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