Blending pipe surfaces with piecewise algebraic surfaces

Given the positions and orientations of several pipe surfaces (cylinders) in 3D space, a scheme for constructing a piecewise algebraic surface to blend the pipe surfaces is presented. The algorithm starts with a suitable partitioning of the 3D space into tetrahedra or prisms in which the algebraic surface patches are defined. Then a smooth piecewise algebraic surface is constructed which meets the pipe surfaces with a certain order of geometric continuity. The proper choice of free parameters is briefly discussed.