Surface shape and curvature scales
Image and Vision Computing
The NURBS book
A new approach to the surface intersection problem
Computer Aided Geometric Design
Curves and surfaces for CAGD: a practical guide
Curves and surfaces for CAGD: a practical guide
Surface Interrogation Algorithms
IEEE Computer Graphics and Applications
The Curvature of Characteristic Curves on Surfaces
IEEE Computer Graphics and Applications
Methods for surface interrogation
VIS '90 Proceedings of the 1st conference on Visualization '90
IEEE Computer Graphics and Applications
A Procedure for Generating Contour Lines From a B-Spline Surface
IEEE Computer Graphics and Applications
Intersection of Parametric Surfaces and a Plane
IEEE Computer Graphics and Applications
Matlab-based problem-solving environment for geometric processing of surfaces
ICMS'06 Proceedings of the Second international conference on Mathematical Software
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In this paper, a new method for interrogation of parametric surfaces is introduced. The basic idea is to consider the distance measured on certain curves on a surface as an interrogation tool. To this aim, two different sets of characteristic curves are considered: the normal section curves and the geodesic curves. The differential equations of these sets of curves starting radially from a given point of the surface are stated. Then, they are solved numerically, introducing the arc-length on the surface as the integration variable. Associated with those curves we construct the polar isodistance curves which are obtained by joining the points at the same distance from a given point of the surface along the section or geodesic curves. Finally, some illustrative examples for NURBS surfaces, by far the most common surfaces in industry, are also described.