平面多边形曲线分段重建三维欧拉螺旋

Ali Fakih, Frederic Cordier, Yvan Maillot
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引用次数: 0

摘要

在本文中,我们提出了一种从平面多边形曲线重建近似分段三维欧拉螺旋的方法。该方法计算近似欧拉螺旋的三维坐标,使其在二维平面上的正交投影最接近输入曲线。为了实现这一点,创建了一个数据集,包括欧拉螺旋段和它们的正交投影。给定一个输入曲线,对它进行采样并分成几段。每个段与数据集中最接近的欧拉螺旋段匹配,形成候选段池。然后选择最优的连通欧拉螺旋段集来重建近似的分段三维欧拉螺旋。选择优先考虑连接点的平滑连续性,同时最小化正交投影与输入曲线之间的距离。我们通过将我们的重建应用于合成欧拉螺旋的正交投影来评估我们的方法对合成三维欧拉螺旋的影响。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Piecewise Reconstruction of 3D Euler Spirals From Planar Polygonal Curves
In this article, we propose a method for reconstructing approximate piecewise 3D Euler spirals from planar polygonal curves. The method computes the 3D coordinates of approximate Euler spiral such that its orthogonal projection onto the 2D plane is the closest possible to the input curve. To achieve this, a dataset is created, comprising Euler spiral segments and their orthogonal projections. Given an input curve, it is sampled and split into segments. Each segment is matched with the closest Euler spiral segments from the dataset, forming a pool of candidates. The optimal set of connected Euler spiral segments is then selected to reconstruct the approximate piecewise 3D Euler spiral. The selection prioritizes smoothness continuity at connecting points while minimizing the distance between the orthogonal projection and the input curve. We evaluate our method against synthetic 3D Euler spirals by applying our reconstruction to the orthogonal projection of the synthetic Euler spirals.
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