Constructing parametric triangular patches with boundary conditions

The problem of constructing a parametric triangular patch to smoothly connect three surface patches is studied. Usually, these surface patches are de?ned on di?erent parameter spaces. Therefore, it is necessary to de?ne interpolation conditions, with values from the given surface patches, on the boundary of the triangular patch that can ensure smooth transition between di?erent parameter spaces. In this paper we present a new method to de?ne boundary conditions. Boundary conditions de?ned by the new method have the same parameter space if the three given surface patches can be converted into the same form through a?ne transformation. Consequently, any of the classic methods for constructing functional triangular patches can be used directly to construct a parametric triangular patch to connect given surface patches with G1 continuity. The resulting parametric triangular patch preserves precision of the applied classic method.