Density Estimation on Delaunay Triangulations
نویسندگان
چکیده
Density Estimation is a very popular method to compute global illumination solutions in a complex virtual scene. After simulating the re ection paths of a large number of photons in the scene, the illumination at a surface point is approximated by estimating the density of photon hits in the point's surrounding. In this paper we describe a novel approach to compute such a density approximation based on Delaunay triangulation and mesh modi cation techniques.
منابع مشابه
Delaunay Edge Flips in Dense Surface Triangulations
Delaunay flip is an elegant, simple tool to convert a triangulation of a point set to its Delaunay triangulation. The technique has been researched extensively for full dimensional triangulations of point sets. However, an important case of triangulations which are not full dimensional is surface triangulations in three dimensions. In this paper we address the question of converting a surface t...
متن کاملThe Stability of Delaunay Triangulations
We introduce a parametrized notion of genericity for Delaunay triangulations which, in particular, implies that the Delaunay simplices of δ-generic point sets are thick. Equipped with this notion, we study the stability of Delaunay triangulations under perturbations of the metric and of the vertex positions. We quantify the magnitude of the perturbations under which the Delaunay triangulation r...
متن کاملOn the Number of Higher Order Delaunay Triangulations
Higher order Delaunay triangulations are a generalization of the Delaunay triangulation which provides a class of well-shaped triangulations, over which extra criteria can be optimized. A triangulation is order-k Delaunay if the circumcircle of each triangle of the triangulation contains at most k points. In this paper we study lower and upper bounds on the number of higher order Delaunay trian...
متن کاملOn the optimality of functionals over triangulations of Delaunay sets
In this short paper we consider the functional density on sets of uniformly bounded triangulations with fixed sets of vertices. We prove that if a functional attains its minimum on the Delaunay triangulation for every finite set in the plane, then for infinite sets the density of this functional attains its minimum also on the Delaunay triangulations. A Delaunay set in E is a set of points X fo...
متن کاملA Variational Principle for Weighted Delaunay Triangulations and Hyperideal Polyhedra
We use a variational principle to prove an existence and uniqueness theorem for planar weighted Delaunay triangulations (with non-intersecting site-circles) with prescribed combinatorial type and circle intersection angles. Such weighted Delaunay triangulations may be interpreted as images of hyperbolic polyhedra with one vertex on and the remaining vertices beyond the infinite boundary of hype...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2007