Handbook of Discrete and Computational Geometry, 2nd Ed.最新文献_第3页

Polyhedral Maps 多面地图

Handbook of Discrete and Computational Geometry, 2nd Ed. Pub Date : 1900-01-01 DOI: 10.1201/9781420035315.ch21

E. Schulte, U. Brehm

引用次数: 47

Handbook of Discrete and Computational Geometry, 2nd Ed. Pub Date : 1900-01-01 DOI: 10.1201/9781420035315.ch49

D. Dobkin, S. Teller

{"title":"Computer graphics","authors":"D. Dobkin, S. Teller","doi":"10.1201/9781420035315.ch49","DOIUrl":"https://doi.org/10.1201/9781420035315.ch49","url":null,"abstract":"Computer animation is the use of computers to create animations. There are a few different ways to make computer animations. One is 3D animation. One way to create computer animations is to create objects and then render them. This method produces perfect and three dimensional looking animations. Another way to create computer animation is to use standard computer painting tools and to paint single frames and composite them. These can later be either saved as a movie file or output to video. One last method of making computer animations is to use transitions and other special effects like morphing to modify existing images and video. Computer graphics are any types of images created using any kind of computer. There is a vast amount of types of images a computer can create. Also, there are just as many ways of creating those images. Images created by computers can be very simple, such as lines and circles, or extremly complex such as fractals and complicated rendered animations. If you want to create your own computer graphics, no matter how simple or complex, you have to know a few things about computers, computer graphics, and how they work. The following information should help you get started in the field of computer graphics:","PeriodicalId":156768,"journal":{"name":"Handbook of Discrete and Computational Geometry, 2nd Ed.","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130813636","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

Geometric Discrepancy Theory Anduniform Distribution 几何差异理论与均匀分布

Handbook of Discrete and Computational Geometry, 2nd Ed. Pub Date : 1900-01-01 DOI: 10.1201/9781420035315.ch13

J. Alexander, J. Beck, William W. L. Chen

{"title":"Geometric Discrepancy Theory Anduniform Distribution","authors":"J. Alexander, J. Beck, William W. L. Chen","doi":"10.1201/9781420035315.ch13","DOIUrl":"https://doi.org/10.1201/9781420035315.ch13","url":null,"abstract":"A sequence s1, s2, . . . in U = [0, 1) is said to be uniformly distributed if, in the limit, the number of sj falling in any given subinterval is proportional to its length. Equivalently, s1, s2, . . . is uniformly distributed if the sequence of equiweighted atomic probability measures μN (sj) = 1/N , supported by the initial N -segments s1, s2, . . . , sN , converges weakly to Lebesgue measure on U. This notion immediately generalizes to any topological space with a corresponding probability measure on the Borel sets. Uniform distribution, as an area of study, originated from the remarkable paper of Weyl [Wey16], in which he established the fundamental result known nowadays as the Weyl criterion (see [Cas57, KN74]). This reduces a problem on uniform distribution to a study of related exponential sums, and provides a deeper understanding of certain aspects of Diophantine approximation, especially basic results such as Kronecker’s density theorem. Indeed, careful analysis of the exponential sums that arise often leads to Erdős-Turán type upper bounds, which in turn lead to quantitative statements concerning uniform distribution. Today, the concept of uniform distribution has important applications in a number of branches of mathematics such as number theory (especially Diophantine approximation), combinatorics, ergodic theory, discrete geometry, statistics, numerical analysis, etc. In this chapter, we focus on the geometric aspects of the theory.","PeriodicalId":156768,"journal":{"name":"Handbook of Discrete and Computational Geometry, 2nd Ed.","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131869469","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 13

Computational Real Algebraic Geometry 计算实代数几何

Handbook of Discrete and Computational Geometry, 2nd Ed. Pub Date : 1900-01-01 DOI: 10.1201/9781420035315.ch33

B. Mishra

引用次数: 62

Sphere packing and coding theory 球体包装和编码理论

Handbook of Discrete and Computational Geometry, 2nd Ed. Pub Date : 1900-01-01 DOI: 10.1201/9781420035315.ch61

G. Kabatiansky, J. A. Rush

引用次数: 3

Graph drawing 图绘制

Handbook of Discrete and Computational Geometry, 2nd Ed. Pub Date : 1900-01-01 DOI: 10.1201/9781420035315.ch52

R. Tamassia, G. Liotta

引用次数: 0

Polytope Skeletons and Paths 多面体骨架和路径

Handbook of Discrete and Computational Geometry, 2nd Ed. Pub Date : 1900-01-01 DOI: 10.1201/9781420035315.ch20

G. Kalai

引用次数: 44

Solid modeling 坚实的建模

Handbook of Discrete and Computational Geometry, 2nd Ed. Pub Date : 1900-01-01 DOI: 10.1201/9781420035315.ch56

C. Hoffmann

引用次数: 5

Visibility 可见性

Handbook of Discrete and Computational Geometry, 2nd Ed. Pub Date : 1900-01-01 DOI: 10.1201/9781420035315.ch28

Joseph O'Rourke

引用次数: 0

Basic Properties of Convex Polytopes 凸多面体的基本性质

Handbook of Discrete and Computational Geometry, 2nd Ed. Pub Date : 1900-01-01 DOI: 10.1201/9781420035315.pt2

M. Henk, Jürgen Richter-Gebert, G. Ziegler

引用次数: 135