Barnhill / Riesenfeld Computer Aided Geometric Design

1. Auflage 2014
ISBN: 978-1-4832-6848-4
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 336 Seiten, Web PDF

Computer Aided Geometric Design covers the proceedings of the First International Conference on Computer Aided Geometric Design, held at the University of Utah on March 18-21, 1974. This book is composed of 15 chapters and starts with reviews of the properties of surface patch equation and the use of computers in geometrical design. The next chapters deal with the principles of smooth interpolation over triangles and without twist constraints, as well as the graphical representation of surfaces over triangles and rectangles. These topics are followed by discussions of the B-spline curves and surfaces; mathematical and practical possibilities of UNISURF; nonlinear splines; and some piecewise polynomial alternatives to splines under tension. Other chapters explore the smooth parametric surfaces, the space curve as a folded edge, and the interactive computer graphics application of the parametric bi-cubic surface to engineering design problems. The final chapters look into the three-dimensional human-machine communication and a class of local interpolating splines. This book will prove useful to design engineers.

Autoren/Hrsg.

Barnhill, Robert E.

Riesenfeld, Richard F.

Inhaltsverzeichnis

1;Front Cover;1
2;Computer Aided Geometric Design;4
3;Copyright Page;5
4;Table of Contents;6
5;Contributors;8
6;Preface;10
7;CHAPTER 1. SURFACE PATCHES AND B-SPLINE CURVES;12
7.1;Introduction;12
7.2;Surface Patches;12
7.3;A Special Default Condition;17
7.4;B-Splines;17
7.5;Surfaces with B-spline Boundaries;20
7.6;Blending Functions;22
7.7;Initial and Terminal Conditions for a B-Spline;25
7.8;Conclusion;26
7.9;References;27
8;CHAPTER 2. COMPUTATIONAL GEOMETRY - ACHIEVEMENTS AND PROBLEMS;28
8.1;Summary;28
8.2;I. Introduction;28
8.3;II. The Mathematical Basis;30
8.4;III. Implementation;45
8.5;IV. Conclusions;51
8.6;V. References;52
9;CHAPTER 3. SMOOTH INTERPOLATION OVER TRIANGLES;56
9.1;1. Introduction;56
9.2;2. Rational Boolean Interpolants;59
9.3;3. Polynomial Boolean Interpolants;66
9.4;4. Finite Dimensional Interpolants;72
9.5;Acknowledgments;79
9.6;References;80
10;CHAPTER 4. SMOOTH INTERPOLATION WITHOUT TWIST CONSTRAINTS;82
10.1;1. Introduction;82
10.2;2. Smooth C1 Interpolation on Rectangles;84
10.3;3. Smooth C1 Interpolation on Triangles;89
10.4;4. Examples;94
10.5;Acknowledgement;98
10.6;References;98
11;CHAPTER 5. GRAPHICAL REPRESENTATION OF SURFACES OVER TRIANGLES AND RECTANGLES;100
11.1;1. Introduction;100
11.2;2. Implementation;101
11.3;3. Surface Rendering;102
11.4;4. Direction;103
11.5;5. Acknowledgments;104
11.6;References;104
12;CHAPTER 6. B-SPLINE CURVES AND SURFACES;106
12.1;1. Introduction;106
12.2;2. Spline Functions;107
12.3;3. B-spline Basis For S(M,X);108
12.4;4. B-spline Curves;117
12.5;5. Geometric Interpretation of deBoor-Cox Algorithm;119
12.6;6. Geometric Properties of B-Spline Curves;121
12.7;7. Hodographs;124
12.8;8. Nonuniform B-spline Curves;126
12.9;9. Cusps;127
12.10;10. Knots, Nodes, and Vertices;128
12.11;11. The Inversion Problem;129
12.12;12. Adding a New Vertex;131
12.13;13. Designing B-spline Curves;131
12.14;14. B-spline Surfaces;132
12.15;15. Conclusion;134
12.16;16. Acknowledgments;135
12.17;REFERENCES;135
13;CHAPTER 7. MATHEMATICAL AND PRACTICAL POSSIBILITIES OF UNISURF;138
13.1;1. Introduction;138
13.2;2. Purpose;138
13.3;3. Requirements;139
13.4;4. Solution;141
13.5;5. Results;159
13.6;REFERENCES;163
14;CHAPTER 8. CONSTRAINED INTERPOLATION USING BÉZIER CURVES AS A NEW TOOL IN COMPUTER AIDED GEOMETRIC DESIGN;164
14.1;Abstract;164
14.2;1. Introduction;164
14.3;2. Notation and Formulation;166
14.4;3. Solution of the Interpolation Problem;168
14.5;4. Implementation in a Curve Handling Package;174
14.6;5. Applications;177
14.7;6. Conclusion;181
14.8;References;181
15;CHAPTER 9. NONLINEAR SPLINES;184
15.1;Excuses and Thanks;184
15.2;1. Introduction;184
15.3;2. The Intrinsic Equations;187
15.4;3. The Plane Curve;196
15.5;4. Kurgla I;197
15.6;5. Kurgla II;202
15.7;6. Space Curves;205
15.8;7. Conclusion;214
15.9;References;215
15.10;Appendix;217
16;CHAPTER 10. SOME PIECEWISE POLYNOMIAL ALTERNATIVES TO SPLINES UNDER TENSION;220
16.1;1. Introduction;220
16.2;2. Splines Under Tension;221
16.3;3. Piecewise Polynomial Alternatives to Splines in Tension;226
16.4;4. Computational Equations for V-splines;237
16.5;5. Examples;242
16.6;References;246
17;CHAPTER 11. SMOOTH PARAMETRIC SURFACES;248
17.1;1. Introduction;248
17.2;2. Spline Under Tension;251
17.3;3. Tensor Products;256
17.4;4. Fitting Random Data with an Elastic Skin;260
17.5;5. General Parametric Surface;262
17.6;References;263
18;CHAPTER 12. THE SPACE CURVE AS A FOLDED EDGE;266
18.1;References;266
19;CHAPTER 13. interactive computer graphics application of the
PARAMETRIC BI-CUBIC SURFACE
to engineering design problems;270
19.1;1. INTRODUCTION;270
19.2;2. INVESTIGATIVE COMPUTER ENVIRONMENT;270
19.3;3. PARAMETRIC REPRESENTATION;272
19.4;4. THE PARAMETRIC CUBIC SPACE CURVE;274
19.5;5. THE PARAMETRIC BI-CUBIC SURFACE PATCH;286
19.6;6. ENGINEERING DESIGN APPLICATIONS;305
19.7;7. CONCLUSIONS;311
19.8;REFERENCES;312
19.9;ACKNOWLEDGEMENTS;313
20;CHAPTER 14. MAN MACHINE COMMUNICATION IN THREE DIMENSIONS;314
20.1;1. Introduction;314
20.2;2. Input Devices;314
20.3;3. Output Devices;317
20.4;4. Design Systems;321
20.5;5. Conclusions;322
20.6;REFERENCES;324
21;CHAPTER 15. A CLASS OF LOCAL INTERPOLATING SPLINES;328
21.1;1. INTRODUCTION;328
21.2;2. THE MODEL;329
21.3;3. BLENDING FUNCTIONS;330
21.4;4. CALCULATING CARDINAL FUNCTIONS;332
21.5;5. EXAMPLES;332
21.6;6. EXTENSIONS;333
21.7;7. CONCLUSION;334
21.8;REFERENCES;334