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...
Main Authors: | , , |
---|---|
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 |
_version_ | 1818853566322835456 |
---|---|
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. |
first_indexed | 2024-12-19T07:38:51Z |
format | Article |
id | doaj.art-f05044b287c046d29fea049c021cb1b6 |
institution | Directory Open Access Journal |
issn | 2661-3352 2661-3344 |
language | English |
last_indexed | 2024-12-19T07:38:51Z |
publishDate | 2020-12-01 |
publisher | World Scientific Publishing |
record_format | Article |
series | International Journal of Mathematics for Industry |
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 |