Electronic Resource
Springer
Advances in computational mathematics
8 (1998), S. 49-63
ISSN:
1572-9044
Keywords:
curvature
;
curvature variation
;
fairness functionals
;
surface analysis
;
surface smoothness
;
variational surface design
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract Two novel smoothness measures for surfaces are presented in this paper. The second and third order smoothness are defined as the squared normal curvature and the squared variation in normal curvature integrated over all directions in the tangent plane. Both quantities are truly geometric in the sense that they are invariant with respect to the actual parametrization of the surface. All the same, all formulae are derived in terms of an arbitrary parametrization. In addition to providing a basis for variational surface construction, the second and third order smoothness can also be used for evaluation and assessment of the quality of an existing surface.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1018931910836
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