Stationary Subdivision

Stationary Subdivision
Author: Alfred S. Cavaretta
Publisher: American Mathematical Soc.
Total Pages: 197
Release: 1991
Genre: Algorithms
ISBN: 0821825070

This monograph presents a systematic development of the basic mathematical principles and concepts associated with stationary subdivision algorithms which are used for generating curves and surfaces in computer graphics. Special attention is given to the structure of such algorithms in a multidimensional settings, and the convergence issue is analyzed using appropriate tools from Fourier analysis and functional analysis.

Subdivision Surface Modeling Technology

Subdivision Surface Modeling Technology
Author: Wenhe Liao
Publisher: Springer
Total Pages: 317
Release: 2017-10-11
Genre: Computers
ISBN: 9811035156

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.

Approximation Theory XVI

Approximation Theory XVI
Author: Gregory E. Fasshauer
Publisher: Springer Nature
Total Pages: 256
Release: 2021-01-04
Genre: Mathematics
ISBN: 3030574644

These proceedings are based on the international conference Approximation Theory XVI held on May 19–22, 2019 in Nashville, Tennessee. The conference was the sixteenth in a series of meetings in Approximation Theory held at various locations in the United States. Over 130 mathematicians from 20 countries attended. The book contains two longer survey papers on nonstationary subdivision and Prony’s method, along with 11 research papers on a variety of topics in approximation theory, including Balian-Low theorems, butterfly spline interpolation, cubature rules, Hankel and Toeplitz matrices, phase retrieval, positive definite kernels, quasi-interpolation operators, stochastic collocation, the gradient conjecture, time-variant systems, and trivariate finite elements. The book should be of interest to mathematicians, engineers, and computer scientists working in approximation theory, computer-aided geometric design, numerical analysis, and related approximation areas.

Advanced Methods for Processing and Visualizing the Renewable Energy

Advanced Methods for Processing and Visualizing the Renewable Energy
Author: Samsul Ariffin Abdul Karim
Publisher: Springer Nature
Total Pages: 157
Release: 2020-10-21
Genre: Technology & Engineering
ISBN: 9811586063

This book is a collection of research work conducted by researchers at Centre for Smart Grid Energy Research (CSMER), Institute of Autonomous System, Universiti Teknologi PETRONAS (UTP), and Seismic Modelling and Inversion Group, King Abdullah University of Science and Technology (KAUST), Saudi Arabia. The book covers topics in the field of renewable energy where visualization, artificial neural network and deep learning techniques have been applied to optimize the performance of various applications in energy-related industries. These examples include a natural gas vehicle (NGV), a single axis and a fixed axis solar tracker, seismic inversion enhanced oil recovery, viability of a PV system and construction of a septic B-spline tensor product scheme. Readers will benefit from these examples, which describe the current trend of energy optimization techniques in renewable energy applications making it a good reference for the researchers and industrial practitioners working in the field of renewable energy and optimization techniques.

Mathematical Aspects of Geometric Modeling

Mathematical Aspects of Geometric Modeling
Author: Charles A. Micchelli
Publisher: SIAM
Total Pages: 265
Release: 1995-01-01
Genre: Mathematics
ISBN: 9781611970067

This monograph examines in detail certain concepts that are useful for the modeling of curves and surfaces and emphasizes the mathematical theory that underlies these ideas. The two principal themes of the text are the use of piecewise polynomial representation (this theme appears in one form or another in every chapter), and iterative refinement, also called subdivision. Here, simple iterative geometric algorithms produce, in the limit, curves with complex analytic structure. In the first three chapters, the de Casteljau subdivision for Bernstein-Bezier curves is used to introduce matrix subdivision, and the Lane-Riesenfield algorithm for computing cardinal splines is tied into stationary subdivision. This ultimately leads to the construction of prewavelets of compact support. The remainder of the book deals with concepts of "visual smoothness" of curves, along with the intriguing idea of generating smooth multivariate piecewise polynomials as volumes of "slices" of polyhedra. The final chapter contains an evaluation of polynomials by finite recursive algorithms. Each chapter contains introductory material as well as more advanced results.

Technologies for E-Learning and Digital Entertainment

Technologies for E-Learning and Digital Entertainment
Author: Zhigeng Pan
Publisher: Springer
Total Pages: 808
Release: 2008-06-19
Genre: Computers
ISBN: 3540697365

With the widespread interest in digital entertainment and the advances in the tech- logies of computer graphics, multimedia and virtual reality technologies, a new area–– “Edutainment”––has been accepted as a union of education and computer entertainment. Edutainment is recognized as an effective way of learning through a medium, such as a computer, software, games or VR applications, that both educates and entertains. The Edutainment conference series was established and followed as a special event for the new interests in e-learning and digital entertainment. The main purpose of Edutainment conferences is the discussion, presentation, and information exchange of scientific and technological developments in the new community. The Edutainment conference series is a very interesting opportunity for researchers, engineers and graduate students who wish to communicate at these international annual events. The conference series includes plenary invited talks, workshops, tutorials, paper presen- tion tracks and panel discussions. The Edutainment conference series was initiated in Hangzhou, China in 2006. Following the success of the first event (Edutainment 2006 in Hangzhou, China) and the second one (Edutainment 2007 in Hong Kong, China), Edutainment 2008 was held June 25–27, 2007 in Nanjing, China. This year, we received 219 submissions from 26 different countries and regions, including United Arab Emirates, Canada, Thailand, New Zealand, Austria, Turkey, Germany, Switzerland, Brazil, Cuba, Australia, Hong Kong (China), Pakistan, M- ico, Czech Republic, USA, Malaysia, Italy, Spain, France, UK, The Netherlands, Taiwan (China), Japan, South Korea, and China.

Mathematical Methods for Curves and Surfaces

Mathematical Methods for Curves and Surfaces
Author: Morten Dæhlen
Publisher: Springer
Total Pages: 453
Release: 2010-02-12
Genre: Computers
ISBN: 3642116205

This volume constitutes the thoroughly refereed post-conference proceedings of the 7th International Conference on Mathematical Methods for Curves and Surfaces, MMCS 2008, held in Tønsberg, Norway, in June/July 2008. The 28 revised full papers presented were carefully reviewed and selected from 129 talks presented at the conference. The topics addressed by the papers range from mathematical analysis of various methods to practical implementation on modern graphics processing units.

Geometric Modeling and Processing - GMP 2006

Geometric Modeling and Processing - GMP 2006
Author: Myung-Soo Kim
Publisher: Springer Science & Business Media
Total Pages: 709
Release: 2006-07-11
Genre: Computers
ISBN: 354036711X

This book constitutes the refereed proceedings of the 4th International Conference on Geometric Modeling and Processing, GMP 2006, held in Pittsburgh, PA, USA in July 2006. The 36 revised full papers and 21 revised short papers presented were carefully reviewed and selected from a total of 84 submissions. All current issues in the area of geometric modeling and processing are addressed and the impact in such areas as computer graphics, computer vision, machining, robotics, and scientific visualization is shown. The papers are organized in topical sections on shape reconstruction, curves and surfaces, geometric processing, shape deformation, shape description, shape recognition, geometric modeling, subdivision surfaces, and engineering applications.

The Mathematics of Surfaces IX

The Mathematics of Surfaces IX
Author: Roberto Cipolla
Publisher: Springer Science & Business Media
Total Pages: 510
Release: 2012-12-06
Genre: Technology & Engineering
ISBN: 1447104951

These proceedings collect the papers accepted for presentation at the bien nial IMA Conference on the Mathematics of Surfaces, held in the University of Cambridge, 4-7 September 2000. While there are many international con ferences in this fruitful borderland of mathematics, computer graphics and engineering, this is the oldest, the most frequent and the only one to concen trate on surfaces. Contributors to this volume come from twelve different countries in Eu rope, North America and Asia. Their contributions reflect the wide diversity of present-day applications which include modelling parts of the human body for medical purposes as well as the production of cars, aircraft and engineer ing components. Some applications involve design or construction of surfaces by interpolating or approximating data given at points or on curves. Others consider the problem of 'reverse engineering'-giving a mathematical descrip tion of an already constructed object. We are particularly grateful to Pamela Bye (at the Institue of Mathemat ics and its Applications) for help in making arrangements; Stephanie Harding and Karen Barker (at Springer Verlag, London) for publishing this volume and to Kwan-Yee Kenneth Wong (Cambridge) for his heroic help with com piling the proceedings and for dealing with numerous technicalities arising from large and numerous computer files. Following this Preface is a listing of the programme committee who with the help of their colleagues did much work in refereeing the papers for these proceedings.

Approximation Theory

Approximation Theory
Author: Narenda Govil
Publisher: CRC Press
Total Pages: 548
Release: 2021-01-31
Genre: Mathematics
ISBN: 1000110184

"Contains the contributions of 45 internationally distinguished mathematicians covering all areas of approximation theory-written in honor of the pioneering work of Arun K. Varma to the fields of interpolation and approximation of functions, including Birhoff interpolation and approximation by spline functions."