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Estimation of the principle curvatures of approximated surfaces

โœ Scribed by Christian Wollmann

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
237 KB
Volume
17
Category
Article
ISSN
0167-8396

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โœฆ Synopsis

This paper presents a method for estimating curvature values of a surface, which is given only approximatively, e.g., by measured data. The presented method requires estimates of the curvature of curves. These lead, along with the theorems from Euler and Meusnier, to the values of surface curvature. Methods are presented, which converge with the different error order of O(h 2 ) and O(h 2n ). For the first of them explicit formulae are given. It is proved that the error order remains the same through all further calculations until the final estimation of surface curvature is found.

๐Ÿ“œ SIMILAR VOLUMES

Numerical estimation of the curvature of
Numerical estimation of the curvature of surfaces
โœ P.H. Todd; R.J.Y. McLeod ๐Ÿ“‚ Article ๐Ÿ“… 1986 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 517 KB

Meusnier's and Euler's theorems relating to surface curvature are given as is a brief discussion on the Dupin indicatrix. The connection between Gaussian curvature and growth ratio is outlined. A method for approximating the Dupin indicatrix from surface-point data is given and, by way of comparison