| Description |
1 online resource (242 pages) |
| Contents |
Cover; Half Title; Title Page; Copyright Page; Dedication; Table of Contents; Preface; 1: The Bare Basics; 1.1 Points and Vectors; 1.2 Operations; 1.3 Products; 1.4 Affine Maps; 1.5 Triangles and Tetrahedra; 1.6 Exercises; 2: Lines and Planes; 2.1 Linear Interpolation; 2.2 Line Forms; 2.3 Planes; 2.4 Linear Pieces: Polygons; 2.5 Linear Pieces: Triangulations; 2.6 Working with Triangulations; 2.7 Exercises; 3: Cubic Bézier Curves; 3.1 Parametric Curves; 3.2 Cubic Bézier Curves; 3.3 Derivatives; 3.4 The de Casteljau Algorithm; 3.5 Subdivision; 3.6 Exploring the Properties of Bézier Curves |
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3.7 The Matrix Form and Monomials3.8 Exercises; 4: Bézier Curves: Cubic and Beyond; 4.1 Bézier Curves; 4.2 Derivatives Revisited; 4.3 The de Casteljau Algorithm Revisited; 4.4 The Matrix Form and Monomials Revisited; 4.5 Degree Elevation; 4.6 Degree Reduction; 4.7 Bézier Curves over General Intervals; 4.8 Functional Bézier Curves; 4.9 More on Bernstein Polynomials; 4.10 Exercises; 5: Putting Curves to Work; 5.1 Cubic Interpolation; 5.2 Interpolation Beyond Cubics; 5.3 Aitkenâ#x80;#x99;s Algorithm; 5.4 Approximation; 5.5 Finding the Right Parameters; 5.6 Hermite Interpolation; 5.7 Exercises |
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6: Bézier Patches6.1 Parametric Surfaces; 6.2 Bilinear Patches; 6.3 Bézier Patches; 6.4 Properties of Bézier Patches; 6.5 Derivatives; 6.6 Higher Order Derivatives; 6.7 The de Casteljau Algorithm; 6.8 Normals; 6.9 Changing Degrees; 6.10 Subdivision; 6.11 Ruled Bézier Patches; 6.12 Functional Bézier Patches; 6.13 Monomial Patches; 6.14 Exercises; 7: Working with Polynomial Patches; 7.1 Bicubic Interpolation; 7.2 Interpolation using Higher Degrees; 7.3 Coons Patches; 7.4 Bicubic Hermite Interpolation; 7.5 Trimmed Patches; 7.6 Least Squares Approximation; 7.7 Exercises; 8: Shape |
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8.1 The Frenet Frame8.2 Curvature and Torsion; 8.3 Surface Curvatures; 8.4 Reflection Lines; 8.5 Exercises; 9: Composite Curves; 9.1 Piecewise Bézier Curves; 9.2 C1 and G1 Continuity; 9.3 C2 and G2 Continuity; 9.4 Working with Piecewise Bézier Curves; 9.5 Point-Normal Interpolation; 9.6 Exercises; 10: B-Spline Curves; 10.1 Basic Definitions; 10.2 The de Boor Algorithm; 10.3 Practicalities of the de Boor Algorithm; 10.4 Properties of B-Spline Curves; 10.5 B-Splines: The Building Block; 10.6 Knot Insertion; 10.7 Periodic B-Spline Curves; 10.8 Derivatives; 10.9 Exercises |
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11: Working with B-Spline Curves11.1 Designing with B-Spline Curves; 11.2 Least Squares Approximation; 11.3 Shape Equations; 11.4 Cubic Spline Interpolation; 11.5 Cubic Spline Interpolation in a Nutshell; 11.6 Exercises; 12: Composite Surfaces; 12.1 Composite Bézier Surfaces; 12.2 B-Spline Surfaces; 12.3 B-Spline Surface Approximation; 12.4 B-Spline Surface Interpolation; 12.5 Subdivision Surfaces: Doo-Sabin; 12.6 Subdivision Surfaces: Catmull-Clark; 12.7 Exercises; 13: NURBS; 13.1 Conics; 13.2 Reparametrization and Classification; 13.3 Derivatives; 13.4 The Circle |
| Notes |
13.5 Rational Bézier Curves |
| Bibliography |
Includes bibliographical references and index |
| Notes |
Print version record |
| Subject |
Computer graphics
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Computer-aided design.
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Computer Graphics
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Computer-Aided Design
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computer graphics.
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computer-aided designs (visual works)
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computer-aided design (process)
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COMPUTERS -- General.
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Computer-aided design
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Computer graphics
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| Form |
Electronic book
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| Author |
Hansford, Dianne
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| ISBN |
9781439864111 |
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143986411X |
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