We introduce a new variational formulation for the problem of reconstructing a watertight surface defined by an implicit equation, from a finite set of oriented points; a problem which has attracted a lot of attention for more than two decades. As in the Poisson Surface Reconstruction approach, discretizations of the continuous formulation reduce to the solution of sparse linear systems of equa...

In crisp production inventory problem, let q, a, b, d, R and r be the quantity produced per cycle, the holding cost, production cost, production quantity per day, the total demand quantity and the demand quantity per day, respectively. We consider three fuzzification methods. Firstly, we fuzzify q, a, b, d, R and r to triangular fuzzy numbers. Secondly, we fuzzify d and r to triangular fuzzy nu...

The signed distance function can effectively support many geometry processing tasks such as decimates, smoothing and shape reconstruction since it provides efficient access to distance estimates. In this talk, we present an adaptive method to approximate the signed distance function of a smooth curve by using polynomial splines over type-2 triangulation. The trimmed offsets are also studied.

We propose a parallel ray-tracing technique to visualize signed distance fields generated from triangular meshes based on NVIDIA OptiX. Our method visualizes signed distance fields with various distance offset values at interactive rates (2–12 fps). Our method utilizes a parallel kd-tree implementation to query the nearest triangle and the sphere tracing method to visualize the implicit surface.

We describe a new class of algorithms for generating a variety of geometric interfacial motions by alternating two steps: Construction of the signed distance function (i.e. redistancing) to the interface, and convolution with a suitable kernel. These algorithms can be seen as variants of Merriman, Bence, and Osher’s threshold dynamics [25]. The new algorithms proposed here preserve the computat...

In this paper, we propose a numerical method for computing the signed distance function to a discrete domain, on an arbitrary triangular background mesh. It mainly relies on the use of some theoretical properties of the unsteady Eikonal equation. Then we present a way of adapting the mesh on which computations are held to enhance the accuracy for both the approximation of the signed distance fu...

An efficient algorithm for accurately simulating curvature flow for large networks of curves in two dimensions and surfaces in three dimensions on uniform grids is proposed. This motion arises in the technologically important problem of simulating grain boundary motion in polycrystalline materials. In this formulation grains are zero level sets of signed distance functions. Curvature motion is ...

We extend the resistance distance kernel to the domain of signed dissimilarity values, and show how it can be applied to collaborative rating prediction. The resistance distance is a graph kernel inspired by electrical network models where edges of a graph are interpreted as electrical resistances. We model the similarity between users of a large collaborative rating database using this signed ...