Constrained Modelling of 3‐Valent Meshes Using a Hyperbolic Deformation Metric. (2nd March 2016)

• Record Type: Journal Article
• Authors: Richter, Ronald; Kyprianidis, Jan Eric; Springborn, Boris; Alexa, Marc
• Is Part Of: Computer graphics forum. Volume 36:Number 6(2017)
• Page Start: 62
• Page End: 75
• Publication Date: 2016-03-02
• Subjects: digital geometry processing -- polygonal modelling -- I.3.5 [Computer Graphics]: Computational Geometry and Object Modelling–Curve -- Surface -- Solid and Object Representations; Computer graphics -- Periodicals; 006.605
• DOI: 10.1111/cgf.12805
• Languages: English
• ISSNs: 0167-7055

Abstract

Abstract : Polygon meshes with 3‐valent vertices often occur as the frame of free‐form surfaces in architecture, in which rigid beams are connected in rigid joints. Abstract: Polygon meshes with 3‐valent vertices often occur as the frame of free‐form surfaces in architecture, in which rigid beams are connected in rigid joints. For modelling such meshes, it is desirable to measure the deformation of the joints' shapes. We show that it is natural to represent joint shapes as points in hyperbolic 3‐space. This endows the space of joint shapes with a geometric structure that facilitates computation. We use this structure to optimize meshes towards different constraints, and we believe that it will be useful for other applications as well.