An Intuitive Approach to Geometric Continuity for Parametric Curves and Surfaces - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook An Intuitive Approach to Geometric Continuity for Parametric Curves and Surfaces write by Tony D. DeRose. This book was released on 1986. An Intuitive Approach to Geometric Continuity for Parametric Curves and Surfaces available in PDF, EPUB and Kindle. This report defines the nth order geometric continuity for parametric curves and surfaces, and derived the Beta constraints that are necessary and sufficient for it. Derivation of the Beta constraints is based on a simple principle of reparametrisation in conjunction with the univariate chain rule for curves, and the bivariate chain rule for surfaces. This approach uncovers the connection between geometric continuity for curves and geometric continuity for surfaces, provides new insight into the nature of geometric continuity in general, and allows the determination of the Beta constraints with less effort than previously required. Use of the Beta constraints for G to the nth power continuity allows the introduction of n shape parameters for curves, and n (n +3) shape functions for surfaces. The shape parameters and shape functions may be used to modify the shape of a geometrically continuous curve or surface, respectively. However, geometric continuity is only appropriate for applications where rate aspects of the parametrisations are unimportant since discontinuities in rate are allowed. (Reprints).
Geometric Continuity of Curves and Surfaces
Geometric Continuity of Curves and Surfaces - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Geometric Continuity of Curves and Surfaces write by Przemysław Kiciak. This book was released on 2022-05-31. Geometric Continuity of Curves and Surfaces available in PDF, EPUB and Kindle. This book is written for students, CAD system users and software developers who are interested in geometric continuity—a notion needed in everyday practice of Computer-Aided Design and also a hot subject of research. It contains a description of the classical geometric spline curves and a solid theoretical basis for various constructions of smooth surfaces. Textbooks on computer graphics usually cover the most basic and necessary information about spline curves and surfaces in order to explain simple algorithms. In textbooks on geometric design, one can find more details, more algorithms and more theory. This book teaches how various parts of the theory can be gathered together and turned into constructions of smooth curves and smooth surfaces of arbitrary topology. The mathematical background needed to understand this book is similar to what is necessary to read other textbooks on geometric design; most of it is basic linear algebra and analysis. More advanced mathematical material is introduced using elementary explanations. Reading Geometric Continuity of Curves and Surfaces provides an excellent opportunity to recall and exercise necessary mathematical notions and it may be your next step towards better practice and higher understanding of design principles.
Curves and Surfaces in Geometric Modeling
Curves and Surfaces in Geometric Modeling - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Curves and Surfaces in Geometric Modeling write by Jean H. Gallier. This book was released on 2000. Curves and Surfaces in Geometric Modeling available in PDF, EPUB and Kindle. "Curves and Surfaces in Geometric Modeling: Theory and Algorithms offers a theoretically unifying understanding of polynomial curves and surfaces as well as an effective approach to implementation that you can apply to your own work as a graduate student, scientist, or practitioner." "The focus here is on blossoming - the process of converting a polynomial to its polar form - as a natural, purely geometric explanation of the behavior of curves and surfaces. This insight is important for more than just its theoretical elegance - the author demonstrates the value of blossoming as a practical algorithmic tool for generating and manipulating curves and surfaces that meet many different criteria. You'll learn to use this and other related techniques drawn from affine geometry for computing and adjusting control points, deriving the continuity conditions for splines, creating subdivision surfaces, and more." "It will be an essential acquisition for readers in many different areas, including computer graphics and animation, robotics, virtual reality, geometric modeling and design, medical imaging, computer vision, and motion planning."--BOOK JACKET.Title Summary field provided by Blackwell North America, Inc. All Rights Reserved
Curve and Surface Design
Curve and Surface Design - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Curve and Surface Design write by Hans Hagen. This book was released on 1992-01-01. Curve and Surface Design available in PDF, EPUB and Kindle. This collection of ideas and results on topics of curve and surface design is intended for research in the academic environment as well as for practical use in industrial applications. Main emphasis is on minimal energy splines and geometric spline curves, and on techniques beyond tensor product surfaces.
Designing Fair Curves and Surfaces
Designing Fair Curves and Surfaces - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Designing Fair Curves and Surfaces write by Nickolas S. Sapidis. This book was released on 1994-01-01. Designing Fair Curves and Surfaces available in PDF, EPUB and Kindle. The authors define fairness mathematically, demonstrate how newly developed curve and surface schemes guarantee fairness, and assist the user in identifying and removing shape aberrations in a surface model without destroying the principal shape characteristics of the model. A valuable resource for engineers working in CAD, CAM, or computer-aided engineering.
