# CS 184: COMPUTER GRAPHICS

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

## Review and Use of Splines

-- 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:

• Smooth camera paths.
• Rollercoaster tracks.
• Snake bodies.
• Curved smooth bodies and shells.
• 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.
•               -- A variant for indoor scenes, floor plans: Split along major occluding walls near middle.
• BSP (Binary Space Partitioning) -- A generalization for scenes with big, non-axis-aligned divider polygons.

## Reading Assignment:

Study: 2ndEd: Ch 10.5-10.7; 11.6-11.7
Study: 3rdEd: Ch  10.5-10.7; 11.6-11.7

## ASG#10  Final Project

Project Due Date is Monday, December 13, 7:59pm.

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