Curvature of Stratified Volumes

@inproceedings{MalletRM2006,
 abstract = { Curvatures of a surface S represented by a parametric equation x(u, v) is a classic and well defined problem which is extensively studied in the literature (e.g., see [1, 2, 3]). In this article, we address a slightly different problem where, instead of one unique surface S, we have an infinity of surfaces filling, continuously, a given domain of interest of the 3D space. For example, in the frame of the GeoChron model, this is of particular interest if we want to address the problem of defining and computing the curvatures of the geologic horizon passing by any arbitrary point in the subsurface. Our presentation comprises three main complementary parts: a first part introducing the classical curvature of planar curves, a second part dedicated to the curvatures of parametric surfaces and a third part dedicated to the curvatures of stratified volumes. In addition, we show how the relationships between curvatures and strains can be deduced from the famous “Theorema Egregium” discovered by Karl Friedrich Gauss. From a practical point of view, two different algorithms are proposed to compute the curvatures of stratified volumes. },
 author = { Mallet, Jean-Laurent },
 booktitle = { 26th gOcad Meeting },
 month = { "june" },
 publisher = { ASGA },
 title = { Curvature of Stratified Volumes },
 year = { 2006 }
}