> >  1 file 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
> > --
> > 1.9.1
> >
> > _______________________________________________
> > Pixman mailing list
> > Pixman at lists.freedesktop.org
> > http://lists.freedesktop.org/mailman/listinfo/pixman
>
> Reviewed-by: Oded Gabbay <oded.gabbay at gmail.com>
>
> p.s. if we have additional versions of this patch series, and patches
> that got r-b are not modified, then please add my r-b to the patch so
> I would know I don't need to spend even a second over that patch.
>
> Thanks
>
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