|Title||Modeling Contours of Trivariate Data
|in||Mathematical Modelling and Numerical Analysis (Modelisation Mathematique et Analysis Numerique)|
Bernd Hamann |
|Keyword(s)||Contour, curvature, data reduction, G1 surface, topology, triangulation, trivariate data|
A general scheme for computing contours of trivariate data is discussed. It is assumed that three-dimensional points with associated function values are given without any other information. The goal is to construct a smooth approximation to a contour of these data. Usually, an interpolating or approximating function is constructed in order to estimate values on a whole three-dimensional domain. Very often, the resulting function is represented by a set of contours which are surfaces in space. Here, a method is described that first estimates points on a particular contour, generates a piecewise linear approximation to that contour, and finally uses this linear approximation as input for a surface scheme. The surface scheme than yields a surface which approximates the desired contour. Applications for this technique are found in medicine (Computerized Tomography (CT), Magnetic Resonance Imaging (MRI), meteorology, (temperature measurements) and physics in general. Particularly in medical applications one is more interested in contours and the shape of objects than in a function that interpolates measurements.