CS142: Topics for the Week of February 5, 2007

• Look at student web pages for lab 3 images.

• Lab 4: Lathe Objects

• Review Matrices from last week.
  • What is a matrix?
  • How do you multiply a matrix times a point, to get a new point?
  • What is the matrix for
    • A 2D scale. A 3D scale.
    • A 2D rotation, A 3D rotation about x, y, or z axes.
    • A 2D shear. A 3D shear.
    • A 2D translation. A 3D translation. What are homogeneous coordinates.
  • Povray stores matrices a little different from the normal representation. How would your write the above 3D matrices in Povray?

• New Material on Matrices

  • Multiplication
    • How do you multiply 2 matrices together? What does it mean? Why is it useful?
    • In 2D: How do you show that order matters when doing e.g. a scale along x and a 90 degree rotation?
  • Matrix inverses

    povray code

    • What are inverses and how do you calculate them?
    • How do you use inverses to rotate/scale about arbitrary points?
  • Matrix Macros - defining matrices that can vary.

    povray code

• Lathe Objects Generating shapes by rotating points around the y-axis:

  povray code

  Smoothing: Linear vs cubic:

  

  Creating a Scene

  

• Creating your own include file.