We present a fast algorithm for solving the eikonal equation in three dimensions, based on the fast marching method. The algorithm is of the order O(N log N), where N is the total number of grid points in the computational domain. The algorithm can be used in any orthogonal coordinate system and globally constructs the solution to the eikonal equation for each point in the coordinate domain. Th...

This paper presents the application of the Voronoi Fast Marching method to Path Planning of Mobile Formation Robots. The Voronoi Fast Marching method uses the propagation of a wave (Fast Marching) operating on the world model to determine a motion plan over a viscosity map (similar to the refraction index in optics) extracted from the updated map model. The computational efficiency of the metho...

This paper presents a marching method for computing intersection curves between two solids represented by subdivision surfaces of Catmull-Clark or Loop type. It can be used in trimming and boolean operations for subdivision surfaces. The main idea is to apply a marching method with geometric interpretation to trace the intersection curves. We first determine all intersecting regions, then find ...

We present a simple, robust, and practical method for object simplification for applications where gradual elimination of high frequency details is desired. This is accomplished by converting an object into multi-resolution volume rasters using a controlled filtering and sampling technique. A multiresolution triangle-mesh hierarchy can then be generated by applying the Marching Cubes algorithm....

This paper presents an adaptive modification of the Edge spinning method for polygonization of implicit surfaces. The method insists on the shape of triangles and the accuracy of resulting approximation as well. The main advantages of the triangulation presented are simplicity and the stable features that can be used for next expanding. The implementation is not complicated and only the standar...

As a continuation of the e cient and accurate polynomial interpolation time-marching technique in one-dimensional and two-dimensional cases, this paper proposes a method to extend it to threedimensional problems. By stacking all two-dimensional (x, y) slice matrices along Z direction, threedimensional derivative matrices are constructed so that the polynomial interpolation time-marching can be ...

In this paper we present a novel probabilistic sampling-based motion planning algorithm called the Fast Marching Tree algorithm (FMT*). The algorithm is specifically aimed at solving complex motion planning problems in high-dimensional configuration spaces. This algorithm is proven to be asymptotically optimal and is shown to converge to an optimal solution faster than its state-of-the-art coun...

Lighting simulation is very important in realistic image synthesis, and the simulation of subsurface scattering has recently attracted much attention. Although the dipole/multipole model has succeeded in creating realistic images, it is still difficult to deal with volumetric features in subsurface scattering, which is important when rendering optically thin objects. This paper proposes a novel...

An efficient and accurate computational method is developed for analyzing finite layers of crossed arrays of circular cylinders, including woodpile structures as special cases. The method relies on marching a few operators (approximated by matrices) from one side of the structure to another. The marching step makes use of the Dirichlet-to-Neumann (DtN) maps for two-dimensional unit cells in eac...

The finite iterative method is compared to an industry-hardened fast marching method for accelerating the redistancing step essential for Level Set-based process simulations in the area of technology computer-aided design. We discuss our implementation of the finite iterative method and depict extensions to improve the method for process simulations, in particular regarding stability. Contrary ...