The geometric kernel (or simply the kernel) of a polyhedron is the set of points from which the whole polyhedron is visible. Whilst the computation of the kernel for a polygon has been largely addressed in the literature, fewer methods have been proposed for polyhedra. The most acknowledged solution for the kernel estimation is to solve a linear programming problem. On the contrary, we present a geometric approach that extends our previous method, optimizes it anticipating all calculations in a pre-processing step and introduces the use of geometric exact predicates. Experimental results show that our method is more efficient than the algebraic approach on generic tessellations and in detecting if a polyhedron is not star-shaped. Details on the technical implementation and discussions on pros and cons of the method are also provided.
翻译:多元面的几何内核(或仅仅是内核)是整个多元面都能看到的一组点。 虽然文献中已基本涉及多边形内核的计算,但对于多面体提出的方法较少。对于内核估计最公认的解决办法是解决线性编程问题。相反,我们提出了一个几何方法,扩展了我们以前的方法,优化了预处理步骤中的所有计算,并引入了几何精确的前提。实验结果显示,我们的方法比一般熔融的代数法以及如果多面体不是恒星形的探测方法更有效率。还提供了关于该方法的利弊的技术实施和讨论的详细情况。