Introduction To The Mathematics Of Subdivision Surfaces

Author : Lars-Erik Andersson,Neil F. Stewart
Publisher : SIAM
Page : 373 pages
File Size : 49,6 Mb
Release : 2010-01-01
Category : Mathematics
ISBN : 9780898717617

Get Book

Introduction to the Mathematics of Subdivision Surfaces by Lars-Erik Andersson,Neil F. Stewart Pdf

This is an introduction to the mathematical theory which underlies subdivision surfaces, as it is used in computer graphics and animation. Subdivision surfaces enable a designer to specify the approximate form of a surface that defines an object and then to refine it to get a more useful or attractive version. A considerable amount of mathematical theory is needed to understand the characteristics of the resulting surfaces, and this book explains the material carefully and rigorously. The text is highly accessible, organising subdivision methods in a unique and unambiguous hierarchy which builds insight and understanding. The material is not restricted to questions related to regularity of subdivision surfaces at so-called extraordinary points, but gives a broad discussion of the various methods. It is therefore an excellent preparation for more advanced texts that delve more deeply into special questions of regularity.

Author : Wenhe Liao,Hao Liu,Tao Li
Publisher : Springer
Page : 307 pages
File Size : 41,8 Mb
Release : 2017-10-11
Category : Computers
ISBN : 9789811035159

Get Book

Subdivision Surface Modeling Technology by Wenhe Liao,Hao Liu,Tao Li Pdf

This book offers a comprehensive introduction to Subdivision Surface Modeling Technology focusing not only on fundamental theories but also on practical applications. It furthers readers’ understanding of the contacts between spline surfaces and subdivision surfaces, enabling them to master the Subdivision Surface Modeling Technology for analyzing subdivision surfaces. Subdivision surface modeling is a popular technology in the field of computer aided design (CAD) and computer graphics (CG) thanks to its ability to model meshes of any topology. The book also discusses some typical Subdivision Surface Modeling Technologies, such as interpolation, fitting, fairing, intersection, as well as trimming and interactive editing. It is a valuable tool, enabling readers to grasp the main technologies of subdivision surface modeling and use them in software development, which in turn leads to a better understanding of CAD/CG software operations.

Author : Lars-Erik Andersson,Neil F. Stewart
Publisher : SIAM
Page : 372 pages
File Size : 47,9 Mb
Release : 2010-05-13
Category : Mathematics
ISBN : 9780898716979

Get Book

Introduction to the Mathematics of Subdivision Surfaces by Lars-Erik Andersson,Neil F. Stewart Pdf

This is an introduction to the mathematical theory which underlies subdivision surfaces, as it is used in computer graphics and animation. Subdivision surfaces enable a designer to specify the approximate form of a surface that defines an object and then to refine it to get a more useful or attractive version. A considerable amount of mathematical theory is needed to understand the characteristics of the resulting surfaces, and this book explains the material carefully and rigorously. The text is highly accessible, organising subdivision methods in a unique and unambiguous hierarchy which builds insight and understanding. The material is not restricted to questions related to regularity of subdivision surfaces at so-called extraordinary points, but gives a broad discussion of the various methods. It is therefore an excellent preparation for more advanced texts that delve more deeply into special questions of regularity.

Author : Jörg Peters,Ulrich Reif
Publisher : Springer Science & Business Media
Page : 212 pages
File Size : 46,7 Mb
Release : 2008-05-07
Category : Computers
ISBN : 9783540764052

Get Book

Subdivision Surfaces by Jörg Peters,Ulrich Reif Pdf

Since their first appearance in 1974, subdivision algorithms for generating surfaces of arbitrary topology have gained widespread popularity in computer graphics and are being evaluated in engineering applications. This development was complemented by ongoing efforts to develop appropriate mathematical tools for a thorough analysis, and today, many of the fascinating properties of subdivision are well understood. This book summarizes the current knowledge on the subject. The focus of the book is on the development of a comprehensive mathematical theory, and less on algorithmic aspects. It is intended to serve researchers and engineers - both new to the beauty of the subject - as well as experts, academic teachers and graduate students or, in short, anybody who is interested in the foundations of this flourishing branch of applied geometry.

Author : Nathan Carter
Publisher : American Mathematical Soc.
Page : 462 pages
File Size : 48,5 Mb
Release : 2016-12-31
Category : Mathematics
ISBN : 9781614441229

Get Book

Introduction to the Mathematics of Computer Graphics by Nathan Carter Pdf

This text, by an award-winning [Author];, was designed to accompany his first-year seminar in the mathematics of computer graphics. Readers learn the mathematics behind the computational aspects of space, shape, transformation, color, rendering, animation, and modeling. The software required is freely available on the Internet for Mac, Windows, and Linux. The text answers questions such as these: How do artists build up realistic shapes from geometric primitives? What computations is my computer doing when it generates a realistic image of my 3D scene? What mathematical tools can I use to animate an object through space? Why do movies always look more realistic than video games? Containing the mathematics and computing needed for making their own 3D computer-generated images and animations, the text, and the course it supports, culminates in a project in which students create a short animated movie using free software. Algebra and trigonometry are prerequisites; calculus is not, though it helps. Programming is not required. Includes optional advanced exercises for students with strong backgrounds in math or computer science. Instructors interested in exposing their liberal arts students to the beautiful mathematics behind computer graphics will find a rich resource in this text.

Author : Jean H. Gallier
Publisher : Morgan Kaufmann
Page : 512 pages
File Size : 43,7 Mb
Release : 2000
Category : Computers
ISBN : 1558605991

Get Book

Curves and Surfaces in Geometric Modeling by Jean H. Gallier Pdf

"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

Author : Michael J. Wilson,Ralph R. Martin
Publisher : Springer
Page : 400 pages
File Size : 50,6 Mb
Release : 2003-11-03
Category : Mathematics
ISBN : 9783540394228

Get Book

Mathematics of Surfaces by Michael J. Wilson,Ralph R. Martin Pdf

This book constitutes the refereed proceedings of the 10th IMA International Conference on the Mathematics of Surfaces, held in Leeds, UK in September 2003. The 25 revised full papers presented were carefully reviewed and selected from numerous submissions. Among the topics addressed are triangulated surface parameterization, bifurcation structures, control vertex computation, polyhedral surfaces, watermarking 3D polygonal meshed, subdivision surfaces, surface reconstruction, vector transport, shape from shading, surface height recovery, algebraic surfaces, box splines, the Plateau-Bezier problem, spline geometry, generative geometry, manifold representation, affine arithmetic, and PDE surfaces.

Author : Ralph Martin,Malcolm Sabin,Joab Winkler
Publisher : Springer
Page : 514 pages
File Size : 47,5 Mb
Release : 2007-08-28
Category : Computers
ISBN : 9783540738435

Get Book

Mathematics of Surfaces XII by Ralph Martin,Malcolm Sabin,Joab Winkler Pdf

This book constitutes the refereed proceedings of the 12th IMA International Conference on the Mathematics of Surfaces, held in Sheffield, UK in September 2007. The papers cover a range of ideas from underlying theoretical tools to industrial uses of surfaces. Research is reported on theoretical aspects of surfaces as well as more practical topics.

Author : Richard Evan Schwartz
Publisher : American Mathematical Soc.
Page : 330 pages
File Size : 40,6 Mb
Release : 2011
Category : Mathematics
ISBN : 9780821853689

Get Book

Mostly Surfaces by Richard Evan Schwartz Pdf

The goal of the book is to present a tapestry of ideas from various areas of mathematics in a clear and rigorous yet informal and friendly way. Prerequisites include undergraduate courses in real analysis and in linear algebra, and some knowledge of complex analysis. --from publisher description.

Author : Joe Warren,Joseph D. Warren,Henrik Weimer
Publisher : Morgan Kaufmann
Page : 326 pages
File Size : 44,9 Mb
Release : 2002
Category : Art
ISBN : 1558604464

Get Book

Subdivision Methods for Geometric Design by Joe Warren,Joseph D. Warren,Henrik Weimer Pdf

Subdivision Methods for Geometric Design provides computer graphics students and designers with a comprehensive guide to subdivision methods, including the background information required to grasp underlying concepts, techniques for manipulating subdivision algorithms to achieve specific effects, and a wide array of digital resources on a dynamic companion Web site. Subdivision Methods promises to be a groundbreaking book, important for both advanced students and working professionals in the field of computer graphics.

Author : Leila de Floriani,Michela Spagnuolo
Publisher : Springer Science & Business Media
Page : 305 pages
File Size : 46,7 Mb
Release : 2007-12-24
Category : Mathematics
ISBN : 9783540332657

Get Book

Shape Analysis and Structuring by Leila de Floriani,Michela Spagnuolo Pdf

With a lot of recent developments in the field, this much-needed book has come at just the right time. It covers a variety of topics related to preserving and enhancing shape information at a geometric level. The contributors also cover subjects that are relevant to effectively capturing the structure of a shape by identifying relevant shape components and their mutual relationships.

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 53,8 Mb
Release : 2024-07-03
Category : Electronic
ISBN : 9789814474665

Get Book

Mathematics and Computation in Imaging Science and Information Processing by Anonim Pdf

Author : Gerald E. Farin,Dianne Hansford
Publisher : Unknown
Page : 128 pages
File Size : 48,5 Mb
Release : 2000
Category : Computer graphics
ISBN : OCLC:765132692

Get Book

The Essentials of CAGD by Gerald E. Farin,Dianne Hansford Pdf

Putting the G into CAGD, the authors provide a much-needed practical and basic introduction to computer-aided geometric design. This book will help readers understand and use the elements of computer-aided geometric design, curves and surfaces, without the mathematical baggage that is necessary only for more advanced work. Though only minimal background in mathematics is needed to understand the book's concepts, the book covers an amazing array of topics such as Bezier and B-spline curves and their corresponding surfaces, subdivision surfaces, and NURBS (Non-Uniform Rational B-Splines) Also included are techniques such as interpolation and least squares methods.

Author : Hans-Christian Hege,Konrad Polthier
Publisher : Springer Science & Business Media
Page : 455 pages
File Size : 51,9 Mb
Release : 2013-11-11
Category : Psychology
ISBN : 9783662051054

Get Book

Visualization and Mathematics III by Hans-Christian Hege,Konrad Polthier Pdf

A collection of state-of-the-art presentations on visualization problems in mathematics, fundamental mathematical research in computer graphics, and software frameworks for the application of visualization to real-world problems. Contributions have been written by leading experts and peer-refereed by an international editorial team. The book grew out of the third international workshop ‘Visualization and Mathematics’, May 22-25, 2002 in Berlin. The variety of topics covered makes the book ideal for researcher, lecturers, and practitioners.

Author : H.-C. Hege,K. Polthier
Publisher : Springer Science & Business Media
Page : 391 pages
File Size : 49,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642591952

Get Book

Visualization and Mathematics by H.-C. Hege,K. Polthier Pdf

Visualization and mathematics have begun a fruitful relationship, establishing links between problems and solutions of both fields. In some areas of mathematics, like differential geometry and numerical mathematics, visualization techniques are applied with great success. However, visualization methods are relying heavily on mathematical concepts. Applications of visualization in mathematical research and the use of mathematical methods in visualization have been topic of an international workshop in Berlin in June 1995. Selected contributions treat topics of particular interest in current research. Experts are reporting on their latest work, giving an overview on this fascinating new area. The reader will get insight to state-of-the-art techniques for solving visualization problems and mathematical questions.