Table of Contents
PPT Slide
PPT Slide
Curve Representations
Surface Representations
Parametric Modeling - Outline
PPT Slide
Polynomial Interpolation
Splines: Piecewise Polynomials
Piecewise Polynomials
Cubic Space Curves
Visualizing Parametric Curves
A Linear Piecewise Polynomial
PPT Slide
Why these in particular?
An Illustrative Example
Piecing together Hermite Curves
Deriving Hermite Splines, 1
Deriving Hermite Splines, 2
Hermite Splines in Matrix Notation
The Cubic Hermite Spline Equation
Bezier Curves
From Hermite to Bezier
The Bezier Spline Matrix
Bezier Basis Functions
Bezier Blending Functions
It’s easy to subdivide Bezier curves!
Catmull-Rom Splines
Catmull-Rom Spline Matrix
Splines with More Continuity?
Natural Cubic Splines
Degrees of Freedom with Natural Cubic Splines
Interpolation, Continuity, and Local Control
B-Splines
B-Spline Basis
Comparison of Basic Cubic Splines
Non-Uniform Splines
Two Types of Continuity
Reducing B-Spline Continuity
Rational Cubic Curves
How to Draw Spline Curves
Drawing Splines, 2
Bicubic Surfaces
From Curves to Surfaces
In Summary...
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