A survey of curve and surface methods in CAGD
Computer Aided Geometric Design
A hierarchical data structure for representing assemblies: part I
Computer-Aided Design
Inference of the positions of components in an assembly: part 2
Computer-Aided Design
Principles of interactive computer graphics (2nd ed.)
Principles of interactive computer graphics (2nd ed.)
An interactive procedure for constructing line and circle tangencies
IEEE Computer Graphics and Applications
Closing the gap: A workstation-mainframe connection
Computers in Mechanical Engineering
GEODERM: Geometric shape design system using an entity-relationship model
Computer-Aided Design
Offsetting operations in solid modelling
Computer Aided Geometric Design
Juno, a constraint-based graphics system
SIGGRAPH '85 Proceedings of the 12th annual conference on Computer graphics and interactive techniques
Representations for Rigid Solids: Theory, Methods, and Systems
ACM Computing Surveys (CSUR)
The Programming Language Aspects of ThingLab, a Constraint-Oriented Simulation Laboratory
ACM Transactions on Programming Languages and Systems (TOPLAS)
Constraint-type statements in programming languages
Communications of the ACM
Design of solids with free-form surfaces
SIGGRAPH '83 Proceedings of the 10th annual conference on Computer graphics and interactive techniques
Variational geometry in computer-aided design
SIGGRAPH '81 Proceedings of the 8th annual conference on Computer graphics and interactive techniques
Characterizing non-ideal shapes in terms of dimensions and tolerances
SIGGRAPH '78 Proceedings of the 5th annual conference on Computer graphics and interactive techniques
Automatic Surface Generation in Computer Aided Design
Automatic Surface Generation in Computer Aided Design
Blending and offsetting solid models (cad/cam, computational geometry, representations, curves, surfaces, approximation)
Piecewise-circular curves for geometric modeling
IBM Journal of Research and Development
ACM Transactions on Graphics (TOG)
Snap-dragging in three dimensions
I3D '90 Proceedings of the 1990 symposium on Interactive 3D graphics
Using degrees of freedom analysis to solve geometric constraint systems
SMA '91 Proceedings of the first ACM symposium on Solid modeling foundations and CAD/CAM applications
Interaction with constraints in 3D modeling
SMA '91 Proceedings of the first ACM symposium on Solid modeling foundations and CAD/CAM applications
Interactive constraint-based solid modeling using allowable motion
SMA '93 Proceedings on the second ACM symposium on Solid modeling and applications
Geometric modeling: a new fundamental framework and its practical implications
SMA '95 Proceedings of the third ACM symposium on Solid modeling and applications
Structured topological complexes: a feature-based API for non-manifold topologies
SMA '97 Proceedings of the fourth ACM symposium on Solid modeling and applications
The generic geometric complex (GGC): a modeling scheme for families of decomposed pointsets
SMA '97 Proceedings of the fourth ACM symposium on Solid modeling and applications
A constraint-based manipulator toolset for editing 3D objects
SMA '97 Proceedings of the fourth ACM symposium on Solid modeling and applications
Representing Dimensions, Tolerances, and Features in MCAE Systems
IEEE Computer Graphics and Applications
IEEE Computer Graphics and Applications
Boolean Operations with Implicit and Parametric Representation of Primitives Using R-Functions
IEEE Transactions on Visualization and Computer Graphics
Branching blend of natural quadrics based on surfaces with rational offsets
Computer Aided Geometric Design
OCTOR: Subset selection in recursive pattern hierarchies
Graphical Models
Rational fixed radius rolling ball blends between natural quadrics
Computer Aided Geometric Design
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The success of solid modelling in industrial design depends on facilities for specifying and editing parameterized models of solids through user-friendly interaction with a graphical front-end. Systems based on a dual representation, which combines Constructive Solid Geometry (CSG) and Boundary representation (BRep), seem most suitable for modelling mechanical parts. Typically they accept a CSG-compatible input (Boolean combinations of solid primitives) and offer facilities for parameterizing and editing part definitions. The user need not specify the topology of the boundary, but often has to solve three-dimensional trigonometric problems to compute the parameters of rigid motions that specify the positions of primitive solids.A front-end that automatically converts graphical input into rigid motions may be easily combined with boundary-oriented input, but its integration in dual systems usually complicates the editing process and limits the possibilities of parameterizing solid definitions. This report proposes a solution based on three main ideas: (1) enhance the semantics of CSG representations with rigid motions that operate on arbitrary collections of sub-solids regardless of their position in the CSG tree, (2) store rigid motions in terms of unevaluated constraints on graphically selected boundary features, (3) evaluate constraints independently, one at a time, in user-specified order. The third idea offers an alternative to known approaches, which convert all constraints into a large system of simultaneous equations to be solved by iterative numerical methods.The resulting front-end is inadequate for solving problems where multiple constraints must be met simultaneously, but provides a powerful tool for specifying and interactively editing parameterized models of mechanical parts and mechanisms. The order in which constraints are evaluated may also be used as a language for specifying the sequence of assembly and set-up operations.An implementation under way is based on the interpreter of a new object oriented programming language, enhanced with geometric classes. Constraint evaluation results in the activation of methods which compute rigid motions from surface information. The set of available methods may be extended by the users, and methods may be integrated in higher level functions whose algorithmic nature simplifies the treatment of degenerate cases. Graphic interaction is provided through a geometrical engine which lets the user manipulate shaded images produced efficiently from the CSG representation of solid models.