Principal curvature ridges and geometrically salient regions of parametric B-spline surfaces

Suraj Musuvathy, Elaine Cohen, James Damon, Jun Kyung Seong

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

Ridges are characteristic curves of a surface that mark salient intrinsic features of its shape and are therefore valuable for shape matching, surface quality control, visualization and various other applications. Ridges are loci of points on a surface where one of the principal curvatures attain a critical value in its respective principal direction. We present a new algorithm for accurately extracting ridges on B-spline surfaces and define a new type of salient region corresponding to major ridges that characterize geometrically significant regions on surfaces. Ridges exhibit complex behavior near umbilics on a surface, and may also pass through certain turning points causing added complexity for ridge computation. We present a new numerical tracing algorithm for extracting ridges that also accurately captures ridge behavior at umbilics and ridge turning points. The algorithm traverses ridge segments by detecting ridge points while advancing and sliding in principal directions on a surface in a novel manner, thereby computing connected curves of ridge points. The output of the algorithm is a set of curve segments, some or all of which may be selected for other applications such as those mentioned above. The results of our technique are validated by comparison with results from previous research and with a brute-force domain sampling technique.

Original languageEnglish
Pages (from-to)756-770
Number of pages15
JournalCAD Computer Aided Design
Volume43
Issue number7
DOIs
Publication statusPublished - 2011 Jul 1
Externally publishedYes

Fingerprint

Splines
Surface properties
Quality control
Visualization
Sampling

Keywords

  • Geometrically salient region
  • Parametric B-spline surface
  • Ridge

ASJC Scopus subject areas

  • Computer Graphics and Computer-Aided Design
  • Computer Science Applications
  • Industrial and Manufacturing Engineering

Cite this

Principal curvature ridges and geometrically salient regions of parametric B-spline surfaces. / Musuvathy, Suraj; Cohen, Elaine; Damon, James; Seong, Jun Kyung.

In: CAD Computer Aided Design, Vol. 43, No. 7, 01.07.2011, p. 756-770.

Research output: Contribution to journalArticle

Musuvathy, Suraj ; Cohen, Elaine ; Damon, James ; Seong, Jun Kyung. / Principal curvature ridges and geometrically salient regions of parametric B-spline surfaces. In: CAD Computer Aided Design. 2011 ; Vol. 43, No. 7. pp. 756-770.
@article{a8f98509325f4aafb0a59b7d27bf424e,
title = "Principal curvature ridges and geometrically salient regions of parametric B-spline surfaces",
abstract = "Ridges are characteristic curves of a surface that mark salient intrinsic features of its shape and are therefore valuable for shape matching, surface quality control, visualization and various other applications. Ridges are loci of points on a surface where one of the principal curvatures attain a critical value in its respective principal direction. We present a new algorithm for accurately extracting ridges on B-spline surfaces and define a new type of salient region corresponding to major ridges that characterize geometrically significant regions on surfaces. Ridges exhibit complex behavior near umbilics on a surface, and may also pass through certain turning points causing added complexity for ridge computation. We present a new numerical tracing algorithm for extracting ridges that also accurately captures ridge behavior at umbilics and ridge turning points. The algorithm traverses ridge segments by detecting ridge points while advancing and sliding in principal directions on a surface in a novel manner, thereby computing connected curves of ridge points. The output of the algorithm is a set of curve segments, some or all of which may be selected for other applications such as those mentioned above. The results of our technique are validated by comparison with results from previous research and with a brute-force domain sampling technique.",
keywords = "Geometrically salient region, Parametric B-spline surface, Ridge",
author = "Suraj Musuvathy and Elaine Cohen and James Damon and Seong, {Jun Kyung}",
year = "2011",
month = "7",
day = "1",
doi = "10.1016/j.cad.2010.09.013",
language = "English",
volume = "43",
pages = "756--770",
journal = "CAD Computer Aided Design",
issn = "0010-4485",
publisher = "Elsevier Limited",
number = "7",

}

TY - JOUR

T1 - Principal curvature ridges and geometrically salient regions of parametric B-spline surfaces

AU - Musuvathy, Suraj

AU - Cohen, Elaine

AU - Damon, James

AU - Seong, Jun Kyung

PY - 2011/7/1

Y1 - 2011/7/1

N2 - Ridges are characteristic curves of a surface that mark salient intrinsic features of its shape and are therefore valuable for shape matching, surface quality control, visualization and various other applications. Ridges are loci of points on a surface where one of the principal curvatures attain a critical value in its respective principal direction. We present a new algorithm for accurately extracting ridges on B-spline surfaces and define a new type of salient region corresponding to major ridges that characterize geometrically significant regions on surfaces. Ridges exhibit complex behavior near umbilics on a surface, and may also pass through certain turning points causing added complexity for ridge computation. We present a new numerical tracing algorithm for extracting ridges that also accurately captures ridge behavior at umbilics and ridge turning points. The algorithm traverses ridge segments by detecting ridge points while advancing and sliding in principal directions on a surface in a novel manner, thereby computing connected curves of ridge points. The output of the algorithm is a set of curve segments, some or all of which may be selected for other applications such as those mentioned above. The results of our technique are validated by comparison with results from previous research and with a brute-force domain sampling technique.

AB - Ridges are characteristic curves of a surface that mark salient intrinsic features of its shape and are therefore valuable for shape matching, surface quality control, visualization and various other applications. Ridges are loci of points on a surface where one of the principal curvatures attain a critical value in its respective principal direction. We present a new algorithm for accurately extracting ridges on B-spline surfaces and define a new type of salient region corresponding to major ridges that characterize geometrically significant regions on surfaces. Ridges exhibit complex behavior near umbilics on a surface, and may also pass through certain turning points causing added complexity for ridge computation. We present a new numerical tracing algorithm for extracting ridges that also accurately captures ridge behavior at umbilics and ridge turning points. The algorithm traverses ridge segments by detecting ridge points while advancing and sliding in principal directions on a surface in a novel manner, thereby computing connected curves of ridge points. The output of the algorithm is a set of curve segments, some or all of which may be selected for other applications such as those mentioned above. The results of our technique are validated by comparison with results from previous research and with a brute-force domain sampling technique.

KW - Geometrically salient region

KW - Parametric B-spline surface

KW - Ridge

UR - http://www.scopus.com/inward/record.url?scp=79957607288&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79957607288&partnerID=8YFLogxK

U2 - 10.1016/j.cad.2010.09.013

DO - 10.1016/j.cad.2010.09.013

M3 - Article

AN - SCOPUS:79957607288

VL - 43

SP - 756

EP - 770

JO - CAD Computer Aided Design

JF - CAD Computer Aided Design

SN - 0010-4485

IS - 7

ER -