57 SOLID MODELING Christoph M
57 SOLID MODELING Christoph M. Hoffmann and Vadim Shapiro INTRODUCTION The objective of solid modeling is to represent, manipulate, and reason about the 3D shape of solid physical objects, by computer. As an application-oriented field, the scope of solid modeling, as well as the rel- ative emphasis on its parts, change over time. Since its inception, [RV82, Bra75], in the 1970s, the focus on modeling shape alone has continued to expand to integrate widening domains of physical properties. Monographs of the subject appeared in the late 1980s and include [Chi88, Hof89, M¨an88]. The expansion was and contin- ues to be driven by major applications that include manufacturing, architecture, construction, computer vision, materials science, medicine, biological engineering, graphics, and virtual reality. With the integration of new applications, and with the availability of inexpensive, powerful computing platforms, the relative impor- tance of specific shape representations can change. Along with such shifts, new modeling and analysis techniques are added. As a result, the field draws on very diverse technologies, including numerical analysis, symbolic algebraic computation, approximation theory, point set and algebraic topology, differential geometry, alge- braic geometry, and computational geometry. In this chapter, we first review the major representations of solids in Sec- tion 57.1. They include constructive solid geometry, boundary representation, spatial subdivisions of various types, and medial surface representations. With changing scope and focus, different representations enter and exit center stage. For instance, polygonal meshes and voxel-based representations became relatively marginal in the late 1990s, only to gain renewed interest and importance recently with the advent of 3D printing, because they allow representing a structured inte- rior of modeled shapes.
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