Publications


Publications Since 2000, Chronologically


Selected Papers by Subject (before 2000)

Geometric Constraint Solving
The work is an integral part of the Erep project, but it has independent applications as well. We investigate geometric constraint solving in the plane and in 3-space, as well as questions how to federate geometric constraint solvers with equation solvers.
Solid Modeling and CAD
General works on solid modeling and CAD issues, other than Erep, including state-of-the-art chapters in handbooks.
Robustness of Geometric Computations
Geometric computations are fragile due to the imperfect match of logical facts, deduced from approximate geometric computations, and due to input data that is not necessarily exact. Robustness is one of the most fundamental problems in geometric computation and is a problem of increasing severity with increasing geometric data complexity.
Editable Representations and Master Model
This work deals with neutral representations of CAD models that contain design features and geometric constraints, and considers in particular semantic issues including persistent naming. Also explored are issues relating to distributed design maintenance and the master model concept.
Geometry Processing
Papers on surface blending, intersection and implicit surfaces.
Dimensionality Paradigm
This work concerns the representation of complex surfaces by a set of equations. Such representations are capable of expressing offsets, procedural blends, medial curves and surfaces, and more.
Medial Axis and Meshing
The medial axis transform is a shape representation that derives from a notion of symmetry. It has fundamental connections to Euclidean distance and relates to many concepts in other areas. One application, for example, is hexahedral mesh generation.
Other Work in Geometric Modeling
Other interesting aspects of geometric computations and applications. For example, note that there are up to 12 common tangents to four spheres in R3 in general position.  Or comment on the chapter to be published in the CAGD Handbook on Parametric Modeling.
Visualization and its Applications
Papers on graphics, visualization, and applications
Tree Pattern Matching
Algorithms for matching tree patters and application to certain programming languages
Graph Isomorphism
Papers using the group-theoretic approach to graph isomorphism and a semigroup algorithms paper.
Lucid
Lucid was a declarative programming language designed to facilitate proving program correctness.  These papers deal with how to compile Lucid.