I've been wondering about methods to render and speed up rendering certain
shapes - notably isosurfaces (IS) and parametric (PAR) surfaces.

It has been pointed out that scertain methods of describing algebraic surfaces,
such as the polynomial, are fast, compared to IS and PAR.

The obvious question is WHY are some of these methods fast and others slow?

Another question I have is:  What method is used to determine the fineness of
subdivision for calculation of the surface?  Is it a bailout sort of thing, or
is there some link to the pixel-coverage, where nothing finer than a pixel is
calculated?

Finally - considering a long, continued, and current interest in using meshes as
CSG objects,

Would it be possible / desirable to define an internal mesh-generation method
for rendering complex, time-consuming shapes?
It seems like constructing a mesh of smooth triangles would save a lot of
calculation for the surface (via interpolation)(but I could be wrong) - and
doing that as an internal function would be MUCH faster than doing it through
SDL.
Paul Nylander's code for rendering a parametric surface via smooth-triangles:
http://bugman123.com/Physics/Calabi-Yau.zip

And, speaking of "parametrics", it appeared to me that there were several
(obviously related) methods of calculating these - one method perhaps better
suited to a particular case than another.
For instance, a shape defined by spherical coordinates would only have 2
parametric equations - one for phi and the other for theta (u and v).
A shape using Cartesian coordinates obviously needs 3 - one each for x, y, and
z.
Presumably one can use cylindrical, hyperbolic, and other coordinate systems as
well.

Depending upon the complexity and number of calculations, it would seem that a
separate parametric for a 2-equation surface might be evaluated in 2/3 the time
as a 3-term surface.  Which could in extreme cases be the difference between 6
hours and 9 hours....

Thanks as always for listening, and offering any comments and explanations  :)

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