论文标题
通过近似通过根部分区通过近似
Non-simplicial Delaunay meshing via approximation by radical partitions
论文作者
论文摘要
我们将多面体Delaunay分区的构建视为功率图序列（激进分区）的限制。双伏罗尼亚图作为加权delaunay分区序列的限制获得。该问题简化为构造两个双凸多面体，并在圆形抛物面周围刻有并取代，这是一对一般的双凸多面体对序列的限制。原始多面体的序列应融合到超级认证的多面体，并将双重多面体的序列收敛于铭刻的多面体。 我们对原始Polyhedra的顶点可以移动或合并在一起的情况很感兴趣，即不允许双重polyhedra的新面孔。这些规则定义了使用半径变化以及球体的运动和消除的初始球集转换为Delaunay球体的集合。存在定理仍然不可用，但我们建议一个功能性测量凸多面体与核代核苷中的凸的偏差。它是功率函数的离散功能，它是双顶点与抛物线的垂直距离的线性插值。功能的绝对最小化器可在恒定功率场上获得，这意味着可以通过简单的翻译获得铭刻的多面体。双面表面功能的这种表述不是二次的，因为未知数是原始多面体的顶点，因此，一组球体向Delaunay球体的转化不是唯一的。 我们专注于对方法可行性的实验确认，并抛弃网格质量问题。所提出的功能的梯度的零值定义了描述Delaunay球的演变的流形。因此，可以使用歧管作为约束来优化Delaunay-Voronoi网格。
We consider the construction of a polyhedral Delaunay partition as a limit of the sequence of power diagrams (radical partitions). The dual Voronoi diagram is obtained as a limit of the sequence of weighted Delaunay partitions. The problem is reduced to the construction of two dual convex polyhedra, inscribed and superscribed around a circular paraboloid, as a limit of the sequence of pairs of general dual convex polyhedra. The sequence of primal polyhedra should converge to the superscribed polyhedron and the sequence of the dual polyhedra converges to the inscribed polyhedron. We are interested in the case when the vertices of primal polyhedra can move or merge together, i.e., no new faces are allowed for dual polyhedra. These rules define the transformation of the set of initial spheres into the set of Delaunay spheres using radius variation and sphere movement and elimination. Existence theorems are still unavailable but we suggest a functional measuring the deviation of the convex polyhedron from the one inscribed into the paraboloid. It is the discrete Dirichlet functional for the power function which is a linear interpolant of the vertical distance of the dual vertices from the paraboloid. The functional's absolute minimizer is attained on the constant power field, meaning that the inscribed polyhedron can be obtained by a simple translation. This formulation of the functional for the dual surface is not quadratic since the unknowns are the vertices of the primal polyhedron, hence, the transformation of the set of spheres into Delaunay spheres is not unique. We concentrate on the experimental confirmation of the approach viability and put aside mesh quality problems. The zero value of the gradient of the proposed functional defines a manifold describing the evolution of Delaunay spheres. Hence, Delaunay-Voronoi meshes can be optimized using the manifold as a constraint.
