Theory of R-functions [12] provides the methodology for constructing exact implicit functions for any semianalytic set. This paper systematically explores and compares the known constructions in terms of their differential properties and explains how such functions may be constructed automatically from CSG and boundary representations of solids. The constructed functions may be automatically differentiated and integrated and have many important applications in meshfree engineering analysis, motion planning, and scientific visualization.

The field of solid modeling has developed a variety of techniques for unambiguous representations of three-dimensional objects. Feature recognition is a sub-discipline of solid modeling that focuses on the design and implementation of algorithms for detecting manufacturing information from solid models produced by computer-aided design (CAD) systems. Examples of this manufacturing information include features such as holes, slots, pockets and other shapes that can be created on modern computer numerically controlled machining systems.

Nearly all major commercial computer-aided design systems have adopted a feature-based design approach to solid modeling. Models are created via a sequence of operations which apply design features to incremental versions of a design model. Even surfacing, free-form surface shaping, and deformation operations are internally represented in modeling systems as features in a "history tree" that generates the final design. Much in the same manner that Constructive Solid Geometry (CSG) trees for an individual model can be non-unique, these design feature histories for solid models might be ordered in a number of ways and still result in the same final geometry and topology. We formulate this problem symbolically and present geometric reasoning techniques to generate a canonical form for certain classes of design feature histories. We define this representation as a Model Dependency Graph (MDG) and show how it can be used as a basis for developing techniques for managing databases of solid ...

This paper deals with the problem of creating and maintaining a spatial

....................................... ix 1 INTRODUCTION . . .............................. 1 1.1 ProblemStatement ............................... 1 1.2 OverviewofApproach............................. 4 1.3 Outline of Thesis . . .............................. 5 2 BACKGROUND . . . .............................. 6 2.1 GraphMatching ................................ 6 2.1.1 Definitions and Background . . ....................... 8 2.1.2 CommonApproaches ............................ 9 2.1.3 Invariants................................... 11 2.1.4 ConventionalApproaches .......................... 13 2.1.5 OtherApproaches .............................. 17 2.2 SolidModelingandFeatureBasedDesign................... 22 2.2.1 Constructive Solid Geometry (CSG) . . . . . ................ 22 2.2.2 Boundary Representation (B-rep) . . . . . . ................ 22 2.2.3 Feature-based Modeling . . . . ....................... 23 2.2.4 Feature Recognition From Solid Models . . ...................

The ability to transform between distinct geometric representations is the key to success of multiple-representation modeling systems. But the existing theory of geometric modeling does not directly address or support construction, conversion, and comparison of geometric representations. A study of classical problems of CSG $ b-rep conversions, CSG optimization, and other representation conversions suggests a natural relationship between a representation scheme and an appropriate decomposition of space. We show that a hierarchy of space decompositions corresponding to different representation schemes can be used to enhance the theory and to develop a systematic approach to maintenance of geometric representations. 1. Motivation 1.1. Modern theory of representations The modern field of solid modeling owes much of its success to the theoretical foundations laid by members of the Production Automation Project at the University of Rochester in the 1970's. The history of these development...

This paper describes a feature-based algorithm for automated design of multi-piece sacrificial molds. Our mold design algorithm consists of the following three steps. First, the desired gross mold shape is created based on the feature-based description of the part geometry. Second, if the desired gross mold shape is not machinable as a single component, then the gross mold shape is decomposed into simpler geometric components to make sure that each component is machinable using 3-axis CNC machining. The decomposition is performed to ensure that each component is accessible to end-milling tools, and decomposed components can be assembled together to form the gross mold shape. Finally, assembly features are added to mold components to eliminate unnecessary degrees of freedom from the final mold assembly to facilitate molding.

inversion for a global shear velocity

Dual representation systems rely on a parametric model to create and to manipulate the boundary representation of a solid. Parametric and boundary representations remain consistent if they continue to model the same solid, after updates applied to the parametric model and/or to the boundary representation. We consider the problem of verifying the consistency between the boundary representation and the CSG representation which is a restricted case of parametric representation. We determine the necessary and sufficient conditions for consistency of the two representations, identify the required computational utilities, and describe two implemented and tested algorithms.

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