Rigidity and flexibility analysis of a kind of surfaces of revolution and visualization

In this paper we consider a class of toroids generated by a meridian in a shape of quadrangle in an arbitrary position to the axis of revolution.We give geometrical meaning of the non-rigidity condition based on the position of the diagonals of meridian. Special classes of quadrangular meridians (trapezium, parallelogram, deltoid, … ) are discussed. The number of flexible toroids is considered. A tool SurfBend is developed for the rigidity and visualization.