Smooth Spline Surfaces over Arbitrary Meshes: a Survey on Smooth Surface Generation Algorithms on Irregular Meshes

The construction of smooth parametric surfaces, such as Bézier patches and B-spline surfaces, is a basic problem in computer graphics, geometric modeling, CAGD and reverse engineering. In more of surface generation methods, a control mesh, which is a set of vertices, edges and faces, are used. There are several methods to generate smooth spline surface over regular and irregular meshes. These methods can be categorized into two groups: subdivision surfaces and spline surfaces. The first group iteratively applies refinement procedure over a mesh of polygons. In the limit, a smooth surface is created. The second group usually uses once or more refinement procedure over an irregular mesh, then a parametric surface patch is constructed to each vertex of the new refined mesh. This book intended to consider these two categories of smooth surface generation algorithms. In addition, this book outlines the basic concepts and definitions behind parametric curves and surfaces, smoothness, control meshes, and subdivision surfaces.