The composite rational curves and their smoothness

A model for computing the weights of the control vertices of a rational curve with respect to the continuity constraints is presented. The described method generates for one control polygon a family of curves created from many rational curve segments. The join points of the adjoining curve segments lie along some edges of the control polygon and each curve segment can be controlled by different number of vertices. An initial presentation of the (2,2)-rational patch and the conditions of positional and cross-derivative continuity for linking two patches is offered