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Computer Aided Geometric Design
Robert E. Barnhill,Richard F. Riesenfeld
- 336 pages
- English
- PDF
- Only available on web
Computer Aided Geometric Design
Robert E. Barnhill,Richard F. Riesenfeld
About This Book
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.
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Table of contents
- Front Cover
- Computer Aided Geometric Design
- Copyright Page
- Table of Contents
- Contributors
- Preface
- CHAPTER 1. SURFACE PATCHES AND B-SPLINE CURVES
- CHAPTER 2. COMPUTATIONAL GEOMETRY - ACHIEVEMENTS AND PROBLEMS
- CHAPTER 3. SMOOTH INTERPOLATION OVER TRIANGLES
- CHAPTER 4. SMOOTH INTERPOLATION WITHOUT TWIST CONSTRAINTS
- CHAPTER 5. GRAPHICAL REPRESENTATION OF SURFACES OVER TRIANGLES AND RECTANGLES
- CHAPTER 6. B-SPLINE CURVES AND SURFACES
- CHAPTER 7. MATHEMATICAL AND PRACTICAL POSSIBILITIES OF UNISURF
- CHAPTER 8. CONSTRAINED INTERPOLATION USING BĂZIER CURVES AS A NEW TOOL IN COMPUTER AIDED GEOMETRIC DESIGN
- CHAPTER 9. NONLINEAR SPLINES
- CHAPTER 10. SOME PIECEWISE POLYNOMIAL ALTERNATIVES TO SPLINES UNDER TENSION
- CHAPTER 11. SMOOTH PARAMETRIC SURFACES
- CHAPTER 12. THE SPACE CURVE AS A FOLDED EDGE
- CHAPTER 13. interactive computer graphics application of the PARAMETRIC BI-CUBIC SURFACE to engineering design problems
- CHAPTER 14. MAN MACHINE COMMUNICATION IN THREE DIMENSIONS
- CHAPTER 15. A CLASS OF LOCAL INTERPOLATING SPLINES