Efficient Generation of Contour Trees in Three Dimensions

Many scientific fields generate data in three-dimensional space. These fields include fluid dynamics, medical imaging, and X-ray crystallography. In all contexts, a common difficulty exists: how best to represent the data visually and analytically. One approach involves generating level sets: two-dimensional surfaces consisting of all points with a given value in the space. With large datasets common, efficient generation of these level sets is critical. Several methods exist: one such is the contour tree approach used by van Kreveld et al. [26]. This thesis extends the results of van Kreveld et al. [26] and Tarasov & Vyalyi [23]. An efficient algorithm for generating contour trees in any number of dimensions is presented, followed by details of an implementation in three dimensions.