Computer Graphics Homework Set #1

Model Space

1.

The Platonic solids are widely used as sample objects. Develop model data files for the Platonic solids: The tetrahedron, hexahedron, octahedron, icosahedron, and dodecahedron. Blinn [Bli96] and Hill [Hil90] are two books that have complete descriptions of the Platonic solids. Platonic Realms at MathAcademy.com [Mat99] and Scared Geometry Objects by Beall [Bea99] are two on-line references that may be interesting.

Transformations

1.

Show that a weighted sum of points is a vector when the weights add to zero.

2.

Find a matrix that will scale an object uniformly by 2 leaving the point $[3\:1\:4]$ fixed.

3.

Find a matrix that will rotate an object by $\pi/4$ radians about the axis through the origin with direction vector $\langle 1,\,-1,\,1\rangle$.

4.

Find a matrix that will scale an object uniformly by 0.5 leaving $[1\:1\:1]$ fixed.

5.

Find the parametric equation of the line from $[3\:1\:4]$ to $[2\:7\:8]$.

Bibliography

Bea99

J.Vincent Beall.
Sacred geometry objects.
http://home.dmv.com/ vincent, September 9 1999.

Bli96

Jim Blinn.
Jim Blinn's Corner: a trip down the graphics pipeline.
Morgan Kaufmann Publishers, Inc., 1996.
1-55860-387-5.

Hil90

F. S. Hill Jr.
Computer Graphics.
MacMillan Publishing Company, 1990.

Mat99

MathAcademy.com.
Platonic realms.
http://www.mathacademy.com/platonic_realms/Platohom.html, September 9 1999.