A point-based redesign algorithm for designing geometrically complex surfaces. A case study: Miralles's croissant paradox

Abstract

This study explores the use of point clouds for both representation and genetic morphogenesis of complex geometry. The accurate representation of existing objects of complex curved geometry, which are subsequently geometrically modified by evolutionary morphogenetic processes, is analysed. To this end, as a method of representation and generation of complex geometries, a point-based genetic algorithm and the use of large unstructured point clouds are proposed. A study of convergence and diversity of the implemented algorithm is detailed, as well as a comparison with the Coyote optimisation algorithm in terms of representation error demonstrating its efficiency. Some commonly used three-dimensional formats in architecture, such as NURBS and polygon meshes, are analysed, and compared against point clouds. This study also includes an evaluation regarding whether the use of point clouds is a more suitable format for realistic representation, rationalisation and genetic morphogenesis.