LAR-ABC, a representation of architectural geometry From concept of spaces, to design of building fabric, to construction simulation. In: Advances in Architectural Geometry

This paper discusses the application of LAR (Linear Algebraic Repre- sentation) scheme to the architectural design process. LAR is a novel represen- tation scheme for geometric design of curves, surfaces and solids, using simple, general and well founded concepts from algebraic topology [Dicarlo et al. 2014]. LAR supports all topological incidence structures, including enumerative (images), decompositive (meshes) and boundary (CAD) representations. It is dimension- independent, and not restricted to regular complexes. Furthermore, LAR enjoys a neat mathematical format, being based on chains, the domains of discrete in- tegration, and cochains, the discrete prototype of differential forms, so naturally integrating the geometric shape with the supported physical properties. The LAR representation find his roots in the design language PLaSM [Paoluzzi et al. 1995; Paoluzzi 2003], and is being embedded in Python and Javascript, providing the de- signer with powerful and simple tools for a geometric calculus of shapes. In this paper we introduce the motivation of this approach, discussing how it compares to other mixed-dimensionality representations of geometry and is supported by open- source software projects. We also discuss simple examples of use.