ECS 178 -- Geometric Modeling

Unit 8 -- Subdivision Curves

Looking at curves in a different way!

Home

Video Lectures and Notes

FAQs

 

joy@cs.ucdavis.edu

Unit 8 -- Subdivision Curves

Section Description Video Notes Exercises

Subdivision Curves

     
QuadSplit

Splitting a Quadratic Uniform B-Spline Curve

We can use the matrix notation of a quadratic uniform B-spline curve to generate splitting matrices that separate the curve into two segments.

Video Here Notes Here  
Quadratic  Sub

Subdivision Curves based upon the Quadratic Uniform B-Spline Curve

We can develop a subdivision/refinement procedure based on quadratic uniform B-spline curves that looks exactly like Chaikin's algorithm.

Video Here Notes Here  
Cubic Split

Splitting a Cubic Uniform B-Spline Curve

We can use the matrix notation of a cubic uniform B-spline curve to generate splitting matrices that separate the curve into two segments.

Video Here Notes Here  
Cubic Sub

Subdivision Curves based upon the Cubic Uniform B-Spline Curve

We can extend these methods to develop a subdivision/refinement procedure based on the cubic uniform B-spline curve.

Video Here Notes Here  
Vertex and Edge

Vertex and Edge Points

We can classify points on the uniform cubic B-spline refinement in a simple way.

Video Here Notes Here  
Direct Calculation

Direct Calculation of Points on a Cubic Subdivision Curve

We can generate methods to directly calculate points on the curve, greatly simplifying the refinement process.

Notes Here  
Tangent

Calculating Tangent Vectors to Subdivision Curves

By modifying the procedure to directly generate points, we can directly calculate tangent vectors on the surfaces.

Notes Here  

 
 

Copyright 2012 UC Davis. All Rights Reserved