Warp wrote:

>   The measurement of volume depends on your definition of volume.

My measurement goes off of eval_pigment and the object pattern in MegaPov. I
leave the metaphysics up to those functions.

>   If so, how do you calculate the volume of this kind of object:
> difference { box { -1,1 }  sphere { 0, 1.1 }}

That's 2.609  cubic units, to a 0.25% precision.  See my macro.  I keep taking
smaller and smaller intervals until the difference between two sucessive
values for volume is less than a certain percentage.

> (and suppose the same situation with more complex objects than a box and a
> sphere, eg. a lathe and an isosurface.)

I tried this isosurface and got a volume of  288737 cubic units.

isosurface{
          function{y/290+noise3d(x*0.05,y**0.05,z**0.05)}
           accuracy 0.01
           threshold .21
           contained_by {sphere{0,100}}
        pigment{SeaGreen}
        finish{ambient 0.1}
        }


As I was tossing in my sleep last night, however, I realized that my macro can
easily handle any of the above discussed objects, but it's not very good for
its original purpose: determining *whether* the intersection between two
objects has zero volume. It's not that great if say I have one object with a
huge bounding box-- say a landscape-- and a bunch of tiny things.  But I guess
if one had enough patience or set a low bailout, it would work here OK too.

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