Geometric continuity C1G2C1G2 of blending surfaces

In this paper, we study the C1G2C1G2 continuity of surfaces by a shape-blending process. Furthermore, we study the continuity of the ruled surfaces constructed by linear interpolation between two pairs of C1G2C1G2 continuous curves. We give some conditions for the C1G2C1G2 continuity of composite surfaces in a shape-blending process. A practical approach is proposed to maintain the C1G2C1G2 continuity of Bézier surfaces pairs in a shape-blending process by adjusting the control points along the common boundary of the resulting surface-pair. We finish by proving and justifying the efficiency of the approaching method with some graphical examples.

► A study of C1G2C1G2 continuity of surfaces by a shape-blending surface.
► The ruled surfaces are constructed by linear interpolation between two pairs of C1G2C1G2 continuous curves.
► In practice, the C1G2C1G2 continuity of Bézier surfaces pairs is studied.