ABSTRACT Based on the offset of the feature inflection point, the one-sided offsetting and smoothing algorithm of 3D trimming curve is proposed for trimming insert steel of automotive panels. The core of the algorithm is to determine the curve’s 3D offset direction and its feature inflection point. It obtains the offset direction of 3D discrete point by cross-multiplying the trimming direction with the vector of the two adjacent points of the 2D projection of them. Therefore, the offset direction of the 3D curve is not unique, and each discrete point has its own offset direction. To avoid the curve distortion caused by excessive discrete point offset, only by offsetting the feature inflection points, that control the curve shape and trend, to improve the curve smoothness. The 3D feature inflection points in the plane and trimming direction are determined by the abrupt change in curvature and perturbation, so the offset curve maintains the original curve’s characteristics. Self-intersecting defects of the offset curve are eliminated by pre-offsetting the 2D projection points. The target points are obtained by offsetting the feature inflection points and distribution points, and the one-sided offsetting and smoothing curve is obtained by constructing the spline curve.

中文翻译：

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汽车面板切边镶钢复杂3D切边曲线单边偏移平滑算法

摘要 基于特征拐点的偏移，提出了一种3D修整曲线的单边偏移平滑算法，用于汽车面板镶钢修整。该算法的核心是确定曲线的3D偏移方向及其特征拐点。它通过将修剪方向与它们的2D投影的两个相邻点的向量交叉乘以得到3D离散点的偏移方向。因此，3D曲线的偏移方向不是唯一的，每个离散点都有自己的偏移方向。为避免离散点偏移过大导致曲线失真，只能通过偏移控制曲线形状和趋势的特征拐点来提高曲线的平滑度。平面和修剪方向的3D特征拐点由曲率和扰动的突变决定，因此偏移曲线保持了原始曲线的特性。通过预偏移二维投影点消除偏移曲线的自相交缺陷。通过对特征拐点和分布点进行偏移得到目标点，通过构造样条曲线得到单边偏移平滑曲线。