Introduction to the Mathematics of Subdivision Surfaces

by Lars-Erik Andersson

Author	: Lars-Erik Andersson
Publisher	: SIAM
Total Pages	: 372
Release	: 2010-05-13
Genre	: Mathematics
ISBN	: 0898716977

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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.

Introduction to the Mathematics of Subdivision Surfaces

by Lars-Erik Andersson

Author	: Lars-Erik Andersson
Publisher	: SIAM
Total Pages	: 373
Release	: 2010-01-01
Genre	: Mathematics
ISBN	: 0898717612

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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.

Subdivision Surfaces

by Jörg Peters

Author	: Jörg Peters
Publisher	: Springer Science & Business Media
Total Pages	: 212
Release	: 2008-05-07
Genre	: Computers
ISBN	: 3540764054

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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.

Subdivision Surfaces

by Jörg Peters

Author	: Jörg Peters
Publisher	: Springer Science & Business Media
Total Pages	: 212
Release	: 2008-08-24
Genre	: Mathematics
ISBN	: 3540764062

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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. It contains both meanwhile classical results as well as brand-new, unpublished material, such as a new framework for constructing C^2-algorithms. 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.

Introduction to the Mathematics of Computer Graphics

by Nathan Carter

Author	: Nathan Carter
Publisher	: American Mathematical Soc.
Total Pages	: 462
Release	: 2016-12-31
Genre	: Mathematics
ISBN	: 1614441227

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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.

Curves and Surfaces in Geometric Modeling

by Jean H. Gallier

Author	: Jean H. Gallier
Publisher	: Morgan Kaufmann
Total Pages	: 512
Release	: 2000
Genre	: Computers
ISBN	: 9781558605992

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"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

Mostly Surfaces

by Richard Evan Schwartz

Author	: Richard Evan Schwartz
Publisher	: American Mathematical Soc.
Total Pages	: 330
Release	: 2011
Genre	: Mathematics
ISBN	: 0821853686

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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.

Geometry Processing for Design and Manufacturing

by Robert E. Barnhill

Author	: Robert E. Barnhill
Publisher	: SIAM
Total Pages	: 207
Release	: 1992-01-01
Genre	: Mathematics
ISBN	: 0898712807

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This text includes papers covering topics in geometry processing applications, such as surface-surface intersections and offset surfaces. Present methods fundamental to geometric modelling are highlighted.

3D Computer Graphics

by Samuel R. Buss

Author	: Samuel R. Buss
Publisher	: Cambridge University Press
Total Pages	: 397
Release	: 2003-05-19
Genre	: Computers
ISBN	: 1139440381

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This textbook, first published in 2003, emphasises the fundamentals and the mathematics underlying computer graphics. The minimal prerequisites, a basic knowledge of calculus and vectors plus some programming experience in C or C++, make the book suitable for self study or for use as an advanced undergraduate or introductory graduate text. The author gives a thorough treatment of transformations and viewing, lighting and shading models, interpolation and averaging, Bézier curves and B-splines, ray tracing and radiosity, and intersection testing with rays. Additional topics, covered in less depth, include texture mapping and colour theory. The book covers some aspects of animation, including quaternions, orientation, and inverse kinematics, and includes source code for a Ray Tracing software package. The book is intended for use along with any OpenGL programming book, but the crucial features of OpenGL are briefly covered to help readers get up to speed. Accompanying software is available freely from the book's web site.