Discretization of three-dimensional objects: approximation and convergence

Yukiko Kenmochi; Atsushi Imiya

doi:10.1117/12.323275

2 October 1998 Discretization of three-dimensional objects: approximation and convergence

Yukiko Kenmochi, Atsushi Imiya

Proceedings Volume 3454, Vision Geometry VII; (1998) https://doi.org/10.1117/12.323275
Event: SPIE's International Symposium on Optical Science, Engineering, and Instrumentation, 1998, San Diego, CA, United States

Abstract

In this paper, we employ a polyhedron whose vertices are only lattice points as a discrete representation of any 3D object, in order to treat the shape in a lattice space. We present a method for generating such polyhedra corresponding to the original objects in Euclidean space, and call this process discretization. Moreover, we prove that our polyhedra converge to the original objects when the grid interval is infinitely decreased to zero. The proof implies that our discretization method has the guarantee of the shape approximation for the sufficiently small grid interval. Finally, we investigate the maximum grid interval which guarantees the shape approximation.

Citation Download Citation

Yukiko Kenmochi and Atsushi Imiya "Discretization of three-dimensional objects: approximation and convergence", Proc. SPIE 3454, Vision Geometry VII, (2 October 1998); https://doi.org/10.1117/12.323275

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available