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Essentials of CAGD

ISBN-10: 1568811233
ISBN-13: 9781568811239
Edition: 2000
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Book details

Copyright year: 2000
Publisher: A K Peters, Limited
Publication date: 10/25/2000
Binding: Hardcover
Pages: 248
Size: 7.25" wide x 9.50" long x 0.75" tall
Weight: 1.298
Language: English

Preface
The Bare Basics
Points and Vectors
Operations
Products
Affine Maps
Triangles and Tetrahedra
Exercises
Lines and Planes
Linear Interpolation
Line Forms
Planes
Linear Pieces: Polygons
Linear Pieces: Triangulations
Working with Triangulations
Exercises
Cubic Bezier Curves
Parametric Curves
Cubic Bezier Curves
Derivatives
The de Casteljau Algorithm
Subdivision
Exploring the Properties of Bezier Curves
The Matrix Form and Monomials
Exercises
Bezier Curves: Cubic and Beyond
Bezier Curves
Derivatives Revisited
The de Casteljau Algorithm Revisited
The Matrix Form and Monomials Revisited
Degree Elevation
Degree Reduction
Bezier Curves over General Intervals
Functional Bezier Curves
More on Bernstein Polynomials
Exercises
Putting Curves to Work
Cubic Interpolation
Interpolation Beyond Cubics
Aitken's Algorithm
Approximation
Finding the Right Parameters
Hermite Interpolation
Exercises
Bezier Patches
Parametric Surfaces
Bilinear Patches
Bezier Patches
Properties of Bezier Patches
Derivatives
Higher Order Derivatives
The de Casteljau Algorithm
Normals
Changing Degrees
Subdivision
Ruled Bezier Patches
Functional Bezier Patches
Monomial Patches
Exercises
Working with Polynomial Patches
Bicubic Interpolation
Interpolation using Higher Degrees
Coons Patches
Bicubic Hermite Interpolation
Trimmed Patches
Least Squares Approximation
Exercises
Shape
The Frenet Frame
Curvature and Torsion
Surface Curvatures
Reflection Lines
Exercises
Composite Curves
Piecewise Bezier Curves
C[superscript 1] and G[superscript 1] Continuity
C[superscript 2] and G[superscript 2] Continuity
Working with Piecewise Bezier Curves
Point-Normal Interpolation
Exercises
B-Spline Curves
Basic Definitions
The de Boor Algorithm
Practicalities of the de Boor Algorithm
Properties of B-Spline Curves
B-Splines: The Building Block
Knot Insertion
Periodic B-Spline Curves
Derivatives
Exercises
Working with B-Spline Curves
Designing with B-Spline Curves
Least Squares Approximation
Shape Equations
Cubic Spline Interpolation
Cubic Spline Interpolation in a Nutshell
Exercises
Composite Surfaces
Composite Bezier Surfaces
B-Spline Surfaces
B-Spline Surface Approximation
B-Spline Surface Interpolation
Subdivision Surfaces: Doo-Sabin
Subdivision Surfaces: Catmull-Clark
Exercises
Nurbs
Conics
Reparametrization and Classification
Derivatives
The Circle
Rational Bezier Curves
Rational B-Spline Curves
Rational Bezier and B-spline Surfaces
Surfaces of Revolution
Exercises
Hunting Geometry Bugs
Solutions to Selected Exercises
Notation
Bibliography
Index

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