A smooth T-surface can be thought of as a generalization of a surface of revolution in such a way that the axis of rotation is not fixed at one point but rather traces a smooth path on the base plane. Furthermore, the action, by which the aforementioned surface is obtained does not need to be merely rotation but any ``suitable" planar equiform transformation applied to the points of a certain smooth profile curve. In analogy to the smooth setting, if the axis footpoints sweep a polyline on the base plane and if the profile curve is discretely chosen then a T-hedra (discrete T-surface) with trapezoidal faces is obtained. The goal of this article is to reconstruct a T-hedron from an already given point cloud of a T-surface. In doing so, a kinematic approach is taken into account, where the algorithm at first tries to find the aforementioned axis direction associated with the point cloud. Then the algorithm finds a polygonal path through which the axis footpoint moves. Finally, by properly cutting the point cloud with the planes passing through the axis and its footpoints, it reconstructs the surface. The presented method is demonstrated on base of examples. From an applied point of view, the straightforwardness of the generation of these surfaces predestines them for building and design processes. In fact, one can find many built objects belonging to the sub-classes of T-surfaces such as \emph{surfaces of revolution} and \emph{moulding surfaces}. Furthermore, the planarity of the faces of the discrete version paves the way for steel/glass construction in industry. Finally, these surfaces are also suitable for transformable designs as they allow an isometric deformation.

翻译：光滑T-曲面可视为旋转曲面的一种推广：其旋转轴并非固定于某点，而是在基平面上沿光滑路径移动。此外，生成该曲面的作用不局限于旋转变换，而是可以将任意"恰当"的平面等形变换应用于某光滑轮廓曲线上的点。与光滑情形类似，当轴迹点在基平面上扫过多段线且轮廓曲线呈离散选择时，将生成具有梯形面的T-面体（离散T-曲面）。本文旨在根据给定的T-曲面点云重建T-面体。为此，采用运动学方法：算法首先尝试寻找与点云相关的轴方向，随后确定轴迹点运动的多边形路径，最后通过经轴及其迹点的平面对点云进行适当切割，实现曲面重建。所提方法通过实例进行验证。从应用角度看，此类曲面生成的直接性使其特别适用于建筑与设计过程——事实上，旋转曲面与模压曲面等T-曲面子类物体在实体建筑中已广泛存在。此外，离散版本的平面性特征为工业钢/玻璃结构提供了基础。最后，由于允许等距变形，此类曲面同样适用于可变形设计。