Free-form surfaces are increasingly being used in many architectural projects. These surfaces are typically used as the building skin, canopy or skylight. To produce such surfaces economically, the architect needs to decompose the surface into a set of smaller pieces, called tiles or panels. Such a tiling is created by overlaying a network of curves over the surface such that the induced subdivision has some desirable properties. This curve network therefore functions not only as a basis for further panelization, but also provides the building with its unique aesthetic flavor. Therefore it is desirable to have a tool that can quickly generate a collection of curve networks so that the building designer, using his own expertise, can choose the best curve network among them....[ Read more ]

Free-form surfaces are increasingly being used in many architectural projects. These surfaces are typically used as the building skin, canopy or skylight. To produce such surfaces economically, the architect needs to decompose the surface into a set of smaller pieces, called tiles or panels. Such a tiling is created by overlaying a network of curves over the surface such that the induced subdivision has some desirable properties. This curve network therefore functions not only as a basis for further panelization, but also provides the building with its unique aesthetic flavor. Therefore it is desirable to have a tool that can quickly generate a collection of curve networks so that the building designer, using his own expertise, can choose the best curve network among them.

In this thesis, we propose a method to generate quad-meshes on curved surfaced by superposition of a pair of curves. Our scheme is simple and efficient enough to allow for almost real-time generation of patterns, and therefore it provides a new tool for architectural designers. For a particular kind of spiral, namely Archimedean spiral, we have tested the robustness of our method on various sample models. The key to our approach is the use of a near-isometric parameterization of the surface. The second contribution of this thesis is a convex optimization model that automatically and efficiently re-meshes a designed network by dislocation of the vertices in order to minimize the local variations in quad-edge lengths. Minimizing local variations is a well-established aesthetic principle, and similar measures are often used in other design applications such a fairing of interpolating curves or surfaces. Together, our approach is a 2-stage quad mesh design system with applications in architecture design.