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Apr 24, 1986, 7:50:12 AM4/24/86

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I am beginning some work on graphing 2-d and 3-d curves and surfaces and

I have run across the following problem:

If given an equation of a 3-dimensional surface in the form

f(x, y, z) = ...

and a range of values for x, y, and z

x1 < x < x2

y1 < y < y2

z1 < z < z2

is there an algorith for determining the parametric equations for the

same surface

fx(t) = ...

fy(t) = ...

fz(t) = ...

where 0 <= t <= 1

In short, is there an algorithmic way of generating parametric equations

from nonparametric ones?

I would appreciate any pointers, ideas, program code, etc. that anyone

would post.

Thanks in advance,

Gary Letourneau

letourneau@nlm-mcs

Apr 29, 1986, 1:09:06 PM4/29/86

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In article <14...@nlm-mcs.ARPA> ga...@nlm-mcs.ARPA (Gary Letourneau) writes:

> If given an equation of a 3-dimensional surface in the form

> f(x, y, z) = ...

> and a range of values for x, y, and z

> x1 < x < x2, y1 < y < y2, z1 < z < z2> If given an equation of a 3-dimensional surface in the form

> f(x, y, z) = ...

> and a range of values for x, y, and z

> is there an algorith for determining the parametric equations for the

> same surface

First, you'll never get a full surface from a univariate function; you need

two variables:

fx(u,v), fy(u,v), fz(u,v), 0 <= u <= 1, 0 <= v <= 1

Otherwise, you'll get a curve instead of a surface.

--

Ken Turkowski @ CIMLINC, Menlo Park, CA

UUCP: {amd,decwrl,hplabs,seismo}!turtlevax!ken

ARPA: turtlevax!k...@DECWRL.DEC.COM

Apr 30, 1986, 3:57:26 PM4/30/86

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An excellent book that covers the mathematical representations of parametric

curves, surfaces, and solid plus their generation from non-parametric

objects is one entitled _Geometric Modeling_ by Michael E. Mortenson from

John Wiley & Sons (1985). You should find everything you need in there

plus more about the analytical properties of these objects, transformations,

and some information on solid modeling.

David E. Lee

UCLA ACM Chairman

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