Boundary to constructive solid geometry mappings: a focus on 2D issues
Computer-Aided Design
Construction and optimization of CSG representations
Computer-Aided Design - Beyond solid modelling
Algorithmic aspects of alternating sum of volumes. Part 2: Nonvergence and its remedy
Computer-Aided Design
Modeling closed surfaces: a comparison of existing methods
Mathematical methods in computer aided geometric design II
Separation for boundary to CSG conversion
ACM Transactions on Graphics (TOG)
Introduction to Implicit Surfaces
Introduction to Implicit Surfaces
Computational Geometry for Design and Manufacture
Computational Geometry for Design and Manufacture
Recognizing Shape Features in Solid Models
IEEE Computer Graphics and Applications
IEEE Computer Graphics and Applications
Three-dimensional binary space partitioning tree and constructive solid geometry tree construction from algebraic boundary representations
Distance functions and skeletal representations of rigid and non-rigid planar shapes
Computer-Aided Design
A family of skeletons for motion planning and geometric reasoning applications
Artificial Intelligence for Engineering Design, Analysis and Manufacturing - Representing and Reasoning About Three-Dimensional Space
Medial zones: Formulation and applications
Computer-Aided Design
Efficient evaluation of continuous signed distance to a polygonal mesh
Proceedings of the 28th Spring Conference on Computer Graphics
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This paper presents a new method to compute constructive solid geometry (CSG) tree representations of an object whose faces consist of planar and non-planar surfaces. The algorithm described accepts as input a valid boundary representation of an object consisting of piecewise implicit surfaces, and computes a halfspace CSG representation of the object. A class of objects that are describable by the surfaces bounding them are valid input for the algorithm of this work, although methods currently exist to compute the additional information necessary to process non-describable quadric objects as well. This work builds on and complements the other work in this area, in which dominating halfspaces are used to simplify the b-rep to CSG conversion process. We include factored faces to enable the factorization of dominating halfspaces throughout the algorithm. Thus, an efficient disjoint decomposition of the solid is obtained as a matter of course in the algorithm, so that CSG minimization is generally not necessary.This work is motivated by reverse engineering of mechanical parts, in which a model of a part is recovered from information obtained by some sort of sensing technique (e.g. CAT scanning, laser range finding). The recovery of a valid CSG-tree description of an object from a boundary representation of it can provide useful information to an engineer in the area of reverse engineering and in other areas related to solid modeling as well. The CSG tree also provides a relatively neutral representation that can enhance form feature recognition and translation.