论文标题
Delaunay分解最小化加权环形图的能量
Delaunay decompositions minimizing energy of weighted toroidal graphs
论文作者
论文摘要
给定加权的环形图，每个实现欧几里得圆环都与dirichlet能量有关。通过将所有可能的欧几里得结构的能量和固定同型类中的所有实现上的所有实现中最小化，就可以将谐波图获得到最佳的欧几里得圆环中。我们表明，只有使用这种最佳的欧几里得结构，谐波图和边缘的重量是由加权的Delaunay分解引起的。
Given a weighted toroidal graph, each realization to a Euclidean torus is associated with the Dirichlet energy. By minimizing the energy over all possible Euclidean structures and over all realizations within a fixed homotopy class, one obtains a harmonic map into an optimal Euclidean torus. We show that only with this optimal Euclidean structure, the harmonic map and the edge weights are induced from a weighted Delaunay decomposition.
