**Up:** *Lab Assignment #2b: Animation*

# Some Project Ideas:

The following are some simple and not-so-simple animation projects
that you could try during this lab. Choose one that sounds
interesting to you, or make up one of your own.
## Straight-Forward Projects:

- Create a saddle surface in polar form and rotate it to view it
from different views. Recall that a saddle has the form
*z* =
*r*^2 sin(2 *theta*).

- Create a higher order saddle in polar form (the standard saddle
has two "ups" and two "downs" due to the factor of 2 in the equation
above). Make a saddle with 3 ups and downs, and view it from various
angles.

- Create the graph of the function
*z* = *x*^3 + *ax*
- *y*^2 for *x* in [-1.5,1.5] and *y* in [-1.2,1.2].
Choose an interesting value for *a*. Using the standard file
`square.quad`

that comes with Geomview, slice the graph of
the surface by horizontal planes. Make a movie of the plane
slicing the surface as it moves from *z* = -1 to *z* = 1.

- Make a helicoid (it is parameterized by (
*u* cos(*v*),
*u* sin(*v*), *a* *v*)) and animate it so that it
translates along its axis while rotating. Try to make the rotation
rate such that the helicoid appears to "screw" through space.

## More Challenging:

- For the cubit surface in the third example anove, animate the
surface as the parameter
*a* changes from -1 to 1.

- Create a surface in space (for example, you could use one of the
surfaces from the previous examples) and animate a point moving along
a path on the surface. You might use a very small sphere to represent
the point on the surface.

- Make a movie of a ball bouncing off a wall. Can you make the ball
deform when it hits?

- Make a movie of a ball bouncing several times on the ground under
the influence of gravity.

- Make a movie of a collision between two unequal spherical masses.
Make sure that momentum is conserved. (You might try having one mass
be at rest for your first attempt).

- Make a movie of two balloons connected by a rigid pipe: have one
balloon shrink and the other expand. Can you make the changes in
volume between the two spheres match?

**Up:** *Lab Assignment #2b: Animation*

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Created: Jun 01 1996 ---
Last modified: Jun 01 1996