Spatial computing is a research field that is aimed at developing formalisms, lan- guages and architectures in order to take into account the notion of space in computer science. We present MGS, a programming language dedicated to the representation and the handling of arbitrary complex spatial organizations. To achieve this goal, we defin e an unconventional formalism based on two notions: topological collections, a new data structure relying on the notion of cellular complex developed in algebraic topology, andtransformations, an original kind of case-based definition of functions to handle topological collections b y rewriting. We illustrate this formalism by describing the representation in terms of topological collections a particular class of spaces, the quasi-manifolds, and by implementing with transformations a standart mesh refinement algorithm. MOTS-CL´ ES : Systde r´´ collection topologique, transformation,MGS

/pdf/representation-et-manipulation-de-structures-topologiques-205ipy8iz1.pdf

Représentation et manipulation de structures topologiques dans un langage fonctionnel

This paper focuses on the general parameterization in geometric modeling. We have adapted the λ-calculus formalism to an existing geometrical model which has an applicative representation: the generalized maps embedded in the plane. We investigated how this allows us to parameterize geometric objects by other objects, which can themselves be functional, rather than just by values such as size, shape or position. Thus, conditional, iterative, recursive and shared objects can be built and managed in an homogenous way. We have based the study on an interactive prototype implemented in Objective Caml. Its interface offers two consistent working views. The first interacts with geometric objects while the second interacts with the corresponding programs. We have examined in detail various higher-order operations where λ-calculus abstraction and application are used extensively to demonstrate how such objects can be built and manipulated. We will illustrate the force of our proposals using more complex constructions.

Parametrizing geometric objects using λ-calculus

This paper presents a framework for general parameterization in geometric modeling. We have adapted the l-calculus formalism to the geometrical model of the generalized maps embedded in the plane. We investigated how this allows us to parameterize geo-metric objects by size, shape or position but also by other objects or operators. Thus, conditional, iterative, recursive and shared objects can be built and managed in an homogenous way. We have based the study on an interactive prototype implemented in Objective Caml. Its interface offers two consistent working views. The first interacts with geometric objects while the second interacts with the corresponding programs. We have examined in detail various higher-order operations and constructions where l-calculus abstraction and application are used extensively.

Interacting with parametrized geometric objects using lambda-terms

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Parametrizing geometric objects using λ-calculus

Interacting with parametrized geometric objects using lambda-terms