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
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
Thanks in advance,
First, you'll never get a full surface from a univariate function; you need
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
David E. Lee
UCLA ACM Chairman