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Am 14.08.2018 um 14:21 schrieb Bald Eagle:
> Mike Horvath <mik### [at] gmail com> wrote:
>> On 8/13/2018 10:41 PM, Mike Horvath wrote:
>>> Is there a list somewhere of parametric surfaces that take three
>>> parameters?
>
>> Er, I mean solids, not surfaces.
>
>
> I toyed with this a while back:
>
http://news.povray.org/povray.advanced-users/thread/%3Cweb.579fc21ee9f788f45e7df57c0@news.povray.org%3E/
>
> Any parametric surface would become a parametric solid, given a variable third
> parameter, since - using the sphere for example, you'd have the r value of the
> radius.
> Varying the radius from 0 to unity would give you a solid sphere.
>
> But "solids" in POV-Ray are really only surfaces with insides and outsides,
> aren't they...?
Technically, "solids" in POV-Ray are objects with...
(1a) a well-defined surface,
(1b) an algorithm to compute the intersection points between a ray and
said surface, as well as the surface normals at those points
(2a) a well-defined volume,
(2b) an algorithm to compute whether a given point in 3D space is inside
said volume
3-parametric solids would generally satisfy (1a) and (2a) (except in
pathological cases), but for the general case I guess (1b) and (2b)
would effectively boil down to generating an approximate mesh representaion.
If the 3-parametric equation does not "fold back" into itself, the
surface of the solid can also be modeled using six 2-parametric surfaces.
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