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The Gaussian and mean curvature criteria for curvature continuity between surfaces

Author:

Xiuzi YeAuthors Info & Claims

Computer Aided Geometric Design, Volume 13, Issue 6

Pages 549 - 567

https://doi.org/10.1016/0167-8396(95)00044-5

Published: 01 August 1996 Publication History

Abstract

In this paper, the influence of the tangent-plane continuity of two surfaces along a common linkage curve on (1) the Dupin indicatrices of the surfaces in terms of squared Dupin indicatrices; and (2) the Gaussian and mean curvatures of the surfaces in terms of ratios of differences between Gaussian and mean curvatures is studied. Alternative sets of curvature continuity conditions in terms of intrinsic geometry of surfaces are developed. Relationships between the equalities of Gaussian and mean curvatures and curvature continuity of the surfaces along the linkage curve are studied. For two surfaces which are tangent-plane continuous along a linkage curve, the following two criteria individually guarantee their curvature continuity along the linkage curve: (1) The Gaussian Curvature Criterion: the Gaussian curvatures along the linkage curve are the same, if the linkage curve does not contain straight lines or binormal generators of the two surfaces; (2) The Mean Curvature Criterion: the mean curvatures are the same along the linkage curve. Also an alternative proof for the Linkage Curve Theorem is provided. These criteria can be used in shape interrogations, such as in visual detection of curvature discontinuity between two surfaces.

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Cited By

Shi KYong JSun JPaul J(2011)-G2 B-spline surface interpolationComputer Aided Geometric Design10.1016/j.cagd.2011.06.00228:6(368-381)Online publication date: 1-Aug-2011
https://dl.acm.org/doi/10.1016/j.cagd.2011.06.002
Kiciak P(2010)Surfaces filling polygonal holes with G1 quasi G2 continuityMachine Graphics & Vision International Journal10.5555/1890906.189091019:1(63-96)Online publication date: 1-Jan-2010
https://dl.acm.org/doi/10.5555/1890906.1890910
Shi KYong JSun JPaul J(2010)Gn blending multiple surfaces in polar coordinatesComputer-Aided Design10.1016/j.cad.2009.11.00942:6(479-494)Online publication date: 1-Jun-2010
https://dl.acm.org/doi/10.1016/j.cad.2009.11.009
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Index Terms

The Gaussian and mean curvature criteria for curvature continuity between surfaces
1. Computing methodologies
  1. Computer graphics
    1. Shape modeling
      1. Parametric curve and surface models
      2. Volumetric models
2. Theory of computation
  1. Randomness, geometry and discrete structures

Index terms have been assigned to the content through auto-classification.

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cover image Computer Aided Geometric Design

Computer Aided Geometric Design Volume 13, Issue 6

August, 1996

85 pages

ISSN:0167-8396

Issue’s Table of Contents

Copyright © Elsevier Science B.V. All rights reserved © 1996.

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Elsevier Science Publishers B. V.

Netherlands

Publication History

Published: 01 August 1996

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Cited By

Shi KYong JSun JPaul J(2011)-G2 B-spline surface interpolationComputer Aided Geometric Design10.1016/j.cagd.2011.06.00228:6(368-381)Online publication date: 1-Aug-2011
https://dl.acm.org/doi/10.1016/j.cagd.2011.06.002
Kiciak P(2010)Surfaces filling polygonal holes with G1 quasi G2 continuityMachine Graphics & Vision International Journal10.5555/1890906.189091019:1(63-96)Online publication date: 1-Jan-2010
https://dl.acm.org/doi/10.5555/1890906.1890910
Shi KYong JSun JPaul J(2010)Gn blending multiple surfaces in polar coordinatesComputer-Aided Design10.1016/j.cad.2009.11.00942:6(479-494)Online publication date: 1-Jun-2010
https://dl.acm.org/doi/10.1016/j.cad.2009.11.009
Zhang JYou L(2004)Analytical C2 smooth blending surfacesFuture Generation Computer Systems10.5555/1708178.170831420:8(1317-1326)Online publication date: 1-Nov-2004
https://dl.acm.org/doi/10.5555/1708178.1708314
Zhang JYou L(2004)Analytical C2 smooth blending surfacesFuture Generation Computer Systems10.5555/1044364.104437220:8(1317-1326)Online publication date: 1-Nov-2004
https://dl.acm.org/doi/10.5555/1044364.1044372

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