Constraint programming languages: their specification and generation
Constraint programming languages: their specification and generation
Voronoi diagram for multiply-connected polygonal domains 1: algorithm
IBM Journal of Research and Development
Mechanical geometry theorem proving
Mechanical geometry theorem proving
Algebraic methods for geometric reasoning
Annual review of computer science: vol. 3, 1988
CAD Based Programming for Sensory Robots
Introduction to Solid Modeling
Introduction to Solid Modeling
Curves and surfaces for computer aided geometric design: a practical guide
Curves and surfaces for computer aided geometric design: a practical guide
Generating blend surfaces using partial differential equations
Computer-Aided Design
Geometric and solid modeling: an introduction
Geometric and solid modeling: an introduction
Applications of spatial data structures: Computer graphics, image processing, and GIS
Applications of spatial data structures: Computer graphics, image processing, and GIS
The design and analysis of spatial data structures
The design and analysis of spatial data structures
Solid representation and operation using extended octrees
ACM Transactions on Graphics (TOG)
A solid modelling system free from topological inconsistency
Journal of Information Processing
Binary space partitioning trees as an alternative representation of polytopes
Computer-Aided Design
Constructive non-regularized geometry
Computer-Aided Design - Beyond solid modelling
Representations of semi-algebraic sets in finite algebras generated by space decompositions
Representations of semi-algebraic sets in finite algebras generated by space decompositions
Modeling of curves and surfaces in CAD/CAM
Modeling of curves and surfaces in CAD/CAM
Separation for boundary to CSG conversion
ACM Transactions on Graphics (TOG)
Joining smooth patches around a vertex to form a Ck surface
Computer Aided Geometric Design
A mechanism for persistently naming topological entities in history-based parametric solid models
SMA '95 Proceedings of the third ACM symposium on Solid modeling and applications
What is a parametric family of solids?
SMA '95 Proceedings of the third ACM symposium on Solid modeling and applications
Assembly sequencing with toleranced parts
SMA '95 Proceedings of the third ACM symposium on Solid modeling and applications
Computing the medial surface of a solid from a domain Delaunay triangulation
SMA '95 Proceedings of the third ACM symposium on Solid modeling and applications
Polyhedral modelling with exact arithmetic
SMA '95 Proceedings of the third ACM symposium on Solid modeling and applications
Shelling and offsetting bodies
SMA '95 Proceedings of the third ACM symposium on Solid modeling and applications
Medial axis transform to boundary representation conversion
Medial axis transform to boundary representation conversion
Representations for Rigid Solids: Theory, Methods, and Systems
ACM Computing Surveys (CSUR)
Solid Modeling with Designbase: Theory and Implementation
Solid Modeling with Designbase: Theory and Implementation
Function Representation for Sweeping by a Moving Solid
IEEE Transactions on Visualization and Computer Graphics
Volume-Preserving Free-Form Solids
IEEE Transactions on Visualization and Computer Graphics
An Algorithm for the Medial Axis Transform of 3D Polyhedral Solids
IEEE Transactions on Visualization and Computer Graphics
A systematic approach for design-manufacturing feature mapping
Selected and Expanded Papers from the IFIP TC5/WG5.2 Working Conference on Geometric Modeling for Product Realization
Erep: An editable, high-level representation for geometric design and analysis
Selected and Expanded Papers from the IFIP TC5/WG5.2 Working Conference on Geometric Modeling for Product Realization
Constraint solving for computer-aided design
Constraint solving for computer-aided design
Necessary conditions for boundary representation variance
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
An approach to modeling multi-material objects
SMA '97 Proceedings of the fourth ACM symposium on Solid modeling and applications
Boundary representation deformation in parametric solid modeling
ACM Transactions on Graphics (TOG)
Planning Geometric Constraint Decomposition via Optimal Graph Transformations
AGTIVE '99 Proceedings of the International Workshop on Applications of Graph Transformations with Industrial Relevance
Building 3D Models of Vehicles for Computer Vision
VISUAL '99 Proceedings of the Third International Conference on Visual Information and Information Systems
Constructive modeling of G1 bifurcation
Computer Aided Geometric Design
Constraint-based model synthesis
2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling
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The objective of solid modeling is to represent, manipulate, and reason about, the three-dimensional shape of solid physical objects, by computer. Such representations should be unambiguous.Solid modeling is an application-oriented field that began in earnest in the early 1970s. [46]. Major application areas include design, manufacturing, computer vision, graphics, and virtual reality. Technically, the field draws on diverse sources including numerical analysis, symbolic algebraic computation, approximation theory, applied mathematics, point set topology, algebraic geometry, computational geometry, and data bases. Monographs and major surveys of solid modeling include [13], [19], [27], [37], [44], [45], [46].In this road map article, we begin with some mathematical foundations of the field. We review next the major representation schemata of solids. Then, major layers of abstraction in a typical solid modeling system are characterized: The lowest level of abstraction comprises a substratum of basic service algorithms. At an intermediate level of abstraction there are algorithms for larger, more conceptual operations. Finally, a yet higher level of abstraction presents to the user a functional view that is typically targeted towards solid design. Here, we will look at some applications and at user interaction concepts.The classical design paradigms of Solid Modeling concentrated on obtaining one specific final shape. Those paradigms are becoming supplanted by feature-based, constraint-based design paradigms that are oriented more toward the design process and define classes of shape instances. These new paradigms venture into territory that has yet to be explored systematically. Concurrent with this paradigm shift, there is also a shift in the system architecture towards modularized confederations of plug-compatible functional components. We explore these trends lightly in the last section.