Re: [Gnash-dev] Re:Matrix math (strk)

[Mark Voorhies]

On Wednesday 03 September 2008 09:40:27 Mark Voorhies wrote:
> On Wednesday 03 September 2008 04:10:54 strk wrote:
> > On Tue, Sep 02, 2008 at 11:23:01PM -0700, Mark Voorhies wrote:
> > 
> > > I think that pushing the reflection into sx gives the expected behavior 
as 
> > > long as the sx != 0 (choosing sx rather than sy is arbitrary).
> > > 
> > > For the reflection case, atan2 returns the wrong sign (the logic for 
> assigning 
> > > quadrants assumes only rotation), so it is still necessary to do the 
sign 
> > > correction in get_rotation:
> > > 
> > > E.g.
> > > 
> > > double
> > > matrix::get_x_scale() const
> > > {
> > >     if(determinant() < 0)
> > >     {
> > >        // Capture reflection in x-scale
> > >        return -sqrt(((double)sx * sx + (double)shx * shx)) / 65536.0;
> > >     }
> > >     else
> > >     {
> > >        return sqrt(((double)sx * sx + (double)shx * shx)) / 65536.0;
> > >     }
> > > }
> > > 
> > > double
> > > matrix::get_y_scale() const
> > > {
> > >     return sqrt(((double)sy * sy + (double)shy * shy)) / 65536.0;
> > > }
> > 
> > Using sqrt here would make it impossible for Y scale to be negative.
> > 
> > --strk;
> > 
> 
> Correct.  If x_scale and y_scale are both positive then there is no 
> reflection.  If x_scale xor y_scale is negative then there is a reflection 
> (about the y-axis or x-axis respectively).  If both x_scale and y_scale are 
> negative then there is no net reflection; instead, the reflections about 
both 
> axes yield a rotation, which is redundant to the rotation component.
> 
> Since the rotation and translation components _can't_ describe a reflection, 
> we have to capture it as a negative value in one of the scale components.  I 
> arbitrarily chose x_scale, which should work in all cases except for x_scale 
> = 0.  (x_scale = 0 xor y_scale = 0 will give a zero determinant and collapse 
> the image to a line.  In this case, capturing a reflection as a 180 degree 
> rotation _will_ work.  If both x_scale and y_scale = 0, the image will 
> collapse to a point and both reflection and rotation become moot).
> 
> --Mark
> 
> 

Oops! x_scale = 0 xor y_scale = 0 does not, in general, give a zero 
determinant.  I'm pretty sure the rest of the logic is correct.

--Mark