Solid shape
Modeling of curves and surfaces in CAD/CAM
Modeling of curves and surfaces in CAD/CAM
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
Extracting feature lines from 3D unstructured grids
VIS '97 Proceedings of the 8th conference on Visualization '97
Two- and three-dimensional patterns of the face
Two- and three-dimensional patterns of the face
Landmark-based registration using features identified through differential geometry
Handbook of medical imaging
Geometric constraint solver using multivariate rational spline functions
Proceedings of the sixth ACM symposium on Solid modeling and applications
Geometric modeling with splines: an introduction
Geometric modeling with splines: an introduction
Shape Interrogation for Computer Aided Design and Manufacturing
Shape Interrogation for Computer Aided Design and Manufacturing
Shape intrinsic fingerprints for free-form object matching
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
Ridges and Ravines on Implicit Surfaces
CGI '98 Proceedings of the Computer Graphics International 1998
Enhancing Transparent Skin Surfaces with Ridge and Valley Lines
VIS '95 Proceedings of the 6th conference on Visualization '95
Ridge-valley lines on meshes via implicit surface fitting
ACM SIGGRAPH 2004 Papers
The implicit structure of ridges of a smooth parametric surface
Computer Aided Geometric Design
Robust Feature Classification and Editing
IEEE Transactions on Visualization and Computer Graphics
Smooth feature lines on surface meshes
SGP '05 Proceedings of the third Eurographics symposium on Geometry processing
Fast and Faithful Geometric Algorithm for Detecting Crest Lines on Meshes
PG '07 Proceedings of the 15th Pacific Conference on Computer Graphics and Applications
ACM SIGGRAPH 2008 papers
Finding ridges and valleys in a discrete surface using a modified MLS approximation
Computer-Aided Design
Extracting Principal Curvature Ridges from B-Spline Surfaces with Deficient Smoothness
ISVC '09 Proceedings of the 5th International Symposium on Advances in Visual Computing: Part I
Interior Medial Axis Transform computation of 3D objects bound by free-form surfaces
Computer-Aided Design
Ridge extraction of a smooth 2-manifold surface based on vector field
Computer Aided Geometric Design
Computing medial axes of generic 3D regions bounded by B-spline surfaces
Computer-Aided Design
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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 either of the principal curvatures attain a critical value in its respective principal direction. These curves have 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 algorithm for numerically tracing ridges on B-Spline surfaces 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.