基于变形多边形概念的加权直骨架构造的通用预估-校正型增量算法
A universal predictor-corrector type incremental algorithm for the construction of weighted straight skeletons based on the notion of deforming polygon
摘要：
基于变形多边形的概念，提出了一种新的预测-校正型增量算法，用于精确构造任意复杂度的二维一般平面多边形的加权直骨架。在该算法中，由多边形本身提供的原始输入足以解决边折叠和边分裂事件。既不需要构造运动三角剖分，也不需要计算摩托车图。由于其增量性质，在算法中始终存在用于直骨架的交互式构造的空间。所提出的算法是预测校正型。在该算法中，边缘折叠和边缘分裂事件是由一个完全不同的新的原始方法，这是第一次。在预测步骤中，顶点的位置通过假设没有事件的直接积分在时间上提前。然后，如果在相同增量内存在边缘塌陷或边缘分裂事件，则通过使用线性插值来校正预测位置。在该算法中，边缘塌陷和边缘分裂事件分别检测边缘交换和边缘渗透。该算法已被用来构建屋顶拓扑结构从各种复杂的平面图，从简单的凸高度非凸孔。为了构造、改进和测试底层算法的构建块，作者还使用C++程序设计语言并行开发了图形用户界面--直骨架开发工具包。
英文摘要：
A new predictor-corrector type incremental algorithm is proposed for the exact construction of weighted straight skeletons of 2D general planar polygons of arbitrary complexity based on the notion of deforming polygon. In the proposed algorithm, the raw input provided by the polygon itself is enough to resolve edge collapse and edge split events. Neither the construction of a kinetic triangulation nor the computation of a motorcycle graph is required. Due to its incremental nature, there is always a room in the algorithm for the interactive construction of the straight skeleton. The proposed algorithm is of predictor-corrector type. In the algorithm, the edge collapse and edge split events are tackled by a completely different novel original approach which is first of its kind. In the predictor step, the position of the vertices is advanced in time by direct integration assuming no event. Then predicted positions are corrected by using linear interpolation if there are edge collapse or edge split events within the same increment. In the algorithm edge collapse and edge split events are detected by, respectively, edge swap and edge penetration. The proposed algorithm has been used to construct roof topology starting from a floor plan of various complexity ranging from simple convex to highly nonconvex with holes. In order to construct, improve and test the building blocks of the underlying algorithm, a graphical user interface, Straight Skeleton Development Kit, has also been developed in parallel by the author using C++ programming language.
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