Extending Editing Capabilities of Subdivision Schemes by Refinement of Point–Normal Pairs. (September 2020) - Lipovetsky, Evgeny; Dyn, Nira
Abstract: In this paper we extend the 2D circle average of Lipovetsky and Dyn (2016) to a 3D binary average of point-normal pairs, and study its properties. We modify classical surface-generating linear subdivision schemes with this average obtaining surface-generating schemes refining point-normal pairs. The modified schemes give the possibility to generate more geometries by editing the initial normals. For the case of input data consisting of a mesh only, we present a method for computing "naive" initial normals from the initial mesh. The performance of several modified schemes is compared to their linear variants, when operating on the same initial mesh, and examples of the editing capabilities of the modified schemes are given. In addition we provide a link to our repository, where we store the initial and refined mesh files, and the implementation code. Several videos, demonstrating the editing capabilities of the initial normals are provided in our Youtube channel. Graphical abstract: Highlights: A binary operation (circle average) on point-normal pairs in 3D is introduced. This average is used as the core refinement in four surface subdivision schemes. A choice of initial normals for a given initial control mesh is presented. Meshes generated by the new and their corresponding linear schemes are compared. Editing capabilities of modified schemes are discussed and demonstrated.