An Introduction to Splines for Use in Computer Graphics and Geometric Modeling
An Introduction to Splines for Use in Computer Graphics and Geometric Modeling

Author: Richard H. Bartels

Publisher: Morgan Kaufmann

Published: 1995-09

Total Pages: 504

ISBN-13: 9781558604001

DOWNLOAD EBOOK

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.

Geometric Modeling
Geometric Modeling

Author: Hans Hagen

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 291

ISBN-13: 3642764045

DOWNLOAD EBOOK

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.

Geometric Modeling with Splines
Geometric Modeling with Splines

Author: Elaine Cohen

Publisher: CRC Press

Published: 2001-07-18

Total Pages: 638

ISBN-13: 1439864209

DOWNLOAD EBOOK

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

Approximation and Modeling with B-Splines
Approximation and Modeling with B-Splines

Author: Klaus Hollig

Publisher: SIAM

Published: 2015-07-01

Total Pages: 228

ISBN-13: 1611972949

DOWNLOAD EBOOK

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.

Geometric Modeling
Geometric Modeling

Author: Hans Hagen

Publisher: Springer

Published: 1991-07-18

Total Pages: 286

ISBN-13: 9783540536444

DOWNLOAD EBOOK

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.

A Blossoming Development of Splines
A Blossoming Development of Splines

Author: Stephen Mann

Publisher: Morgan & Claypool Publishers

Published: 2006

Total Pages: 109

ISBN-13: 1598291165

DOWNLOAD EBOOK

In this lecture, author Stephen Mann presents Bezier and B-spline curves and surfaces, mathematical representations for free-form curves and surfaces that are common in CAD systems. They are used to design aircraft and automobiles, as well as having uses in modeling packages used by the computer animation industry. Bezier/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 allow us to analyze their properties geometrically. Blossoming is used to explore both Bezier 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.

Fundamentals of Computer Graphics
Fundamentals of Computer Graphics

Author: Peter Shirley

Publisher: CRC Press

Published: 2009-07-21

Total Pages: 792

ISBN-13: 1498760465

DOWNLOAD EBOOK

With contributions by Michael Ashikhmin, Michael Gleicher, Naty Hoffman, Garrett Johnson, Tamara Munzner, Erik Reinhard, Kelvin Sung, William B. Thompson, Peter Willemsen, Brian Wyvill. The third edition of this widely adopted text gives students a comprehensive, fundamental introduction to computer graphics. The authors present the mathematical fo

Introduction to Implicit Surfaces
Introduction to Implicit Surfaces

Author: Jules Bloomenthal

Publisher: Morgan Kaufmann

Published: 1997-08

Total Pages: 360

ISBN-13: 9781558602335

DOWNLOAD EBOOK

Implicit surfaces offer special effects animators, graphic designers, CAD engineers, graphics students, and hobbyists a new range of capabilities for the modeling of complex geometric objects. In contrast to traditional parametric surfaces, implicit surfaces can easily describe smooth, intricate, and articulatable shapes. These powerful yet easily understood surfaces are finding use in a growing number of graphics applications. This comprehensive introduction develops the fundamental concepts and techniques of implicit surface modeling, rendering, and animating in terms accessible to anyone with a basic background in computer graphics. + provides a thorough overview of implicit surfaces with a focus on their applications in graphics + explains the best methods for designing, representing, and visualizing implicit surfaces + surveys the latest research With contributions from seven graphics authorities, this innovative guide establishes implicit surfaces as a powerful and practical tool for animation and rendering.