**garl@nlm-mcs.ARPA (Gary Letourneau)** (04/24/86)

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

**ken@turtlevax.UUCP (Ken Turkowski)** (04/29/86)

In article <1450@nlm-mcs.ARPA> garl@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 > is there an algorith for determining the parametric equations for the > same surface > fx(t) = ... , fy(t) = ... , fz(t) = ... , 0 <= t <= 1 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!ken@DECWRL.DEC.COM

**acm@ucla-cs.ARPA (Assoc for Computing Machinery )** (04/30/86)

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