论文标题
具有规定区域和方向的最佳三角投影仪，应用于基于位置的动态
An Optimal Triangle Projector with Prescribed Area and Orientation, Application to Position-Based Dynamics
论文作者
论文摘要
绝大多数基于网格的建模应用程序在规定的几何条件下迭代地改变了网格顶点。这特别是在通过约束集（例如基于位置的动力学（PBD））循环的方法中发生。一个常见的情况是在外部编辑限制下近似三角形2D网格的局部区域保存。在约束级别上，这会在规定的区域问题下产生非convex最佳三角投影，目前尚不存在直接解决方案方法。在当前的PBD实现中，该区域保存约束是线性化的。该解决方案通过迭代出现，没有最佳保证，并且该过程可能会失败，而这些输入的归化输入或结合了。我们提出了一种封闭形式的解决方案方法及其数值强大的代数实现。我们的方法通过对问题的通用歧义进行两次分析来处理退化的输入。我们在基于区域的2D网格编辑的一系列实验中显示，这些实验使用最佳投影代替PBD速度的区域约束线性化速度并稳定收敛。
The vast majority of mesh-based modelling applications iteratively transform the mesh vertices under prescribed geometric conditions. This occurs in particular in methods cycling through the constraint set such as Position-Based Dynamics (PBD). A common case is the approximate local area preservation of triangular 2D meshes under external editing constraints. At the constraint level, this yields the nonconvex optimal triangle projection under prescribed area problem, for which there does not currently exist a direct solution method. In current PBD implementations, the area preservation constraint is linearised. The solution comes out through the iterations, without a guarantee of optimality, and the process may fail for degenerate inputs where the vertices are colinear or colocated. We propose a closed-form solution method and its numerically robust algebraic implementation. Our method handles degenerate inputs through a two-case analysis of the problem's generic ambiguities. We show in a series of experiments in area-based 2D mesh editing that using optimal projection in place of area constraint linearisation in PBD speeds up and stabilises convergence.
