CS184 Lecture Fall 04

-- Interpolating Splines (pass through all the data points; example Hermite splines), and
-- Approximating Splines (only come close to data points; example B-Splines).
-- Parametric Continuity: differentiability of the parametric representation (C0, C1, C2, ...)
-- Geometric Continuity: smoothness of the resulting displayed shape (G0=C0, G1=tangent-cont., G2=curvature-cont. )
-- Cubic Bezier Curves: How to draw them with deCasteljau method.
-- Approximating a given curve: How to find suitable Bezier control points.

Use of Splines in Final Project:

A good introductory booklet on Splines with interactive demos:
"Interactive Curves and Surfaces," (with Multimedia Tutorial on CAGD),
A. Rockwood and P. Chambers, Morgan Kaufman Publishers, Inc.

Splines, Subdivision Surfaces, and Fractal Mountains

see Powerpoint slides.

Remarks about Final Project

Due dates, deliverables.

Commonly Used Spatial Subdivision and Indexing Structures

Useful in many different contexts:
    -- They can be traversed in "front-to-back" order for ray-tracing,
    -- or they can be traversed "back-to-front" for an object-space "painter's algorithm".
    -- They are also useful in collision detection, haptics interfaces, path planning ...

Regular Grid -- Simplest method; OK for scene with uniformly distributed content.
Octree -- You are already familiar with this: Nice regular, adaptive "grid".
kD-Tree -- A generalization: Recursively split bounding box along longest axis near median of data.

indoor scenes, floor plans

BSP (Binary Space Partitioning) -- A generalization for scenes with big, non-axis-aligned divider polygons.

CS 184: COMPUTER GRAPHICS

Lecture #25 -- Tu: 11/30, 2004

Review and Use of Splines

Use of Splines in Final Project:

Splines, Subdivision Surfaces, and Fractal Mountains

Remarks about Final Project

Commonly Used Spatial Subdivision and Indexing Structures

Reading Assignment:

ASG#10 Final Project