Proceedings on Mathematics of surfaces II
Curves and surfaces for computer aided geometric design
Curves and surfaces for computer aided geometric design
Real rational curves are not “unit speed”
Computer Aided Geometric Design
Finding shortest paths on surfaces
Proceedings of the international conference on Curves and surfaces in geometric design
Umbilics and lines of curvature for shape interrogation
Computer Aided Geometric Design
Shape Interrogation for Computer Aided Design and Manufacturing
Shape Interrogation for Computer Aided Design and Manufacturing
Finding Shortest Paths on Surfaces Using Level Sets Propagation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Anisotropic polygonal remeshing
ACM SIGGRAPH 2003 Papers
Lines of curvature and umbilical points for implicit surfaces
Computer Aided Geometric Design
Constrained design of polynomial surfaces from geodesic curves
Computer-Aided Design
Extracting lines of curvature from noisy point clouds
Computer-Aided Design
Computing lines of curvature for implicit surfaces
Computer Aided Geometric Design
Parametric representation of a surface pencil with a common asymptotic curve
Computer-Aided Design
An approach for designing a developable surface through a given line of curvature
Computer-Aided Design
Rotation-minimizing osculating frames
Computer Aided Geometric Design
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Line of curvature on a surface plays an important role in practical applications. A curve on a surface is a line of curvature if its tangents are always in the direction of the principal curvature. By utilizing the Frenet frame, the surface pencil can be expressed as a linear combination of the components of the local frame. With this parametric representation, we derive the necessary and sufficient condition for the given curve to be the line of curvature on the surface. Moreover, the necessary and sufficient condition for the given curve to satisfy the line of curvature and the geodesic requirements is also analyzed.