The quintic polynomial composite spline with parameters is presented in this study to overcome the disadvantages of the cubic parametric B-spline in shape adjustment and local aspects. First

a class of quintic polynomial basis functions with parameters is constructed. The quintic polynomial composite spline curves with parameters are then defined according to the same composite way with the cubic B-spline curves. The optimal parameter value of the quintic composite spline curves based on the energy optimization method is discussed. Finally

the corresponding composite spline surfaces are defined

and the problem of the optimal parameter values of the surfaces utilizing the particle swarm algorithm is studied. The quintic composite spline not only inherits most properties of the cubic B-spline

but also has stronger local and shape properties than the cubic B-spline. Given that the quintic composite spline is still a polynomial model

the equation structure is relatively simple

which is more in line with the requirements of the actual projects. The smooth quintic composite spline curves and surfaces can be obtained by the energy optimization method. The quintic composite spline overcomes the disadvantages of the cubic parametric B-spline in shape adjustment and local aspects

which is a practical method for free curve and surface modeling.