LAR-ABC, a representation of architectural geometry. From concept of spaces, to design of building fabric, to construction simulation

This paper discusses the application of LAR (Linear Algebraic Representation) scheme to the architectural design process. LAR is a novel representation scheme for geometric design of curves, surfaces and solids, using simple, general and well founded concepts from algebraic topology (Dicarlo et al., Comput Aided Des 46:269–274, 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 integration, 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., ACM Trans. Graph 14(3):266–306, 1995; Paoluzzi, Geometric programming for computer aided design. Wiley, Chichester 2003), and is being embedded in Python and Javascript, providing the designer 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