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Introduction to Geometric Computing
The geometric ideas in computer science, mathematics, engineering, and physics have considerable overlap and students in each of these disciplines will eventually encounter geometric computing problems. The topic is traditionally taught in mathematics departments via geometry courses, and in computer science through computer graphics modules. This text isolates the fundamental topics affecting these disciplines and lies at the intersection of classical geometry and modern computing.
Hyperbolic Geometry
The geometry of the hyperbolic plane has been an active and fascinating field of mathematical inquiry for most of the past two centuries. The basic approach taken is to define hyperbolic lines and develop a natural group of transformations preserving hyperbolic lines, and then study hyperbolic geometry as those quantities invariant under this group of transformations. Topics covered include the upper half-plane model of the hyperbolic plane, Möbius transformations, the general Möbius group, and their subgroups preserving the upper half-plane, hyperbolic arc-length and distance as quantities invariant under these subgroups, the Poincaré disc model, convex subsets of the hyperbolic plane, hyperbolic area, the Gauss-Bonnet formula and its applications.
Geometry for Computer Graphics : Formulae, Examples and Proofs
Geometry is the cornerstone of computer graphics and computer animation, and provides the framework and tools for solving problems in two and three dimensions. This may be in the form of describing simple shapes such as a circle, ellipse, or parabola, or complex problems such as rotating 3D objects about an arbitrary axis. Geometry for Computer Graphics draws together a wide variety of geometric information that will provide a sourcebook of facts, examples, and proofs for students, academics, researchers, and professional practitioners.
Essays in Constructive Mathematics
This book aims to promote constructive mathematics, not by defining it or formalizing it, but by practicing it, by basing all definitions and proofs on finite algorithms. The topics covered derive from classic works of nineteenth century mathematics---among them Galois' theory of algebraic equations, Gauss's theory of binary quadratic forms and Abel's theorem about integrals of rational differentials on algebraic curves. It is not surprising that the first two topics can be treated constructively---although the constructive treatments shed a surprising amount of light on them---but the last topic, involving integrals and differentials as it does, might seem to call for infinite processes. In this case too, however, finite algorithms suffice to define the genus of an algebraic curve, to prove that birationally equivalent curves have the same genus, and to prove the Riemann-Roch theorem. The main algorithm in this case is Newton's polygon, which is given a full treatment. Other topics covered include the fundamental theorem of algebra, the factorization of polynomials over an algebraic number field, and the spectral theorem for symmetric matrices.
Discrete Geometry, Combinatorics and Graph Theory ; 7th China-Japan Conference, CJCDGCGT 2005, Tianjin, China, November 18-20, 2005, and Xi'an, China, November 22-24, 2005, Revised Selected Papers
Theis book includes discrete algorithmic geometry, combinatorics and graph theory
Discrete and computational geometry; Japanese Conference, JCDCG 2004, Tokyo, Japan, October 8-11, 2004
This book constitutes the thoroughly refereed post-proceedings of the Japanese Conference on Discrete Computational Geometry, JCDCG 2004, held in Tokyo, Japan in October 2004, to honor Janos Pach on his fiftieth year. The 20 revised full papers presented were carefully selected during two rounds of reviewing and improvement from over 60 talks at the conference. All current issues in discrete algorithmic geometry are addressed.
Courbes algébriques planes = Plane Algebraic Curves
Resulting from a master's course at the University of Paris VII, this text is re-edited as it appeared in 1978. Various tools are introduced in connection with Bézout's theorem necessary for the development of the notion of the multiplicity of intersection of two algebraic curves in the complex projective plane. Starting from elementary notions on affine and projective algebraic subsets, we define the intersection multiplicities and interpret their sum in terms of the resultant of two polynomials. The local study is a pretext for the introduction of formal or convergent series rings; it culminates in Puiseux's theorem, the convergence of which is reduced by splits to that of the theorem of implicit functions. Various figures illuminate the text: we "see" in particular that the homogeneous equation x3 + y3 + z3 = 0 defines a torus in the complex projective plane.
Computer graphics and geometric modelling : Implementation & algorithms
Possibly the most comprehensive overview of computer graphics as seen in the context of geometric modelling, this two volume work covers implementation and theory in a thorough and systematic fashion. Computer Graphics and Geometric Modelling: Implementation and Algorithms, covers the computer graphics part of the field of geometric modelling and includes all the standard computer graphics topics. The first part deals with basic concepts and algorithms and the main steps involved in displaying photorealistic images on a computer. The second part covers curves and surfaces and a number of more advanced geometric modelling topics including intersection algorithms, distance algorithms, polygonizing curves and surfaces, trimmed surfaces, implicit curves and surfaces, offset curves and surfaces, curvature, geodesics, blending etc. The third part touches on some aspects of computational geometry and a few special topics such as interval analysis and finite element methods. The volume includes two companion programs.
Computational Geometry and Graph Theory ; International Conference, KyotoCGGT 2007, Kyoto, Japan, June 11-15, 2007. Revised Selected Papers
This book constitutes the thoroughly refereed post-conference proceedings of the Kyoto Conference on Computational Geometry and Graph Theory, KyotoCGGT 2007, held in Kyoto, Japan, in June 2007.
Combinatorial geometry and graph theory ; Indonesia-Japan Joint Conference, IJCCGGT 2003, Bandung, Indonesia, September 13-16, 2003, Revised Selected Papers
This volume consists of the refereed papers presented at the Indonesia-JapanJoint Conference on Combinatorial Geometry and Graph Theory (IJCCGGT2003), held on Indonesia. This confer-ence can also be considered as a series of the Japan Conference on Discrete andComputational Geometry (JCDCG), 2002.
Common Chinese materia medica ; Vol.2
Contains 231 species of 40 families of medicinal plants. The most important family of which are Magnoliaceae, such as Magnolia officinalis and Magnolia officinalis subsp. biloba; Schisandra chinensis of Schisandraceae; Cinnamomum aromaticum of Lauraceae, Coptis chinensis Franch., Coptis omeiensis and Coptis teeta of Berberidaceae; Isatis indigotica, Lepidium apetalum and Raphanus sativus of Cruciferae; Rheum palmatum, Rheum officinale and Rheum taguticum of Polygonaceae, etc. In each specie, it introduces the scientific names, herbal medicine names, characteristics, habitats, distributions, Acquisition and processing methods, medicinal traits, tastes, functions, use and dosages, and other information of medicinal plants, and attaches unedited color pictures and pictures of part herbal medicines for each species. This book series has totally 10 volumes, which covers 2000 kinds of Chinese medicines that are commonly seen or used. These volumes not only introduce the efficacy, function and some prescriptions of the medicines, but also introduce the biological characteristics of them in detail with clear photos of the habitats, so that readers can identify them in the field. Apart from the growing environment, the books expound the distribution areas and other information to facilitate researches and other applications. The volumes are targeted at readers of general interests and it is also of high referential value for scientific researcher and teachers. It can be used as a guide to researchers, clinical doctors, and students in the department of pharmaceutics and traditional Chinese medicine.
Advances in Discrete Differential Geometry
On a newly emerging field of discrete differential geometry and an excellent way to access this exciting area. It surveys the fascinating connections between discrete models in differential geometry and complex analysis, integrable systems and applications in computer graphics. The authors take a closer look at discrete models in differential geometry and dynamical systems. Their curves are polygonal, surfaces are made from triangles and quadrilaterals, and time is discrete. Nevertheless, the difference between the corresponding smooth curves, surfaces and classical dynamical systems with continuous time can hardly be seen. This is the paradigm of structure-preserving discretizations. Current advances in this field are stimulated to a large extent by its relevance for computer graphics and mathematical physics.
