Singularities of Principal Direction Fields from 3-D Images
IEEE Transactions on Pattern Analysis and Machine Intelligence
Implicit Curves and Surfaces in CAGD
IEEE Computer Graphics and Applications - Special issue on computer-aided geometric design
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
On the curvature of curves and surfaces defined by normalforms
Computer Aided Geometric Design
A survey of methods for recovering quadrics in triangle meshes
ACM Computing Surveys (CSUR)
Ridges and Ravines on Implicit Surfaces
CGI '98 Proceedings of the Computer Graphics International 1998
Multi-level partition of unity implicits
ACM SIGGRAPH 2003 Papers
Anisotropic polygonal remeshing
ACM SIGGRAPH 2003 Papers
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
Curvature formulas for implicit curves and surfaces
Computer Aided Geometric Design - Special issue: Geometric modelling and differential geometry
Computing lines of curvature for implicit surfaces
Computer Aided Geometric Design
Ridge extraction of a smooth 2-manifold surface based on vector field
Computer Aided Geometric Design
Parametric representation of a surface pencil with a common line of curvature
Computer-Aided Design
Multi-view stereo point clouds visualization
ISVC'11 Proceedings of the 7th international conference on Advances in visual computing - Volume Part I
An approach for designing a developable surface through a given line of curvature
Computer-Aided Design
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This paper develops a method to analyze and compute the lines of curvature and their differential geometry defined on implicit surfaces. With our technique, we can explicitly obtain the analytic formulae of the associated geometric attributes of an implicit surface, e.g. torsion of a line of curvature and Gaussian curvature. Additionally, it can be used to directly derive the closed formulae of principal directions and corresponding principal curvature of an implicit surface. We also present a novel criterion for non-umbilical points and umbilical points on an implicit surface.