Capturing information on curves and surfaces from their projected images

• Hasegawa, Masaru

• Kabata, Yutaro

• Saji, Kentaro

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.

Journal

• International Journal of Mathematics for Industry

  International Journal of Mathematics for Industry 12 (1), 2050004-2050004, 2020-12

  World Scientific Publishing

Keywords

• Contour
• differential geometry
• singularity theory
• curve
• surface
• Koenderink's formulae
• projection

Details

• CRID: 1050294045368886528
• NII Article ID: 120006993629
• DOI: 10.1142/s2661335220500045
• ISSN: 26613344
• ISSN: 26613352
• HANDLE: 20.500.14094/90007970
• Web Site: https://www.worldscientific.com/doi/pdf/10.1142/S2661335220500045
• Text Lang: en
• Article Type: journal article
• Data Source:
  • IRDB
  • Crossref
  • CiNii Articles
  • KAKEN