An Introduction to Splines for Use in Computer Graphics and Geometric Modeling

1st Edition

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Description

As the field of computer graphics develops, techniques for modeling complex curves and surfaces are increasingly important. A major technique is the use of parametric splines in which a curve is defined by piecing together a succession of curve segments, and surfaces are defined by stitching together a mosaic of surface patches.

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.

Table of Contents

An Introduction to Splines for Use in Computer Graphics and Geometric Modeling
by Richard H. Bartels, John C. Beatty, and Brian A. Barsky
    1 Introduction
      1.1 General References

    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

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