This thesis covers some problems related to skin design in modern architectural geometry. We focus on the problem of subdividing the building skin into faces, such that each face is economical to fabricate and assemble. In particular, there are three sub-problems related to this process that we have explored. The first problem is related to k-set clustering of the edges that make up a triangulated mesh. We develop two algorithms that can reduce the number of clusters that can contain at least 95% of the edges in a mesh. The algorithms perform a controlled remeshing; both algorithms use local optimization to enhance pervious work on Centroidal Voronoi Tessellations (CVT) that produces near isometric triangulations. Our approach provides a method to reduce fabrication costs of sup...[ Read more ]

This thesis covers some problems related to skin design in modern architectural geometry. We focus on the problem of subdividing the building skin into faces, such that each face is economical to fabricate and assemble. In particular, there are three sub-problems related to this process that we have explored. The first problem is related to k-set clustering of the edges that make up a triangulated mesh. We develop two algorithms that can reduce the number of clusters that can contain at least 95% of the edges in a mesh. The algorithms perform a controlled remeshing; both algorithms use local optimization to enhance pervious work on Centroidal Voronoi Tessellations (CVT) that produces near isometric triangulations. Our approach provides a method to reduce fabrication costs of supporting structures for surface panels. Secondly, we develop a real-time tool to assist architects to explore generating patterns of meshes on the (free form) surface of a building. To do so, we introduce a simple technique that maps the 3D surface onto a 2D domain via an isotropic parameterization. Then we establish a simple, linear inverse mapping from parameter space to the 3D domain. This allows the user to perform rapid design operations in 2D and instantly see the result of the operations on the surface in 3D. The final part of the thesis addresses the problem of generating rationalized panels to approximate a given 3D surface and its subdivision. We introduce the idea of a shape feature to parametrically represent a generic (or template) panel that can be fabricated economically. We show that the process of generating feature instances that best approximate a connected set of surface patches on the building skin and locating each feature instance optimally can be combined into solving a single non-linear optimization model. We also show that this approach yields improved solutions over a classical 2-stage approach that is currently used in the industry. Real world examples are used for most of our work, showing that all methods developed have significant practical utility in modern architectural design.