Extending Editing Capabilities of Subdivision Schemes by Refinement of Point–Normal Pairs

Evgeny Lipovetsky*, Nira Dyn

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Article number102865
JournalCAD Computer Aided Design
StatePublished - Sep 2020


  • 3D circle average
  • Surface design
  • Surface-generating subdivision refining 3D point-normal pairs


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