Modeling With Ambient B Splines

Author : Nicole Lehmann
Publisher : Logos Verlag Berlin GmbH
ISBN 13 : 3832536027
Total Pages : 126 pages
Book Rating : 4.22/5 ( download)

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Download or read book Modeling with Ambient B-Splines written by Nicole Lehmann and published by Logos Verlag Berlin GmbH. This book was released on 2013 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present thesis introduces a new approach for the generation of CK-approximants of functions defined on closed submanifolds for arbitrary k ∈ N. In case a function on a surface resembles the three coordinates of a topologically equivalent surface in R3, we even obtain Ck-approximants of closed surfaces of arbitrary topology. The key idea of our method is a constant extension of the target function into the submanifold's ambient space. In case the reference submanifolds are embedded and Ck, the usage of standard tensor product B-splines for the approximation of the extended function is straightforward. We obtain a Ck-approximation of the target function by restricting the approximant to the reference submanifold. We illustrate our method by an easy example in R2 and verify its practicality by application-oriented examples in R3. The first treats the approximation of the geoid, an important reference magnitude within geodesy and geophysics. The second and third example treat the approximation of geometric models. The usage of B-splines not only guarantees full approximation power but also allows a canonical access to adaptive refinement strategies. We elaborate on two hierarchical techniques and successfully apply them to the introduced examples. Concerning the modeling of surfaces by the new approach, we derive numerically robust formulas for the determination of normal vectors and curvature information of a target surface which only need the spline approximant as well as the normal vectors and curvature information of the reference surface.

Author : Klaus Hollig
Publisher : SIAM
ISBN 13 : 1611972957
Total Pages : 228 pages
Book Rating : 4.55/5 ( download)

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Download or read book Approximation and Modeling with B-Splines written by Klaus Hollig and published by SIAM. This book was released on 2013-11-14 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: B-splines are fundamental to approximation and data fitting, geometric modeling, automated manufacturing, computer graphics, and numerical simulation. With an emphasis on key results and methods that are most widely used in practice, this textbook provides a unified introduction to the basic components of B-spline theory: approximation methods (mathematics), modeling techniques (engineering), and geometric algorithms (computer science). A supplemental Web site will provide a collection of problems, some with solutions, slides for use in lectures, and programs with demos.

Author : Elaine Cohen
Publisher : CRC Press
ISBN 13 : 1439864209
Total Pages : 638 pages
Book Rating : 4.03/5 ( download)

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Download or read book Geometric Modeling with Splines written by Elaine Cohen and published by CRC Press. This book was released on 2001-07-18 with total page 638 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by researchers who have helped found and shape the field, this book is a definitive introduction to geometric modeling. The authors present all of the necessary techniques for curve and surface representations in computer-aided modeling with a focus on how the techniques are used in design. They achieve a balance between mathematical rigor

Author : E. Y. K. Ng
Publisher : CRC Press
ISBN 13 : 1439869944
Total Pages : 420 pages
Book Rating : 4.49/5 ( download)

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Download or read book Human Eye Imaging and Modeling written by E. Y. K. Ng and published by CRC Press. This book was released on 2012-06-05 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advanced image processing and mathematical modeling techniques are increasingly being used for the early diagnosis of eye diseases. A comprehensive review of the field, Human Eye Imaging and Modeling details the latest advances and analytical techniques in ocular imaging and modeling. The first part of the book looks at imaging of the fundus as wel

Author : Stephen Mann
Publisher : Morgan & Claypool Publishers
ISBN 13 : 1598291173
Total Pages : 108 pages
Book Rating : 4.79/5 ( download)

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Download or read book A Blossoming Development of Splines written by Stephen Mann and published by Morgan & Claypool Publishers. This book was released on 2006-12-01 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this lecture, we study Bézier and B-spline curves and surfaces, mathematical representations for free-form curves and surfaces that are common in CAD systems and are used to design aircraft and automobiles, as well as in modeling packages used by the computer animation industry. Bézier/B-splines represent polynomials and piecewise polynomials in a geometric manner using sets of control points that define the shape of the surface. The primary analysis tool used in this lecture is blossoming, which gives an elegant labeling of the control points that allows us to analyze their properties geometrically. Blossoming is used to explore both Bézier and B-spline curves, and in particular to investigate continuity properties, change of basis algorithms, forward differencing, B-spline knot multiplicity, and knot insertion algorithms. We also look at triangle diagrams (which are closely related to blossoming), direct manipulation of B-spline curves, NURBS curves, and triangular and tensor product surfaces.

Author : Hans Hagen
Publisher : Springer Science & Business Media
ISBN 13 : 3642764045
Total Pages : 291 pages
Book Rating : 4.42/5 ( download)

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Download or read book Geometric Modeling written by Hans Hagen and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 291 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based on lectures presented at an international workshop on geometric modeling held at Hewlett Packard GmbH in Boblingen, FRG, in June 1990. International experts from academia and industry were selected to speak on the most interesting topics in geometric modeling. The resulting papers, published in this volume, give a state-of-the-art survey of the relevant problems and issues. The following topics are discussed: - Methods for constructing surfaces on surfaces: four different solutions to the multidimen sional problem of constructing an interpolant from surface data are provided. - Surfaces in solid modeling: current results on the implementation of free-fonn solids in three well established solid models are reviewed. - Box splines and applications: an introduction to box spline methods for the representation of surfaces is given. Basic properties of box splines are derived, and refinement and evaluation methods for box splines are presented in detail. Shape preserving properties, the construction of non-rectangular box spline surfaces, applications to surface modeling, and imbedding problems, are discussed. - Advanced computer graphics techniques for volume visualization: the steps to be executed in the visualization process of volume data are described and tools are discussed that assist in handling this data. - Rational B-splines: an introduction to the representation of curves and surfaces using rational B-splines is given, together with a critical evaluation of their potential for industrial application.

Author : Les Piegl
Publisher : Springer Science & Business Media
ISBN 13 : 364297385X
Total Pages : 650 pages
Book Rating : 4.57/5 ( download)

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Download or read book The NURBS Book written by Les Piegl and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 650 pages. Available in PDF, EPUB and Kindle. Book excerpt: Until recently B-spline curves and surfaces (NURBS) were principally of interest to the computer aided design community, where they have become the standard for curve and surface description. Today we are seeing expanded use of NURBS in modeling objects for the visual arts, including the film and entertainment industries, art, and sculpture. NURBS are now also being used for modeling scenes for virtual reality applications. These applications are expected to increase. Consequently, it is quite appropriate for The.N'U'R-BS Book to be part of the Monographs in Visual Communication Series. B-spline curves and surfaces have been an enduring element throughout my pro fessional life. The first edition of Mathematical Elements for Computer Graphics, published in 1972, was the first computer aided design/interactive computer graph ics textbook to contain material on B-splines. That material was obtained through the good graces of Bill Gordon and Louie Knapp while they were at Syracuse University. A paper of mine, presented during the Summer of 1977 at a Society of Naval Architects and Marine Engineers meeting on computer aided ship surface design, was arguably the first to examine the use of B-spline curves for ship design. For many, B-splines, rational B-splines, and NURBS have been a bit mysterious.

Author : Sonja Greven
Publisher : Cuvillier Verlag
ISBN 13 : 3867274916
Total Pages : 153 pages
Book Rating : 4.13/5 ( download)

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Download or read book Non-Standard Problems in Inference for Additive and Linear Mixed Models written by Sonja Greven and published by Cuvillier Verlag. This book was released on 2008 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Richard H. Bartels
Publisher : Morgan Kaufmann
ISBN 13 : 9781558604001
Total Pages : 504 pages
Book Rating : 4.06/5 ( download)

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Download or read book An Introduction to Splines for Use in Computer Graphics and Geometric Modeling written by Richard H. Bartels and published by Morgan Kaufmann. This book was released on 1995-09 with total page 504 pages. Available in PDF, EPUB and Kindle. Book excerpt: As the field of computer graphics develops, techniques for modeling complex curves and surfaces are increasingly important. A major technique is the use of parametric splines in which a curve is defined by piecing together a succession of curve segments, and surfaces are defined by stitching together a mosaic of surface patches. An Introduction to Splines for Use in Computer Graphics and Geometric Modeling discusses the use of splines from the point of view of the computer scientist. Assuming only a background in beginning calculus, the authors present the material using many examples and illustrations with the goal of building the reader's intuition. Based on courses given at the University of California, Berkeley, and the University of Waterloo, as well as numerous ACM Siggraph tutorials, the book includes the most recent advances in computer-aided geometric modeling and design to make spline modeling techniques generally accessible to the computer graphics and geometric modeling communities.

Author : Dariush Derakhshani
Publisher : John Wiley & Sons
ISBN 13 : 047027591X
Total Pages : 626 pages
Book Rating : 4.17/5 ( download)

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Download or read book Introducing Maya 2008 written by Dariush Derakhshani and published by John Wiley & Sons. This book was released on 2008-03-04 with total page 626 pages. Available in PDF, EPUB and Kindle. Book excerpt: The new edition of this perennial bestseller is the ideal initiation to 3D and Maya. Starting with the basics, it builds from the ground up, combining straightforward text with practical examples that make it fun and easy to learn Maya's core tools while introducing the latest Maya 2008 features. Follow clear-cut, step-by-step lessons while you learn by doing using a wealth of hands-on files provided on the CD. You'll also find compelling examples in the full-color insert.