## Publications

### 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
**R**^{3} 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.