## Parametric Surfaces

** Introduction. **
This exercise is concerned with building surfaces for computer graphics. It will
introduce various types of parametric surfaces.

**Procedure:**
First you will need to download two files. To do this, click on
each of the filenames shown below. When the text window opens, use the
"save as" option to put the file in your own directory. Name each file with
the same name as shown below.

After downloading the files, start DX then
open and execute parametric.net. Each module (when opened) has a one-line
explanation of its function. One of the
Compute modules
performs the
main
operation of mapping a 2D grid to 3D coordinates to make the parametric
surface.
(The others just produce pi and produce the variables [v,w].)

Quadric surfaces: Modify the Compute in Parametric.net to produce a unit
sphere. Use another Compute module to convert the sphere to a
"superquadric". That is, if the vector [x,y,z] is a quadric surface, then
[x,y,z]^n is a superquadric surface, where the power of a vector just
means the power of each term. Try values of n from .2 to 10 or so. You
will need to handle negative values of x, y, and z in the compute. Make
the value of n set by an interactor.
The two images below show a sphere modified by n=.3 and n=3 respectively.

Figures of rotation: Modify the program to produce a figure of rotation given by
cylinder radius r=abs(w)+.1 where w is the axis of the rotation.
Modify the program to produce a figure of rotation
which approximates the shape of a drink bottle.
Two bottles from spring 1995 are particularly elaborate.

Note that the form a?b:c used in a compute module is a conditional. If a is not equal
to zero, then do b, else do c. This allows arbitrary functions to be constructed. For
example, try r=0.2+(w>=0.4?(w-0.4):0.0) to make a funnel.

Modify the original Parametric.net program to convert the torus into a
spiral spring with four complete turns. Animate the spring so that one
end of the spring remains fixed and the other end undergoes simple
harmonic motion. The spring should not pass through itself and the motion
should repeat every 16 frames. Model a sphere which moves sinusoidally
with the end of the spring and appears to be attached to the spring.
One frame of an animation is shown below.

**Bugs as of 3/7/95 **

- The comment in the Construct module is incorrect. It should read
"make a 21x21 grid spanning (0,0) to (1,1)".

Last modified, Sun Apr 30 14:53:00 1995 by Tom Dietterich.

Copyright (1995) by Cornell University.
*Copyright Statement *