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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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
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author Masaru Hasegawa
Yutaro Kabata
Kentaro Saji
author_facet Masaru Hasegawa
Yutaro Kabata
Kentaro Saji
author_sort Masaru Hasegawa
collection DOAJ
description 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.
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spelling doaj.art-f05044b287c046d29fea049c021cb1b62022-12-21T20:30:31ZengWorld Scientific PublishingInternational Journal of Mathematics for Industry2661-33522661-33442020-12-011212050004-12050004-1310.1142/S266133522050004510.1142/S2661335220500045Capturing information on curves and surfaces from their projected imagesMasaru Hasegawa0Yutaro Kabata1Kentaro Saji2Department of Information Science, Center for Liberal Arts and Sciences, Iwate Medical University, 2-1-1 Idaidori, Yahaba-cho, Shiwa-gun, Iwate, 028-3694, JapanSchool of Information and Data Sciences, Nagasaki University, Bunkyocho 1-14, Nagasaki, 852-8131, JapanDepartment of Mathematics, Graduate School of Science, Kobe University, Rokkodai 1-1, Nada, Kobe 657-8501, JapanObtaining 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.http://www.worldscientific.com/doi/epdf/10.1142/S2661335220500045contourdifferential geometrysingularity theorycurvesurfacekoenderink’s formulaeprojection
spellingShingle Masaru Hasegawa
Yutaro Kabata
Kentaro Saji
Capturing information on curves and surfaces from their projected images
International Journal of Mathematics for Industry
contour
differential geometry
singularity theory
curve
surface
koenderink’s formulae
projection
title Capturing information on curves and surfaces from their projected images
title_full Capturing information on curves and surfaces from their projected images
title_fullStr Capturing information on curves and surfaces from their projected images
title_full_unstemmed Capturing information on curves and surfaces from their projected images
title_short Capturing information on curves and surfaces from their projected images
title_sort capturing information on curves and surfaces from their projected images
topic contour
differential geometry
singularity theory
curve
surface
koenderink’s formulae
projection
url http://www.worldscientific.com/doi/epdf/10.1142/S2661335220500045
work_keys_str_mv AT masaruhasegawa capturinginformationoncurvesandsurfacesfromtheirprojectedimages
AT yutarokabata capturinginformationoncurvesandsurfacesfromtheirprojectedimages
AT kentarosaji capturinginformationoncurvesandsurfacesfromtheirprojectedimages