Solid shape
Modeling of curves and surfaces in CAD/CAM
Modeling of curves and surfaces in CAD/CAM
Journal of Mathematical Imaging and Vision
Using partial derivatives of 3D images to extract typical surface features
Computer Vision and Image Understanding
Umbilics and lines of curvature for shape interrogation
Computer Aided Geometric Design
New feature points based on geometric invariants for 3D image registration
International Journal of Computer Vision
The 3D marching lines algorithm
Graphical Models and Image Processing
The Sub-Parabolic Lines of a Surface
Proceedings of the 6th IMA Conference on the Mathematics of Surfaces
Ridges and Ravines on Implicit Surfaces
CGI '98 Proceedings of the Computer Graphics International 1998
Crest Lines for Surface Segmentation and Flattening
IEEE Transactions on Visualization and Computer Graphics
Ridge-valley lines on meshes via implicit surface fitting
ACM SIGGRAPH 2004 Papers
Lines of curvature and umbilical points for implicit surfaces
Computer Aided Geometric Design
Smooth feature lines on surface meshes
SGP '05 Proceedings of the third Eurographics symposium on Geometry processing
Ridge extraction and its application to surface meshing
Engineering with Computers - Special Issue: 5th Symposium on Trends in Unstructured Mesh Generation in 2006. Guest Editor: Steven J. Owen
Fast, robust, and faithful methods for detecting crest lines on meshes
Computer Aided Geometric Design
Tracing ridges on B-Spline surfaces
2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling
Computing lines of curvature for implicit surfaces
Computer Aided Geometric Design
The implicit structure of ridges of a smooth parametric surface
Computer Aided Geometric Design
Shape Interrogation for Computer Aided Design and Manufacturing
Shape Interrogation for Computer Aided Design and Manufacturing
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This paper presents a general scheme to compute ridges on a smooth 2-manifold surface from the standpoint of a vector field. A ridge field is introduced. Starting with an initial ridge, which may or may not be umbilical, a ridge line is then traced by calculating an associated integral curve of this field in conjunction with a new projection procedure to prevent it from diverging. This projection is the first that can optimize a ridge guess to lie on a ridge line uniquely and accurately. In order to follow this scheme, we not only develop practical ridge formulae but also address their corresponding computational procedures for an analytical surface patch, especially for an implicit surface. In contrast to other existing methods, our new approach is mathematically sound and characterized by considering the full geometric structures and topological patterns of ridges on a generic smooth surface. The resulting ridges are accurate in the numerical sense and meet the requirement of high accuracy with complete topology. Although the objective of this paper is to develop a mathematically sound framework for ridges on a smooth surface, we give a comprehensive review of relevant works on both meshes and smooth surfaces for readers.