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Mathematics and CAD
The use of computer-aided design (CAD) systems always involves the introduction of mathematical concepts. It is important, therefore, for any systems designer to have a good grasp of the mathematical bases used in CAD. The choice of mathematical models in a system also has an effect on the overall quality, although this effect may not always be visible to the final user. Depending on whether Bezier or B-spline functions are used for curves and surfaces, for example, the final user even if not a com puter scientist will notice a difference. If, for example, one of the control points is modified by the user, in a Bezier-type representation, the curve or surface will tend to be modified overall, but in a B-spline representation, the curve or surface will tend to be modified close to the point, and there only. More possibly harmful, however, is the effect of the mathematical model which has a number of properties invisible and unknown to the final user. In every case a model must be chosen with, it is hoped, the most appropriate characteristics and limits for the task in hand.
Photorealism in Computer Graphics
The goal of this book is to present the most advanced research works in realistic computer generated images. It is made up of the papers presented during a Eurographics workshop that has been held in Rennes (France) on June 1990. Although realism in computer graphics has existed for many years, we have considered that two research directions can now clearly be identified. One makes use of empirical methods to efficiently create images that look real. As opposed to this approach, the other orientation makes use of physics to produce images that are exact representations of the real world (at the expense of additional processing time), hence the term photosimulation which indeed was the subjec...
Discrete Geometry for Computer Imagery
This book constitutes the refereed proceedings of the 9th International Conference on Discrete Geometry for Computer Imagery, DGCI 2000, held in Uppsala, Sweden in December 2000. The 40 revised papers presented together with two invited papers were carefully reviewed and selected from 62 submissions. The papers are organized in topical sections on topology, discrete images, surfaces and volumes, shape representation, and shape understanding.
Curve and Surface Design
Two new volumes of carefully refereed and edited papers on the most current developments in the theory and applications of curves and surfaces. These two volumes contain a selection of papers presented at the Saint-Malo Conference on Approximation Theory in July 1999. Each contains several invited survey papers written by experts in the field, along with contributed research papers. They will be of great interest to mathematicians, engineers, and computer scientists working in the fields of Approximation Theory, Computer-Aided Geometric Design (CAGD), Computer Graphics, Numerical Analysis, CAD/CAM, and application areas. Curve and Surface Design includes the following topics: B-bases canal surfaces conics curvature discrete fairing free form surfaces G2-splines highlight lines involute curves multisided patches NURBs and NURPs offsets ray tracing ruled surfaces sculptured surfaces segmentation methods shape preservation texture voronoi diagrams
Mathematical Methods for Curves and Surfaces
"This volume contains a carefully refereed and edited selection of papers that were presented at the Oslo Conference on Mathematical Methods for Curves and Surfaces in July 2000. It contains several invited surveys written by leading experts in the field, along with contributed research papers on the most current developments in the theory and application of curves and surfaces."--Page 4 de la couverture.
Curves and Surfaces
Curves and Surfaces provides information pertinent to the fundamental aspects of approximation theory with emphasis on approximation of images, surface compression, wavelets, and tomography. This book covers a variety of topics, including error estimates for multiquadratic interpolation, spline manifolds, and vector spline approximation. Organized into 77 chapters, this book begins with an overview of the method, based on a local Taylor expansion of the final curve, for computing the parameter values. This text then presents a vector approximation based on general spline function theory. Other chapters consider a nonparametric technique for estimating under random censorship the amplitude of a change point in change point hazard models. This book discusses as well the algorithm for ray tracing rational parametric surfaces based on inversion and implicitization. The final chapter deals with the results concerning the norm of the interpolation operator and error estimates for a square domain. This book is a valuable resource for mathematicians.
Mathematical Methods in Computer Aided Geometric Design II
Mathematical Methods in Computer Aided Geometric Design II covers the proceedings of the 1991 International Conference on Curves, Surfaces, CAGD, and Image Processing, held at Biri, Norway. This book contains 48 chapters that include the topics of blossoming, cyclides, data fitting and interpolation, and finding intersections of curves and surfaces. Considerable chapters explore the geometric continuity, geometrical optics, image and signal processing, and modeling of geological structures. The remaining chapters discuss the principles of multiresolution analysis, NURBS, offsets, radial basis functions, rational splines, robotics, spline and Bézier methods for curve and surface modeling, subdivision, terrain modeling, and wavelets. This book will prove useful to mathematicians, computer scientists, and advance mathematics students.
Curve and Surface Fitting
Two new volumes of carefully refereed and edited papers on the most current developments in the theory and applications of curves and surfaces. These two volumes contain a selection of papers presented at the Saint-Malo Conference on Approximation Theory in July 1999. Each contains several invited survey papers written by experts in the field, along with contributed research papers. They will be of great interest to mathematicians, engineers, and computer scientists working in the fields of Approximation Theory, Computer-Aided Geometric Design (CAGD), Computer Graphics, Numerical Analysis, CAD/CAM, and application areas. Curve and Surface Design includes the following topics: B-bases canal surfaces conics curvature discrete fairing free form surfaces G2-splines highlight lines involute curves multisided patches NURBs and NURPs offsets ray tracing ruled surfaces sculptured surfaces segmentation methods shape preservation texture voronoi diagrams
