Abstract: To address the difficulty of simultaneously achieving interpolation, approximation, and shape adjustability in existing splines, an adjustable quadratic trigonometric spline construction method integrating interpola-tion and approximation is proposed. First, quadratic trigonometric basis functions with shape parameters are constructed according to prescribed endpoint conditions, and their partition-of-unity, symmetry, and nonnegativity properties under specified parameter constraints are established; second, piecewise quadrat-ic trigonometric spline curves are constructed using the proposed basis functions, interpolation, approxi-mation, and hybrid design are realized by adjusting adjacent shape parameters, and the continuity and convex hull properties of the curves are demonstrated; third, the relationship between shape parameters and geometric characteristics is analyzed, admissible parameter ranges for different design modes are pro-vided, and local and global shape adjustment is achieved; finally, the spline curves are extended to quad-ratic trigonometric spline surfaces through the tensor product method, yielding a surface model capable of interpolation, approximation, and hybrid geometric design. Numerical experiments show that each spline curve segment contains four adjustable shape parameters, while each tensor product surface patch contains eight adjustable shape parameters. In a two-dimensional curve example with eight control points and a three-dimensional surface example with a 4×4 control-point grid, the proposed method successfully achieves interpolation, approximation, and hybrid design while preserving the corresponding continuity and convex hull properties within the specified parameter ranges. The proposed method provides a unified construction framework for curve and surface design that combines exact geometric constraints with flexi-ble shape adjustment.