Geometric modeling
Computational geometry: an introduction
Computational geometry: an introduction
Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
On-line construction of the convex hull of a simple polyline
Information Processing Letters
Convex hulls of piecewise-smooth Jordan curves
Journal of Algorithms
An introduction to solid modeling
An introduction to solid modeling
Art gallery theorems and algorithms
Art gallery theorems and algorithms
Polygon properties calculated from the vertex neighborhoods
SCG '87 Proceedings of the third annual symposium on Computational geometry
Sorting Jordan sequences in linear time
SCG '85 Proceedings of the first annual symposium on Computational geometry
Representations for Rigid Solids: Theory, Methods, and Systems
ACM Computing Surveys (CSUR)
Convex Decomposition of Simple Polygons
ACM Transactions on Graphics (TOG)
Digital Logic and Computer Design
Digital Logic and Computer Design
The PADL-1.0/2 system for defining and displaying solid objects
SIGGRAPH '78 Proceedings of the 5th annual conference on Computer graphics and interactive techniques
Binary partitions with applications to hidden surface removal and solid modelling
SCG '89 Proceedings of the fifth annual symposium on Computational geometry
Compliant motion in a simple polygon
SCG '89 Proceedings of the fifth annual symposium on Computational geometry
Sweeping arrangements of curves
SCG '89 Proceedings of the fifth annual symposium on Computational geometry
Finding compact coordinate representations for polygons and polyhedra
IBM Journal of Research and Development
Triangulation and CSG representation of polyhedra with arbitrary genus
SCG '91 Proceedings of the seventh annual symposium on Computational geometry
Optimal binary space partitions for orthogonal objects
SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
Applying parallel processing techniques to classification problems in constructive solid geometry
SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
Practical Point-in-Polygon Tests Using CSG Representations of Polygons
ALENEX '99 Selected papers from the International Workshop on Algorithm Engineering and Experimentation
Proceedings of the 2008 IEEE/ACM International Conference on Computer-Aided Design
International Journal of Geographical Information Science
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
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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 half-spaces 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 boolean formula based on the half-planes supporting the sides of the polygon and using each such half-plane only once. Our main contribution is an efficient and practical O(n log n) algorithm for doing this boundary-to-CSG conversion for a simple polygon of n sides. We also prove that such nice formulæ do not always exist for general polyhedra in three dimensions.