1 research outputs found
Shape Reconstruction of Trapezoidal Surfaces
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