Edges And Smooth Surfaces

Special edition of the Federal register, containing a codification of documents of general applicability and future effect as of ... with ancillaries.

Using an elegant mixture of geometry, graph theory and linear analysis, this monograph completely solves a problem lying at the interface of Isogeometric Analysis (IgA) and Finite Element Methods (FEM). The recent explosion of IgA, strongly tying Computer Aided Geometry Design to Analysis, does not easily apply to the rich variety of complex shapes that engineers have to design and analyse. Therefore new developments have studied the extension of IgA to unstructured unions of meshes, similar to those one can find in FEM. The following problem arises: given an unstructured planar quadrilateral mesh, construct a C1-surface, by piecewise Bézier or B-Spline patches defined over this mesh. This problem is solved for C1-surfaces defined over plane bilinear Bézier patches, the corresponding results for B-Splines then being simple consequences. The method can be extended to higher-order quadrilaterals and even to three dimensions, and the most recent developments in this direction are also mentioned here.

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.

Consistently rated as the best overall introduction to computer-based image processing, The Image Processing Handbook covers two-dimensional (2D) and three-dimensional (3D) imaging techniques, image printing and storage methods, image processing algorithms, image and feature measurement, quantitative image measurement analysis, and more. Incorporating image processing and analysis examples at all scales, from nano- to astro-, this Seventh Edition: Features a greater range of computationally intensive algorithms than previous versions Provides better organization, more quantitative results, and new material on recent developments Includes completely rewritten chapters on 3D imaging and a thoroughly revamped chapter on statistical analysis Contains more than 1700 references to theory, methods, and applications in a wide variety of disciplines Presents 500+ entirely new figures and images, with more than two-thirds appearing in color The Image Processing Handbook, Seventh Edition delivers an accessible and up-to-date treatment of image processing, offering broad coverage and comparison of algorithms, approaches, and outcomes.

This book is designed for upper-division undergraduate and graduate level archaeology students taking courses in ancient technologies, archaeological craft production, material culture, the history of technology, archaeometry, and field methods. This text can also serve as a general introduction and a reference for archaeologists, material culture specialists in socio-cultural disciplines, and engineers/scientists interested in the backgrounds and histories of their disciplines. The study of ancient technologies, that is, the ways in which objects and materials were made and used can reveal insights into economic, social, political, and ritual realms of the past. This book summarizes the current state of ancient technology studies by emphasizing methodologies, some major technologies, and the questions and issues that drive archaeologists in their consideration of these technologies. It shows the ways that technology studies can be used by archaeologists working anywhere, on any type of society and it embraces an orientation toward the practical, not the philosophical. It compares the range of pre-industrial technologies, from stone tool production, fiber crafts, wood and bone working, fired clay crafts, metal production, and glass manufacture. It includes socially contextualized case studies, as well as general descriptions of technological processes. It discusses essential terminology (technology, material culture, chaine operatoire, etc.), primarily from the perspective of how these terms are used by archaeologists.

This volume documents the results and presentations relating to the use of wavelet theory and other methods in surface fitting and image reconstruction of the Second International Conference on Curves and Surfaces, held in Chamonix in 1993. The papers represent directions for future research and development in many areas of application.