Details
| Original language | English |
|---|---|
| Pages (from-to) | 133-161 |
| Number of pages | 29 |
| Journal | Computer aided geometric design |
| Volume | 13 |
| Issue number | 2 |
| Publication status | Published - Mar 1996 |
Abstract
This paper describes a method to extract the generic features of free-form parametric surfaces for shape interrogation. The umbilical points, which are the singular points of the orthogonal net of lines of curvature, have generic features and may act like fingerprints for shape recognition. We investigate the generic features of the umbilics and behavior of lines of curvature which pass through an umbilic on a parametric free-form surface. Our method is based on a coordinate transformation to set the parametric surface in Monge form and on a Taylor expansion to compute the angles of the tangent lines to the lines of curvatures at an umbilic. We also develop a novel and practical criterion which assures the existence of local extrema of principal curvature functions at umbilical points. Finally, numerical experiments illustrate how the generic features of the umbilics can be applied for surface recognition.
Keywords
- CAD, CAGD, Lines of curvature, Monge form, Perturbation, Shape recognition, Umbilics, Vision
ASJC Scopus subject areas
- Mathematics(all)
- Modelling and Simulation
- Engineering(all)
- Automotive Engineering
- Engineering(all)
- Aerospace Engineering
- Computer Science(all)
- Computer Graphics and Computer-Aided Design
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In: Computer aided geometric design, Vol. 13, No. 2, 03.1996, p. 133-161.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Umbilics and lines of curvature for shape interrogation
AU - Maekawa, T.
AU - Wolter, F. E.
AU - Patrikalakis, N. M.
PY - 1996/3
Y1 - 1996/3
N2 - This paper describes a method to extract the generic features of free-form parametric surfaces for shape interrogation. The umbilical points, which are the singular points of the orthogonal net of lines of curvature, have generic features and may act like fingerprints for shape recognition. We investigate the generic features of the umbilics and behavior of lines of curvature which pass through an umbilic on a parametric free-form surface. Our method is based on a coordinate transformation to set the parametric surface in Monge form and on a Taylor expansion to compute the angles of the tangent lines to the lines of curvatures at an umbilic. We also develop a novel and practical criterion which assures the existence of local extrema of principal curvature functions at umbilical points. Finally, numerical experiments illustrate how the generic features of the umbilics can be applied for surface recognition.
AB - This paper describes a method to extract the generic features of free-form parametric surfaces for shape interrogation. The umbilical points, which are the singular points of the orthogonal net of lines of curvature, have generic features and may act like fingerprints for shape recognition. We investigate the generic features of the umbilics and behavior of lines of curvature which pass through an umbilic on a parametric free-form surface. Our method is based on a coordinate transformation to set the parametric surface in Monge form and on a Taylor expansion to compute the angles of the tangent lines to the lines of curvatures at an umbilic. We also develop a novel and practical criterion which assures the existence of local extrema of principal curvature functions at umbilical points. Finally, numerical experiments illustrate how the generic features of the umbilics can be applied for surface recognition.
KW - CAD
KW - CAGD
KW - Lines of curvature
KW - Monge form
KW - Perturbation
KW - Shape recognition
KW - Umbilics
KW - Vision
UR - http://www.scopus.com/inward/record.url?scp=0030104854&partnerID=8YFLogxK
U2 - 10.1016/0167-8396(95)00018-6
DO - 10.1016/0167-8396(95)00018-6
M3 - Article
AN - SCOPUS:0030104854
VL - 13
SP - 133
EP - 161
JO - Computer aided geometric design
JF - Computer aided geometric design
SN - 0167-8396
IS - 2
ER -