Quad Layouts

The efficient, computer aided or automatic generation of quad layouts, i.e. the partitioning of an object's surface into networks of conforming quadrilateral patches, is a task that - despite its importance and utility in Computer Graphics and Geometric Modeling - received relatively low attention in the past. As a consequence, this task is most often performed manually by skilled experts in practice, where quad layouts are of particular interest for surface representation and parameterization tasks (spline surfaces, NURBS, finite element meshes, texture and displacement maps). This thesis is devoted to the development of novel efficient solution strategies and algorithms for the generation of high quality quad layouts. In particular, a fully automatic as well as an interactive method is presented for this task. An important aspect of the quad layout problem is the complexity of the underlying quality objective. A generic set of quality criteria which are common to most use cases is identified and used to drive the automatic approach. To make possible the optimization with respect to more specific design intents, in the interactive approach the user is included in the process, enabling the simple and intuitive infusion of expert knowledge. Significant advantages over previous approaches to the problem are demonstrated and discussed.