Abstract In this paper we present a method for recognising and inserting space curves on 3D shapes. These curves are identified by a set of vertices and approximated with known curves, like helices, which characterise particular curves in the digital models of 3D objects. As the curve recognition method we adopt a generalisation of the Hough Transform (HT), adapting it to space curves. Through the HT we are able to represent generic classes of space curves not necessarily polynomial, like splines and Bezier curves, and we obtain a parametric representation of the curves that allows us to select the points and the curvilinear segments to be inserted directly as constraints in the 3D mesh, thus creating a new hybrid triangle mesh, with both linear and curvilinear elements. The experiments obtained so far on 3D models are encouraging and suggest that the use of such a hybrid mesh is a viable option to avoid to thicken the sampling of the curved parts with respect to the linear parts or to overfit the whole mesh.

中文翻译：

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基于 HT 的 3D 特征曲线识别及其插入 3D 网格

摘要 在本文中，我们提出了一种在 3D 形状上识别和插入空间曲线的方法。这些曲线由一组顶点标识，并用已知曲线（如螺旋线）近似，螺旋线表征 3D 对象数字模型中的特定曲线。作为曲线识别方法，我们采用霍夫变换（HT）的推广，使其适应空间曲线。通过 HT，我们能够表示不一定是多项式的空间曲线的通用类别，如样条曲线和贝塞尔曲线，并且我们获得曲线的参数表示，允许我们选择要直接插入作为约束的点和曲线段3D 网格，从而创建一个新的混合三角形网格，具有线性和曲线元素。