Valley Average of Lines (VAL) and of Directions (VAD) in 3D. (February 2021)

• Record Type: Journal Article
• Authors: Sati, Mukul; Rossignac, Jarek
• Is Part Of: Computer aided design. Volume 131(2021)
• Publication Date: 2021-02
• Subjects: Average -- Lines -- Vectors; 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.2020.102957
• Languages: English
• ISSNs: 0010-4485

Abstract

Abstract: Extending (Sati et al., 2016) to 3D, we propose definitions and closed-form expressions for what we call the Valley Average of Directions (VAD), T →, of a set { T → i } of directions (unit vectors) and for what we call the Valley Average of Lines (VAL), L, of a set { L i } of lines. L is independent of the input order. When the { L i } are parallel, L is parallel to them and passes through the centroid of their intersections with any normal plane. When all { L i } contain point P, L passes through P .