The purpose of this work is to define a new algorithm for converting a CSG representation into a B-Rep representation. Usually this conversion is done determining the union, intersection or difference from two B-Rep represented solids. Due to the lack of explicit representation of surface boundaries, CSG models must be converted into B-Rep solid models when a description based on polygonal mesh...

We present a method to characterize the topology of the level sets of trilinearly interpolated scalar fields. Our characterization is based on Morse theory, and in particular a variant called Stratified Morse theory capable of treating the piecewise-smooth aspect of trilinear interpolation. Algorithms such as Marching Cubes generate approximations to these level sets to a varying degree of fide...

We present a new Fast Marching algorithm for a non-convex eikonal equation modeling front evolutions in the normal direction. The algorithm is an extension of the Fast Marching Method since the new scheme can deal with a time-dependent velocity without any restriction on its sign. We analyze the properties of the algorithm and we prove its convergence in the class of discontinuous viscosity sol...

This paper presents an alternative way to calculate the next approximate point in marching techniques for the computation of the intersection of two parametric surfaces. Di ering from the classical methods, the algorithm is based on the approximate osculating circle instead of tangent vector to estimate the next point. It provides closer estimation and a larger marching step in each iteration w...

The Fast Marching Method is a numerical algorithm for solving the Eikonal equation on a rectangular orthogonal mesh in O(M log M) steps, where M is the total number of grid points. In this paper we extend the Fast Marching Method to triangulated domains with the same computational complexity. As an application, we provide an optimal time algorithm for computing the geodesic distances and thereb...

Including derivative information in the modelling of moving interfaces has been proposed as one method to increase the accuracy of numerical schemes with minimal additional cost. Here a new level set reinitialization technique using the fast marching method is presented. This augmented fast marching method will calculate the signed distance function and up to the secondorder derivatives of the ...

We present a method for calculating the boundary of objects from Discrete Indicator Functions that store 2material volume fractions with a high degree of accuracy. Although Marching Cubes and its derivatives are effective methods for calculating contours of functions sampled over discrete grids, these methods perform poorly when contouring non-smooth functions such as Discrete Indicator Functio...

We propose a novel method, slice marching 1, for segmenting opacified vessels tree in 3D images (volume data), from multislice computed tomography (MSCT) scans. The method uses fast marching with freezing of boundaries to advance inside the vessel, slice per slice. Large scale features, such as vessel section and curvature, are evaluated for each slice. These features can then be used to influe...

The effect of a continuous 110-km march with a 20-kg backpack load on intraocular pressure (IOP), plasma osmolarity, blood lactate, pH, and other related laboratory parameters was studied in 22 healthy young volunteers. Intraocular pressure decreased significantly at all marching intervals and returned to baseline level 3 hr after the completion of marching. The maximal average reduction during...