CS184 Lecture 2 summary

TIP: When you browse the VRML models, you can click on "View source" in IE or Netscape to see the VRML source.

2D Objects and Transformations

Some basics of VRML files: The header line. Node hierarchies. Keyword-value tuples. Example.

Representation of points in the plane, X-Y coordinates. Point sets in VRML.

Representing lines and Linesets in 2D. Loop lists. Line sets in VRML.

Representing polygons in 2D. Loop lists oriented counter-clockwise. VRML example.

Definition of convex polygon. Specifying convexity in VRML. Example.

2D Transformations

2D translation by vector addition. Translations commute. VRML example.

2D rotations. Linearity of rotation. Rotation matrices. 2D Rotations commute. VRML example.

General 2D transformations. Rotation followed by translation. VRML example.

General 2D transformations do not commute. VRML example.

Homogeneous representation of points. General 2D transformations using 3x3 matrices.

Converting from matrix to translation-rotation representation for general 2D transformations.