Interacting with parametrized geometric objects using lambda-terms

Abstract

This paper presents a framework for general parameterization in geometric modeling. We have adapted the λ-calculus formalism to the geometrical model of the generalized maps embedded in the plane. We investigated how this allows us to parameterize geometric 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 λ-calculus abstraction and application are used extensively.