SiteStat.jsp
AN INTRODUCTION TO SPLINES FOR USE IN COMPUTER GRAPHICS AND GEOMETRIC MODELING
To order this title, and for more information, click here
Richard Bartels
John Beatty
Brian Barsky
Included in series The Morgan Kaufmann Series in Computer Graphics, Description An Introduction to Splines for Use in Computer Graphics and
Geometric Modeling discusses the use of splines from the point of view of the computer scientist. Assuming only a background in
beginning calculus, the authors present the material using many examples and illustrations with the goal of building the reader's intuition.
Based on courses given at the University of California, Berkeley, and the University of Waterloo, as well as numerous ACM Siggraph tutorials,
the book includes the most recent advances in computer-aided geometric modeling and design to make spline modeling techniques generally
accessible to the computer graphics and geometric modeling communities.Contents An Introduction to Splines for Use in Computer Graphics and Geometric Modeling
1 Introduction
2 Preliminaries
3 Hermite and Cubic Spline Interpolation
3.1 Practical Considerations - Computing Natural Cubic Splines
3.2 Other End Conditions For Cubic Interpolating Splines
3.3 Knot Spacing
3.4 Closed Curves
4
A Simple Approximation Technique - Uniform Cubic B-splines
4.1 Simple Preliminaries - Linear B-splines
4.2
Uniform Cubic B-splines
4.3 The Convex Hull Property
4.4 Translation Invariance
4.5 Rotation and Scaling
Invariance
4.6 End Conditions for Curves
4.7 Uniform Bicubic B-spline Surfaces
4.8 Continuity for Surfaces
4.9 How Many Patches Are There?
4.10 Other Properties
4.11 Boundary Conditions for Surfaces
5
Splines in a More General Setting
5.1 Preliminaries
5.2 Continuity
5.3 Segment Transitions
5.4 Polynomials
5.5 Vector Spaces
5.6 Polynomials as a Vector Space
5.7 Bases and Dimension
5.8
Change of Basis
5.9 Subspaces
5.10 Knots and Parameter Ranges: Splines as a Vector Space
5.11 Spline Continuity
and Multiple Knots
6 The One-Sided Basis
6.1 The One-Sided Cubic
6.2 The General
Case
6.3 One-Sided Basis
6.5 Linear Combinations and Cancellation
6.6 Cancellation as a Divided Difference
6.7 Cancelling the Quadratic Term - The Second Difference
6.8 Cancelling the Linear Term - The Third Difference
6.9
The Uniform Cubic B-Spline - A Fourth Difference
7 Divided Differences
7.1 Differentiation
and One-Sided Power Functions
7.2 Divided Differences in a General Setting
7.3 Algebraic and Analytic Properties
8 General B-splines
8.1 A Simple Example - Step Function B-splines
8.2 Linear B-splines
8.3 General B-spline Bases
8.4 Examples - Quadratic B-splines
8.5 The Visual Effect of Knot Multiplicities -
Cubic B-splines
8.6 Altering Knot Spacing - More Cubic B-splines
9 B-spline Properties
9.1 Differencing Products - The Leibniz Rule
9.2 Establishing a Recurrence
9.3 The Recurrence and Examples
9.4 Evaluating B-splines Through Recurrence
9.5 Compact Support, Positivity, and the Convex Hull Property
9.6
Practical Implications
10 Bezier Curves
10.1 Increasing the Degree of a Bezier Curve
10.2 Composite Bezier Curves
10.3 Local vs. Global Curves
10.4 Subdivision and Refinement
10.5 Midpoint
Subdivision of Bezier Curves
10.6 Arbitrary Subdivision of Bezier Curves
10.7 Bezier Curves From B-Splines
10.8
A Matrix Formulation
10.9 Converting Between Representations
10.10 Bezier Surfaces
11.
Knot Insertion
11.1 Knots and Vertices
11.2 Representation Results
12 The Oslo
Algorithm
12.1 Discrete B-spline Recurrence
12.2 Discrete B-spline Properties
12.3 Control Vertex
Recurrence
12.4 Illustrations
13 Parametric vs. Geometric Continuity
13.1 Geometric
Continuity
13.2 Continuity of the First Derivative Vector
13.3 Continuity of the Second Derivative Vector
14 Uniformly-Shaped Beta-spline Surfaces
14.1 Uniformly-Shaped Beta-spline Surfaces
14.2 An
Historical Note
15 Geometric Continuity, Reparametrization, and the Chain Rule
16
Continuously-Shaped Beta-splines
16.1 Locality
16.2 Bias
16.3 Tension
16.4 Convex Hull
16.5 End Conditions
16.6 Evaluation
16.7 Continuously-Shaped Beta-spline Surfaces
17
An Explicity Formulation for Cubic Beta-splines
17.1 Beta-splines with Uniform Knot Spacing
17.2 Formulas
17.3 Recurrence
17.4 Examples
18 Discretely-Shaped Beta-splines
18.1 A Truncated
Power Basis for the Beta-splines
18.2 A Local Basis for the Beta-splines
18.3 Evaluation
18.4 Equivalence
18.5 Beta2-splines
18.6 Examples
19 B-spline Representations for Beta-splines
19.1
Linear Equations
19.2 Examples
20 Rendering and Evaluation
20.1 Values of B-splines
20.2 Sums of B-splines
20.3 Derivatives of B-splines
20.4 Conversion to Segment Polynomials
20.5 Rendering
Curves: Horner's Rule and Forward Differencing
20.6 The Oslo Algorithm - Computing Discrete B-splines
20.7 Parial
Derivatives and Normals
20.8 Locality
20.9 Scan-Line Methods
20.10 Ray-Tracing B-spline Surfaces
21 Selected Applications
21.1 The Hermite Basis and C1 Key-Frame Inbetweening
21.2 A Cardinal
Basis Spline for Interpolation
21.3 Interpolation Using B-splines
21.4 Catmull-Rom Splines
21.5 B-splines
and Least Squares Fitting
References
Index
Bibliographic details
Paperback, 476 pages, publication date: SEP-1995
Price and Ordering
Price:
Books and book related electronic products are priced in US dollars (USD), euro (EUR), and Great Britain Pounds (GBP). USD prices apply to the Americas and Asia Pacific. EUR prices apply in Europe and the Middle East. GBP prices apply to the UK and all other countries.
See also information about conditions of sale & ordering procedures regional sales offices
077/747
Last update: 7 Sep 2009
Home | Elsevier Sites | Privacy Policy | Terms and Conditions | Feedback | Site Map | A Reed Elsevier Company