Abstract: Geodesic curve on a surface is a kind of important one and has its applications in computer
vision and image processing, such as in garment design. A curve is a geodesic if and only if its
rectifying plane coincides with the tangent plane to the surfaces. This fact is used to construct bicubic
Bézier pathes through geodesics, and the continuity of composite Bézier patches through pairs of
geodesics discussed. Finally, some examples are provided to demonstrate the effectiveness of the
proposed method.

Key words: cubic Bézier curve, bicubic Bézier surface, geodesic curve, control point, surface construction