Abstract
Free form architecture involves many problems of a geometric, structural and construction nature. In order to reach a feasible and affordable solution some optimization phases are required. The development of powerful tools such as parametric and algorithmic design software is allowing great freedom for shape design and remarkable control in managing large amounts of data. With these tools structural and construction factors can be integrated as rules for geometrical generation and optimization. The chapter presents a methodology for free form architecture engineering and an applied example, starting from a physical model of an arbitrary shape to a construction-aware detailed project.
TopShape Generation
Overview
The generation of the starting shape is the first phase of the process. It can be achieved directly in the digital environment with CAD software. The most used and flexible digital representation of free form shapes are Non Uniform Rational Basis Splines (NURBS). The shape can also be generated starting with physical models digitized with reverse engineering processes. This last method allows the designer to have more direct control in the resulting shape. Recently some methods have been developed that allow the generation of a 3D digital model of smooth free form shapes starting from single professional sketches, for more details see (Xu, 2014).
The shape thus obtained can be then rationalized through the approximation of the surface with portions of simple geometric solids, ruled, developable (Peternell, 2004) or traslational surfaces (Pottmann, 2003).
In the most general case the shape is represented with a general NURBS surface, in this case we talk about free form in the strict sense, as the one presented hereinafter.
Key Terms in this Chapter
Finite Element Method (FEM): A numerical method for finding an approximate solution for partial derivative problems.
Planar Quad Mesh: A quadrilateral mesh with planar faces.
MeSH: A collection of vertex, edges and faces that define a polyhedral object.
Parallel mesh: A mesh with the same connectivity and parallel corresponding edges.
Computer Numerical Control (CNC): Automation of machine tools with computerized control.
Genetic Algorithm: An algorithm that evaluates a function searching for an optimal solution with methods inspired by natural selection strategies.
Developable Surface: A surface that can be developed on a plane without distortions. Developable surfaces are a subset of ruled surfaces characterized by having zero gaussian curvature.
Ruled Surface: A surface obtained by moving a straight line in the space.
Polyhedral Surface: A surface composed of planar polygons.
Gaussian Curvature: The product K of principal curvatures in a point of a surface. When K > 0 the point is elliptic , when K < 0 the point is hyperbolic . When one of the curvatures vanishes the point is parabolic and when both curvatures vanish the point is called flat .
Funicular Configuration: A shape characterized by only compressive or tensile stresses under his self-weight.
Paneling: The phase of subdivision of a surface in discrete elements.
Torsion-Free Joint: A structural joint in which the symmetry planes of prismatic beams meet along a common axis.
Section Utilization: The percentage of use of the maximum resistance capacity of a section of a structural element.
Generative algorithm: An algorithm whose result is a geometric object.
Incircle: The circle inscribed in a triangle, tangent to each edge.
Circle Packing Mesh: A triangular mesh with the property of having incircles of triangles tangent on common edges.