Geometric Computation (Lecture Notes Series on Computing by Dongming Wang

By Dongming Wang

This e-book comprises instructional surveys and unique study contributions in geometric computing, modeling, and reasoning. Highlighting the function of algebraic computation, it covers: floor mixing, implicitization, and parametrization; automatic deduction with Clifford algebra and in actual geometry; and specified geometric computation. easy recommendations, complex tools, and new findings are awarded coherently, with many examples and illustrations. utilizing this ebook the reader will simply go the frontiers of symbolic computation, computing device aided geometric layout, and automatic reasoning. The ebook can be a necessary reference for individuals operating in different correct parts, comparable to medical computing, special effects, and synthetic intelligence.

Show description

Read or Download Geometric Computation (Lecture Notes Series on Computing Vol. 11) PDF

Similar computational mathematicsematics books

Comparison and Oscillation Theory of Linear Differential Equations

During this e-book, we examine theoretical and useful elements of computing tools for mathematical modelling of nonlinear platforms. a couple of computing ideas are thought of, equivalent to tools of operator approximation with any given accuracy; operator interpolation strategies together with a non-Lagrange interpolation; equipment of procedure illustration topic to constraints linked to recommendations of causality, reminiscence and stationarity; tools of process illustration with an accuracy that's the most sensible inside a given classification of types; equipment of covariance matrix estimation; equipment for low-rank matrix approximations; hybrid equipment in keeping with a mix of iterative strategies and most sensible operator approximation; and strategies for info compression and filtering less than situation clear out version should still fulfill regulations linked to causality and forms of reminiscence.

Hippocampal Microcircuits: A Computational Modeler’s Resource Book

The hippocampus performs an indispensible function within the formation of latest thoughts within the mammalian mind. it's the concentration of extreme examine and our knowing of its body structure, anatomy, and molecular constitution has swiftly improved in recent times. but, nonetheless a lot has to be performed to decipher how hippocampal microcircuits are equipped and serve as.

The Computational Brain

How do teams of neurons engage to let the organism to work out, make a decision, and circulate safely? What are the foundations wherein networks of neurons symbolize and compute? those are the principal questions probed via The Computational mind. Churchland and Sejnowski handle the foundational rules of the rising box of computational neuroscience, study a various diversity of neural community versions, and reflect on destiny instructions of the sphere.

Extra resources for Geometric Computation (Lecture Notes Series on Computing Vol. 11)

Example text

2 F* + 1 , + a57rk5+l = 73/3 + 1 hFf - (1) 44 Feng et al. Assuming that m= E 4**3v**, i = i , . . =i> (4«t)*=i> and (4,t)*=i as unknowns. Solutions of P A S . Solving the system of equations, we obtain the following expressions for the PAS g = 0: {9i=7ifi+PiF*+1=0, 92 = li fi + A ^ + 1 + ai7r* +1 = 0, 93='Y2f2+foF*+1 =0, 94 = 72/2 + p2F%+1 + a 3 7r£ +1 = 0, P5=^/3+i83i;,3*+1=0, . 06 = 73/3 + PsF*+1 + a 5 % * + 1 = 0. As an example, we take n = 4, A? ht = h2 = h% = - , n r 2 rr: 7*3 5" Then there are three free parameters in the solution, and one solution is shown in Fig.

Choose three surface patches g\ = 0, g3 = 0, and #5=0 to meet the three cylinders with Gk continuity, respectively. Now we need other three surface patches g2 = 0, # 4 = 0 , and ge = 0 which serve as the transitional surfaces between g\ = 0, g3 = 0, and g$ = 0. Thus in total we need six surface patches to compose the blending surface. Since the transversal planes Ft = 0 (i = 1,2,3) of the three cylinders intersect at one common point, the defining region of the blending surface can be defined as the composition of six tetrahedrons as shown in Fig.

2 ' 3 ' 4,12 ' 39 ' 40 In this chapter, we focus on blending algebraic surfaces using PAS and discuss four different methods: the direct method, the Grobner basis method, Wu's method, and the syzygy module method, which may be used effectively to deal with the problem. 2. Notations and Preliminaries In this section, we introduce some notations and recall a few basic concepts from computational algebraic geometry. Two good references are the books 10 ' 11 by Cox and others. 2, the definition of geometric continuity is introduced.

Download PDF sample

Rated 4.55 of 5 – based on 43 votes