Spline curve surface is an important part of CAGD. To obtain the parameter spline curve on the hyperbolic paraboloid

the four rational basis functions presented in this paper have a changeable control handle and a unary function. A hyperbolic paraboloid is constructed in the standard tetrahedron. On the surface

the base function defines a parameterized method with the parameters of the shape parameter spline curve surface. The basis function of spline through the rational parameters of the hyperbolic paraboloid is limited. A single-parameter rational basis function of spline is generated. Additionally

the nature of shape preserving and endpoints are considered. The nature of shape preserving and endpoints are considered. The curvature of two endpoints are derived as zero for a range of points. Consequently

a -continuity curve can be attached by this spline curve without any additional requirements. Experiment shows that we use this spline to raise the surface for spatial mesh

which also can implement -continuity with much freedom.