XMAP: Five-Point Interpolating Map. (January 2022)

• Record Type: Journal Article
• Authors: Rossignac, Jarek
• Is Part Of: Computer aided design. Volume 142(2022)
• Publication Date: 2022-01
• Subjects: Interpolating mapping -- Parametric surface-patch -- Similarity -- Logarithmic spiral -- Five-point map -- Lattice; Computer-aided design -- Periodicals; Engineering design -- Data processing -- Periodicals; Computer graphics -- Periodicals; Conception technique -- Informatique -- Périodiques; Infographie -- Périodiques; Computer graphics; Engineering design -- Data processing; Periodicals; Electronic journals; 620.00420285
• DOI: 10.1016/j.cad.2021.103118
• Languages: English
• ISSNs: 0010-4485

Abstract

Abstract: Xmap takes the unit square to a subset of a doubly curved surface. It interpolates five control-points, which are the images of the four corners and of the center of that square. Interactive tweaks of control-points produce unsurprising changes in the map. The Xmap is an extension of the BeCOTS map. When the control-points are coplanar, it is an exact generalization of the COTS map. We conjecture that Xmaps may prove useful for designing aesthetically pleasing 3D structures.