Capturing information on curves and surfaces from their projected images
Differential Geometry
2020-10-08 v2
Abstract
Obtaining complete information about the shape of an object by looking at it from a single direction is impossible in general. In this paper, we theoretically study obtaining differential geometric information of an object from orthogonal projections in a number of directions. We discuss relations between (1) a space curve and the projected curves from several distinct directions, and (2) a surface and the apparent contours of projections from several distinct directions, in terms of differential geometry and singularity theory. In particular, formulae for recovering certain information on the original curves or surfaces from their projected images are given.
Keywords
Cite
@article{arxiv.1904.08633,
title = {Capturing information on curves and surfaces from their projected images},
author = {Masaru Hasegawa and Yutaro Kabata and Kentaro Saji},
journal= {arXiv preprint arXiv:1904.08633},
year = {2020}
}
Comments
22pages, 11figures