Large-scale deformations of a tubular object, or generalized cylinder, are often defined by a target shape for its center curve, typically using a parametric target curve. This task is non-trivial for free-form deformations or direct manipulation methods because it is hard to manually control the centerline by adjusting control points. Most skeleton-based methods are no better, again due to the small number of manually adjusted control points. In this paper, we propose a method to deform a generalized cylinder based on its skeleton composed of a centerline and orthogonal cross sections. Although we are not the first to use such a skeleton, we propose a novel skeletonization method that tries to minimize the number of intersections between neighboring cross sections by means of a relative curvature condition to detect intersections. The mesh deformation is first defined geometrically by deforming the centerline and mapping the cross sections. Rotation minimizing frames are used during mapping to control twisting. Secondly, given displacements on the cross sections, the deformation is decomposed into finely subdivided regions. We limit distortion at these vertices by minimizing an elastic thin shell bending energy, in linear time. Our method can handle complicated generalized cylinders such as the human colon.

中文翻译：

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通过参数中心曲线对没有自相交的广义圆柱进行变形

管状对象或广义圆柱的大规模变形通常由其中心曲线的目标形状定义，通常使用参数目标曲线来定义。对于自由形式的变形或直接操作方法而言，此任务非常重要，因为很难通过调整控制点来手动控制中心线。同样，大多数基于骨骼的方法也不是更好，这也是由于手动调整的控制点数量很少。在本文中，我们提出了一种基于广义圆柱体的骨架变形方法，该骨架由中心线和正交截面组成。尽管我们不是第一个使用这种骨架的人，但是我们提出了一种新颖的骨架化方法，该方法试图通过相对曲率条件来检测相邻横截面之间的相交数量最小。首先，通过变形中心线并绘制横截面，以几何方式定义网格变形。在映射过程中使用最小旋转框架来控制扭曲。其次，给定横截面的位移，变形被分解成细分的区域。通过在线性时间内最小化弹性薄壳弯曲能量，可以限制这些顶点的变形。我们的方法可以处理复杂的广义圆柱体，例如人类结肠。在线性时间内。我们的方法可以处理复杂的广义圆柱体，例如人类结肠。在线性时间内。我们的方法可以处理复杂的广义圆柱体，例如人类结肠。