Minimum Curvature Variation Curves Networks And Surfaces For Fair Free Form Shape Design
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| Author | : University of California, Berkeley. Computer Science Division |
| Publisher | : |
| Total Pages | : 528 |
| Release | : 1992 |
| Genre | : Computational geometry |
| ISBN | : |
We present the details of the techniques outlined above and describe the trade-offs between some alternative approaches. Solutions to difficult interpolation problems and comparisons with traditional methods are provided. Both demonstrate the superiority of curvature variation as a fairness metric and efficacy of optimization as a tool in shape design, albeit at significant computational cost.
| Author | : Gerald Farin |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 363 |
| Release | : 2012-12-06 |
| Genre | : Technology & Engineering |
| ISBN | : 3642557872 |
The nature of the physical Universe has been increasingly better understood in recent years, and cosmological concepts have undergone a rapid evolution (see, e.g., [11], [2],or [5]). Although there are alternate theories, it is generally believed that the large-scale relationships and homogeneities that we see can only be explainedby having the universe expand suddenlyin a very early “in?ationary” period. Subsequent evolution of the Universe is described by the Hubble expansion, the observation that the galaxies are ?ying away from each other. We can attribute di?erent rates of this expansion to domination of di?erent cosmological processes, beginning with radiation, evolving to matter domination, and, relatively recently, to vacuum domination (the Cosmological Constant term)[4]. We assume throughout that we will be relying as much as possible on observational data, with simulations used only for limited purposes, e.g., the appearance of the Milky Wayfrom nearbyintergalactic viewpoints. The visualization of large-scale astronomical data sets using?xed, non-interactive animations has a long history. Several books and ?lms exist, ranging from “Cosmic View: The Universe in Forty Jumps” [3] by Kees Boeke to “Powers of 10” [6,13] by Charles and Ray Eames, and the recent Imax ?lm “Cosmic Voyage” [15]. We have added our own contribution [9], “Cosmic Clock,” which is an animation based entirely on the concepts and implementation described in this paper.
| Author | : Jean Gallier |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 584 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461301378 |
As an introduction to fundamental geometric concepts and tools needed for solving problems of a geometric nature using a computer, this book fills the gap between standard geometry books, which are primarily theoretical, and applied books on computer graphics, computer vision, or robotics that do not cover the underlying geometric concepts in detail. Gallier offers an introduction to affine, projective, computational, and Euclidean geometry, basics of differential geometry and Lie groups, and explores many of the practical applications of geometry. Some of these include computer vision, efficient communication, error correcting codes, cryptography, motion interpolation, and robot kinematics. This comprehensive text covers most of the geometric background needed for conducting research in computer graphics, geometric modeling, computer vision, and robotics and as such will be of interest to a wide audience including computer scientists, mathematicians, and engineers.
| Author | : Pushkar Prakash Joshi |
| Publisher | : |
| Total Pages | : 224 |
| Release | : 2008 |
| Genre | : |
| ISBN | : |
| Author | : R. Albrecht |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 360 |
| Release | : 2012-12-06 |
| Genre | : Computers |
| ISBN | : 3709175844 |
Experts from university and industry are presenting new technologies for solving industrial problems and giving many important and practicable impulses for new research. Topics explored include NURBS, product engineering, object oriented modelling, solid modelling, surface interrogation, feature modelling, variational design, scattered data algorithms, geometry processing, blending methods, smoothing and fairing algorithms, spline conversion. This collection of 24 articles gives a state-of-the-art survey of the relevant problems and issues in geometric modelling.
| 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.
| Author | : Kevin W. Cassel |
| Publisher | : Cambridge University Press |
| Total Pages | : 433 |
| Release | : 2013-07-22 |
| Genre | : Mathematics |
| ISBN | : 1107022584 |
This book reflects the strong connection between calculus of variations and the applications for which variational methods form the foundation.
| Author | : Nickolas S. Sapidis |
| Publisher | : SIAM |
| Total Pages | : 330 |
| Release | : 1994-01-01 |
| Genre | : Computers |
| ISBN | : 9781611971521 |
This state-of-the-art study of the techniques used for designing curves and surfaces for computer-aided design applications focuses on the principle that fair shapes are always free of unessential features and are simple in design. The authors define fairness mathematically, demonstrate how newly developed curve and surface schemes guarantee fairness, and assist the user in identifying and removing shape aberrations in a surface model without destroying the principal shape characteristics of the model. Aesthetic aspects of geometric modeling are of vital importance in industrial design and modeling, particularly in the automobile and aerospace industries. Any engineer working in computer-aided design, computer-aided manufacturing, or computer-aided engineering will want to add this volume to his or her library. Researchers who have a familiarity with basic techniques in computer-aided graphic design and some knowledge of differential geometry will find this book a helpful reference. It is essential reading for statisticians working on approximation or smoothing of data with mathematical curves or surfaces.
| Author | : Giuseppe Buttazzo |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 467 |
| Release | : 2012-04-23 |
| Genre | : Mathematics |
| ISBN | : 1461424356 |
This volume consists of papers presented at the Variational Analysis and Aerospace Engineering Workshop II held in Erice, Italy in September 2010 at the International School of Mathematics "Guido Stampacchia". The workshop provided a platform for aerospace engineers and mathematicians (from universities, research centers and industry) to discuss the advanced problems requiring an extensive application of mathematics. The presentations were dedicated to the most advanced subjects in engineering and, in particular to computational fluid dynamics methods, introduction of new materials, optimization in aerodynamics, structural optimization, space missions, flight mechanics, control theory and optimization, variational methods and applications, etc. This book will capture the interest of researchers from both academia and industry.
| Author | : C. Werner Dankwort |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 171 |
| Release | : 2012-12-06 |
| Genre | : Technology & Engineering |
| ISBN | : 3322848191 |
Looking at modern industrial products, one can recognize a variety of different complex shapes. All these products are not only designed, they are styled. Everybody knows about the importance of styling, if the product is a car, but today even "simple" consumer appliances do not only have to fulfil their function, they must also look nice. In addition, even purely technical products like turbines or valves are designed with very complex shapes to make them work more efficiently. Thus, optimising the shape of products is one of the key factors in the process chain of development. Today, there are various CAx-systems, which have evolved to be the basic tools for design, calculation, simulation and manufacturing in almost all kinds of industrial environments, but the improvement of the product's shape is -in most cases -done manu ally on the physical model. This break in the CAD information flow can be overcome with REVERSE ENGINEERING techniques reconstructing the shape-describing CAD surfaces (Bezier-, NURBS-surfaces or others) from the modified physical model. nd Therefore the 2 Workshop on current CAx-problems was dedicated to REVERSE ENGINEERING. During the workshop were presented • the newest research results of surface reconstruction for a given set of points • the methods and tools for problems.in Reverse Engineering of some of the most important CAD vendors (Holometric Technology, IBM/Dassault, ICEM, Imageware, Matra Data vision, Tebis). Additionally, structural aspects in Reverse Engineering, possible future developments and new research directions were discussed.
