Luiz Henrique de Figueiredo

Lua—an extensible extension language

This paper describes Lua, a language for extending applications. Lua combines procedural features with powerful data description facilities, by using a simple, yet powerful, mechanism of tables . This mechanism implements the concepts of records, arrays and recursive data types (pointers), and adds some object‐oriented facilities, such as methods with dynamic dispatching.

Affine Arithmetic: Concepts and Applications

Affine arithmetic is a model for self-validated numerical computation that keeps track of first-order correlations between computed and input quantities. We explain the main concepts in affine arithmetic and how it handles the dependency problem in standard interval arithmetic. We also describe some of its applications.

The evolution of Lua

We report on the birth and evolution of Lua and discuss how it moved from a simple configuration language to a versatile, widely used language that supports extensible semantics, anonymous functions, full lexical scoping, proper tail calls, and coroutines.

Surface reconstruction from noisy point clouds

We show that a simple modification of the power crust algorithm for surface reconstruction produces correct outputs in presence of noise. This is proved using a fairly realistic noise model. Our theoretical results are related to the problem of computing a stable subset of the medial axis. We demostrate the effectiveness of our algorithm with a number of experimental results.

Computational morphology of curves

We prove that euclidean minimal spanning trees correctly reconstruct differentiable arcs from sufficiently dense samples. The proof is based on a combinatorial characterization of minimal spanning paths and on a description of the local geometry of ares inside tubular neighborhoods. We also present simple heuristics for reconstruting more general curves.

Adaptive Enumeration of Implicit Surfaces with Affine Arithmetic

We discuss adaptive enumeration and rendering methods for implicit surfaces, using octrees computed with affine arithmetic, a new tool for range analysis. Affine arithmetic is similar to standard interval arithmetic, but takes into account correlations between operands and sub‐formulas, generally providing much tighter bounds for the computed quantities. The resulting octrees are accordingly much smaller, and the rendering faster.

Implicit Objects in Computer Graphics

Implicit definition and description of geometric objects and surfaces plays a critical role in the appearance and manipulation of computer graphics. In addition, the mathematical definition of shapes, using an implicit form, has pivotal applications for geometric modeling, visualization and animation.Until recently, the parametric form has been by far the most popular geometric representation used in computer graphics and computer-aided design. Whereas parametric objects and the techniques associated with them have been exhaustively developed, the implicit form has been used as a complementary geometric representation, mainly in the restricted context of specific applications. However, recent developments in graphics are changing this situation, and the community is beginning to draw its attention to implicit objects. This is reflected in the current research of aspects related to this subject. Employing a coherent conceptual framework, Implicit Objects in Computer Graphics addresses the role of implicitly defined objects in the following parts: mathematical foundations of geometric models, implicit formulations for the specification of shapes, implicit primitives, techniques for constructing and manipulating implicit objects, modeling, rendering and animating implicit objects.

A unified approach for hierarchical adaptive tesselation of surfaces

This paper introduces a unified and general tesselation algorithm for parametric and implicit surfaces. The algorithm produces a hierarchial mesh that is adapted to the surface geometry and has a multiresolution and progressive structure. The representation can be exploited with advantages in several applications.

Hierarchical generalized triangle strips

This paper introduces a new refinement method for computing the triangle sequences of a mesh. We apply the method to construct a single generalized triangle strip that completely covers a parametric or implicit surface. A remarkable feature of this application is that our method generates the triangulation and the triangle strip simultaneously, using a mesh refinement scheme. As a consequence, we are able to produce a hierarchy of triangle strips defined at each refinement level. This data structure has many applications in geometry compression and rendering.

INTERSECTING AND TRIMMING PARAMETRIC MESHES ON FINITE-ELEMENT SHELLS

LUIZ CRISTOVAO G. COELHO MARCELO GATTASS˜ Department of Computer Science, PUC-Rio, Rio de Janeiro, BrazilLUIZ HENRIQUE DE FIGUEIREDOLNCC–Laborato´rio Nacional de Computac¸a˜o Cient´ifica, P etro´polis, BrazilABSTRACTWe present an algorithm for intersecting finite-element meshes defined on parametric surface patches. The inter-section curves are modeled precisely and both meshes are adjusted to the newly formed borders, without unwantedreparametrizations. The algorithm is part of an interactive shell modeling program that has been used in the designof large offshore oil structures. To achieve good interactive response, we represent meshes with a topological datastructure that stores its entities in spatial indexing trees instead of linear lists. These trees speed up the intersectioncomputations required to determine points of the trimming curves; moreover, when combined with the topologicalinformation, they allow remeshing using only local queries.