Partitioning Surfaces into Quad Patches

Abstract

The efficient and practical representation and processing of geometrically or topologically complex shapes often demands some form of virtual partitioning into pieces, each of which is of a simpler nature. Due to their regularity, highly structured networks of conforming quadrilateral patches, called quad layouts, or in particular instances quad meshes, are most beneficial in many scenarios; they enable the use of tensor-product representations based on NURBS or Bézier patches, grid-based multiresolution techniques, or discrete pixel-based map representations. However, partitions of this type are particularly complicated to create due to the inherent structural restrictions. Research in geometry processing has led to a variety of automatic or semi-automatic approaches to address this problem. This course provides a detailed introduction to this range of methods, treats their strengths and weaknesses, discusses their applicability and practical limitations, and outlines open problems in this field.