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An Efficient Algorithm for Finding the CSG Representation of a Simple Polygon
, 1989
"... Modeling twodimensional and threedimensional objects is an important theme in computer graphics. Two main types of models are used in both cases: boundary representations, which represent the surface of an object explicitly but represent its interior only implicitly, and constructive solid geometr ..."
Abstract

Cited by 35 (10 self)
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Modeling twodimensional and threedimensional objects is an important theme in computer graphics. Two main types of models are used in both cases: boundary representations, which represent the surface of an object explicitly but represent its interior only implicitly, and constructive solid geometry representations, which model a complex object, surface and interior together, as a boolean combination of simpler objects. Because neither representation is good for all applications, conversion between the two is often necessary. We consider the problem of converting boundary representations of polyhedral objects into constructive solid geometry (CSG) representations. The CSG representations for a polyhedron P are based on the halfspaces supporting the faces of P . For certain kinds of polyhedra this problem is equivalent to the corresponding problem for simple polygons in the plane. We give a new proof that the interior of each simple polygon can be represented by a monotone...
Abstract Computeraided design of porous artifacts
"... objects are all physically manifest in the world as threedimensional (3D) objects with varying surface, internal and volumetric properties and geometries. For instance, a tissue engineered structure, such as bone scaffold for guided tissue regeneration, can be described as a heterogeneous structure ..."
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objects are all physically manifest in the world as threedimensional (3D) objects with varying surface, internal and volumetric properties and geometries. For instance, a tissue engineered structure, such as bone scaffold for guided tissue regeneration, can be described as a heterogeneous structure consisting of 3D extracellular matrices (made from biodegradable material) and seeded donor cells and/or growth factors. The design and fabrication of such heterogeneous structures requires new techniques for solid models to represent 3D heterogeneous objects with complex material properties. This paper presents a representation of model density and porosity based on stochastic geometry. While density has been previously studied in the solid modeling literature, porosity is a relatively new problem. Modeling porosity of biomaterials is critical for developing replacement bone tissues. The paper uses this representation to develop an approach to modeling of porous, heterogeneous materials and provides experimental data to validate the approach. The authors believe that their approach introduces ideas from the stochastic geometry literature to a new set of engineering problems. It is hoped that this paper stimulates researchers to find new opportunities that extend these ideas to be more broadly applicable for other computational geometry, graphics and computeraided design problems.