A view-parametric extension of the d'Ocagne formula for a surface in ℝ³

2023/10/08 by Anjyo, Ken, Kabata, Yutaro
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2310.05087

Abstract

In this paper, we consider the orthogonal projection of a surface in ℝ³ for a given view direction. We then introduce and investigate several invariants of the families of the plane curves that locally configure the projection image of the surface. Using the invariants, we also show an extension of the d'Ocagne formula that associates a local behavior of the projection image of a surface with Gaussian curvature of the surface.

Related

• Mannheim-d'Ocagne-Koenderink type formulas for asymptotic directions
• Characterizing a surface by invariants
• Cr-invariants for surfaces in 4-space
• Geometry of surfaces in \mathbb R⁵ through projections and normal sections
• Osculating-type Ruled Surfaces in the Euclidean 3-space