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Ebook Geometric modeling (2nd edition): Part 2

(BQ) Ebook incorporates references throughout the text to direct the reader to more specialized treatments of the subjects. Carefully designed illustrations and exercises support each mathematical concept presented. Offers hundreds of exercises to test the readers comprehension. | MODEL CONSTRUCTION COMPLEX In models. The completed dimensional must solid, and connectivity we techniques model simple shapes to construct complex a produce valid models. For example, be dimensiDnally homogeneous. If it is a threehave no dangling edges or surfaces. Model are topological properties, so consideration of of the modeling process. part to representing complex models. One approach we modeling, geometric it must homogeneity combine must use topologyis also important There are approaches uses aii implicitconstructiontechnique called and the other uses an explicit oundary-based b (CSG), an two constructive technique solid geometry called CSG scheme defines complex solidsas Boolean (b-rep).Tht The is sometimes solids. combinationsof complete representation referred to as a CSGtree,because uses binary tree whose terminal nodes il are so-called regularized arc simple solids whose nonterminal nodes structure of a b-rep is a graph Boolean combining operations. da ta and surfaces that comprise the boundary ofa solid. the curves the basic elements of a geometric we discussed In early chapters, and implicit model: parametric curves, surfaces, and solids.Appendix discuss the geometric transformations of these and Mortenson (1995) In solid the previous chapter we discussed how to generate simple boundary representation simpler a and The associating the \320\241 The elements. shapes sweeps, and deformations. we build the complexmodels that on which Here we will discuss topology, graphs, schemes models, boundary representations, and space-partitioning using All are of the Boolean of instances of parameterized shapes, form the foundation of this chapter. subject these complex solid models. 281 282 11.1 Construction Model \342\226\240 Complex TOPOLOGY OF MODELS models Complex require attention considerable understand how simpleelementsre a and how its topology is .