Construction of B-spline surface with B-spline curves as boundary geodesic quadrilateral

• An optimized geometric construction method for B-spline geodesic quadrilateral.
• A practical construction scheme for surface interpolating geodesic quadrilateral.
• The constructed surface and geodesics with low degree.

This paper is concerned with construction of a B-spline surface that interpolates a B-spline curvilinear quadrilateral as boundary geodesics. The construction consists of two parts. First, from the corner data (i.e., position, unit tangent vector and curvature at the end points of each curve), a four-quartic B-spline curvilinear quadrilateral with minimum strain energy is constructed to satisfy the constraints of the crossing geodesics on a surface. Second, a tensor-product B-spline surface of degree (5, 5) is constructed to interpolate the quadrilateral as boundary geodesics. The control points of the interpolation surface are determined by two steps, and the surface which adheres to the NURBS standard and employs geometric shape handles meeting the requirements of the design scenario. The method is illustrated with several computational examples.