A long-standing challenge in geometric modeling is providing a natural, intuitive interface for making local deformations to 3D surfaces. Previous approaches have provided either interactive manipulation or physical simulation to control surface deformations. In this paper, we investigate combining these two approaches with a painting interface that gives the user direct, local control over a p...

In this paper we enumerate and classify the “simplest” pairs (M, G) where M is a closed orientable 3-manifold and G is a trivalent graph embedded in M . To enumerate the pairs we use a variation of Matveev’s definition of complexity for 3-manifolds, and we consider only (0, 1, 2)-irreducible pairs, namely pairs (M, G) such that any 2-sphere in M intersecting G transversely in at most 2 points b...

We present a new framework for rendering virtual environments. This framework is proposed as a complete scene description, which embodies the space of all possible renderings, under all possible lighting scenarios of the given scene. In effect, this hypothetical rendering space includes all possible light sources as part of the geometric model. While it would be impractical to implement the gen...

These are sketch notes for my lecture on the MALOA Introductory Day of the meeting ‘Geometric Model theory’, March 25–28 2010, Oxford. They were written after the lecture, but have not been carefully polished. The bibliography is not carefully put together. For an old but wonderful introduction to stable group theory, see [13]. For an update, often with results stated in great generality, see [...

This paper presents a new method for shape indexing from large databases of line-patterns. The basic idea is to exploit both geometric attributes and structural information to construct a shape similarity measure. We realise this goal by computing the N-nearest neighbour graph for the lines-segments for each pattern. The edges of the neighbourhood graphs are used to gate contributions to a two-...

Many of the bottlenecks relative to computational uid dynamics occur because the input geometric model is not directly suitable for analysis. There is a need for mathematical criteria for admissible models and algorithms to determine when those criteria have been met. These results are often presented in more theoretical scientiic forums rather than within engineering venues. This interdiscipli...

In this paper we present the 2D parametric freehand sketch component of an experimental prototype called GEGROSS (GEsture & Geometric ReconstructiOn based Sketch System). The module implements a gesture alphabet and a calligraphic interface to manage geometric constraints found in 2D sections, that are later used to perform modeling operations. We use different elements to implement this module...

Geometric modeling by constraints, whose applications are of interest to communities from various fields such as mechanical engineering, computer aided design, symbolic computation or molecular chemistry, is now integrated into standard modeling tools. In this discipline, a geometric form is specified by the relations that the components of this form must verify instead of explicitly specifying...

In computer graphics and geometric modeling one generally faces the problem to integrate a variety of curve and surface types into a single program. Object-oriented design ooers the opportunity to use the inherent hierarchical structure of curves and surfaces to solve this problem. This paper presents an object-oriented framework together with its C++ implementation that starts from an abstract...

Morse theory is a powerful tool in its applications to computational topology, computer graphics and geometric modeling. It was originally formulated for smooth manifolds. Recently, Robin Forman formulated a version of this theory for discrete structures such as cell complexes. It opens up several categories of interesting objects (particularly meshes) to applications of Morse theory. Once a Mo...