Capturing information on curves and surfaces from their projected images

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 b...

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Bibliographic Details
Main Authors: Masaru Hasegawa, Yutaro Kabata, Kentaro Saji
Format: Article
Language:English
Published: World Scientific Publishing 2020-12-01
Series:International Journal of Mathematics for Industry
Subjects:
Online Access:http://www.worldscientific.com/doi/epdf/10.1142/S2661335220500045
Description
Summary: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.
ISSN:2661-3352
2661-3344