Christoph Hormann wrote:
> The docs are wrong, f_rounded_box() should only be used with radius > 0. 
>  This is not a bug but simply a limitation (although it would of course 
> make sense to add an efficient handling of the case radius=0).
> 
> Note the current f_rounded_box() is not a very efficient solution anyway 
> (you don't need an sqrt() for every evaluation).
Actually I tried the following expression.

return (PARAM_X * PARAM_X
  + PARAM_Y * PARAM_Y
  + PARAM_Z * PARAM_Z
  - PARAM(0)*PARAM(0));

against

return (
  sqrt(PARAM_X * PARAM_X
  + PARAM_Y * PARAM_Y
  + PARAM_Z * PARAM_Z)
  - PARAM(0));

And found that the latter was always faster by about 30%.
I'm not exactly sure why it is that way but one problem
is that a the max_gradient needs higher values.
For the former version a max_gradient of 1.0 is always
suitable whereas for the latter one something
like

2.0*sqrt(3)*RADIUS

is neccessary.
There may be parameters for which the latter one is faster
but in the geral case the square root beats the square.
A least this is the result from the tests renders I did
on my pentium-m 1300MHz machine.

The most promissing solution I found looks like this.

DBL f_rounded_box(DBL *ptr, unsigned int) // 60
{

   DBL x2, y2, z2, x3, y3, z3;

   x2 = PARAM(1) - PARAM(0);
   y2 = PARAM(2) - PARAM(0);
   z2 = PARAM(3) - PARAM(0);

   x3 = fabs(PARAM_X);
   y3 = fabs(PARAM_Y);
   z3 = fabs(PARAM_Z);

   PARAM_X = (x3 < x2) ? 0 : (x3 - x2);
   PARAM_Y = (y3 < y2) ? 0 : (y3 - y2);
   PARAM_Z = (z3 < z2) ? 0 : (z3 - z2);

return (sqrt(PARAM_X * PARAM_X + PARAM_Y * PARAM_Y + PARAM_Z * PARAM_Z) 
  - PARAM(0));

}

Using fabs gave me approx. 2% speed increase in the test scene
(p.b.images).

> 
> To me it seems this offset is specifically for handling the degenerate 
> case.  Choosing 1e-3 simply gets you beyond your accuracy limit.

This was my intention. And yes, this is very likely. I tried the
degenerated case without the offset and the render process stuck
on the first line until I aborted after some minutes.

Sebastian

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