BU
CAS
CS 480
Introduction to Computer Graphics
Spring 1996
Programming Assignment 4:
Shaded Display of Superquadric Toroids
Due before class on Tuesday April 9
The purpose of the assignment is to introduce you to 1) polygonal surface
generation, 2) basic 3-D shaded display in OpenGL, and 3) camera modeling.
The Program You Write
Write a program that allows the user to create and display a superquadric
toroid (donut) in 3-D with shading.
-
Allow the user to modify the toroid's two exponents, the three radii,
and the hole radius. You may also want to allow the user to vary the
number of polygons used to approximate the torus.
-
Allow the user to modify the camera viewpoint to front, back, top,
bottom, left, and right views. In addition, make it possible to
rotate and position the object in 3-D. To make things easier, center
you may want to put your toroid at the world coordinate system
origin.
-
Create an animation by defining a camera trajectory, and ``fly by'' a
model created with your toroid(s). During the fly-by, the camera
motion should be smooth and remain pointed at the center of the
scene.
Parametric Surface and Normal Functions
Given the following equations:
c(w,m) = SGN(cos(w))*pow(fabs(cos(w)),m)
s(w,m) = SGN(sin(w))*pow(fabs(sin(w)),m)
where SGN(x) = -1, 0, or 1, depending on whether x
is less than, equal, or greater than 0. Suggestion: SGN(x) can be
implemented as a C macro.
Points on the surface of a superquadric toroid can be
computed with the following parametric equations:
x(u,v) = rx*(r + c(u,e1))*c(v,e2)
y(u,v) = ry*(r + c(u,e1))*s(v,e2)
z(u,v) = rz*s(u,e1)
where:
rx, ry, rz are the radii,
r is the hole's radius,
e1, e2 are the superquadric exponents,
u, v are the surface parameters, both in the range -PI to PI.
Normals on the surface of a superquadric toroid can
be computed with the following equations:
nx(u,v) = (1.0/rx)*c(u,2-e1)*c(v,2-e2)
ny(u,v) = (1.0/ry)*c(u,2-e1)*s(v,2-e2)
nz(u,v) = (1.0/rz)*s(u,2-e1)
Example Program
Example source files for a simple program
that generates a shaded display of a "regular" torus are
available in ~cs480/courseware/p4 on the CGL
cluster.
This example program was adapted from "The OpenGL Programming Guide."
This program is only provided as an example and you are not required
to use it as basis for your own program.
Demos and Grading
Your project must run on the SGI, therefore you will need
to use one of the SGI workstations in the CGL cluster (unless you have
access to an OpenGL elsewhere).
Your program's source files are to be electronically submitted by using the submit program on cgl. The code you submit
should conform with the program assignment
guidelines.
Part of your grade for this programming assignment will be based on
your giving a short demo (2-3 minutes) in the CGL cluster. You will
be expected to talk about how your program works, and we will see
how well your program performs on some test examples. Demos will be
scheduled for the Friday afternoon following the assignment due date.
Extra Credit
Compute a procedural texture map using fractal techniques and apply it
to your toroid. Allow the user to toggle whether a texture map is
used or not.
Test Cases
You are responsible for testing your own code.
Page Created: Feb 23, 1996
Last Modified: Feb 23, 1996
Maintained by: Stan Sclaroff