Valley Average of Lines (VAL) and of Directions (VAD) in 3D. (February 2021) - Sati, Mukul; Rossignac, Jarek
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 .