A view-parametric extension of the d'Ocagne formula for a surface in $\mathbb{R}^3$

Ken Anjyo; Yutaro Kabata

A view-parametric extension of the d'Ocagne formula for a surface in $\mathbb{R}^3$

Differential Geometry 2024-09-23 v2

Authors: Ken Anjyo , Yutaro Kabata

Abstract

In this paper, we consider the orthogonal projection of a surface in $\mathbb{R}^3$ 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.

Keywords

surface in r3 orthogonal projection view direction plane curve invariants d'ocagne formula gaussian curvature

Cite

@article{arxiv.2310.05087,
  title  = {A view-parametric extension of the d'Ocagne formula for a surface in $\mathbb{R}^3$},
  author = {Ken Anjyo and Yutaro Kabata},
  journal= {arXiv preprint arXiv:2310.05087},
  year   = {2024}
}

Comments

16 pages, 9 figures. Some minor changes have been made (particularly, the title and abstract have been changed)

A view-parametric extension of the d'Ocagne formula for a surface in $\mathbb{R}^3$

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Keywords

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