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.

中文翻译：

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基于变形多边形概念的加权直线骨架构建通用预测校正型增量算法

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，用于精确构建任意复杂度的二维一般平面多边形的加权直线骨架。在所提出的算法中，多边形本身提供的原始输入足以解决边缘塌陷和边缘分裂事件。既不需要构造动力学三角测量，也不需要计算摩托车图。由于其增量性质，算法中总是有空间用于直线骨架的交互式构建。所提出的算法属于预测器-校正器类型。在该算法中，边​​缘塌陷和边缘分裂事件由一种完全不同的新颖原创方法解决，这是同类中的首创。在预测器步骤中，顶点的位置通过假设没有事件的直接积分及时推进。然后，如果在同一增量内存在边缘塌陷或边缘分裂事件，则使用线性插值来校正预测位置。在算法中，边​​缘塌陷和边缘分裂事件分别通过边缘交换和边缘穿透来检测。所提出的算法已用于从各种复杂度的平面图开始构建屋顶拓扑，范围从简单的凸面到带有孔的高度非凸面。为了构建、改进和测试底层算法的构建块，作者还使用C++编程语言并行开发了图形用户界面Straight Skeleton Development Kit。然后，如果在同一增量内存在边缘塌陷或边缘分裂事件，则使用线性插值来校正预测位置。在算法中，边​​缘塌陷和边缘分裂事件分别通过边缘交换和边缘穿透来检测。所提出的算法已用于从各种复杂度的平面图开始构建屋顶拓扑，范围从简单的凸面到带有孔的高度非凸面。为了构建、改进和测试底层算法的构建块，作者还使用C++编程语言并行开发了图形用户界面Straight Skeleton Development Kit。然后，如果在同一增量内存在边缘塌陷或边缘分裂事件，则使用线性插值来校正预测位置。在算法中，边​​缘塌陷和边缘分裂事件分别通过边缘交换和边缘穿透来检测。所提出的算法已用于从各种复杂度的平面图开始构建屋顶拓扑，范围从简单的凸面到带有孔的高度非凸面。为了构建、改进和测试底层算法的构建块，作者还使用C++编程语言并行开发了图形用户界面Straight Skeleton Development Kit。边缘交换和边缘渗透。所提出的算法已用于从各种复杂度的平面图开始构建屋顶拓扑，范围从简单的凸面到带有孔的高度非凸面。为了构建、改进和测试底层算法的构建块，作者还使用C++编程语言并行开发了图形用户界面Straight Skeleton Development Kit。边缘交换和边缘渗透。所提出的算法已用于从各种复杂度的平面图开始构建屋顶拓扑，范围从简单的凸面到带有孔的高度非凸面。为了构建、改进和测试底层算法的构建块，作者还使用C++编程语言并行开发了图形用户界面Straight Skeleton Development Kit。