<p>Approximation and interpolation are two typical strategies for spline curves representation, and shape adjustability is also an important characteristic that spline curves aspire to possess. This paper presents the frameworks for constructing quasi-cubic spline curves that simultaneously support approximation, interpolation, and local shape adjustment. The proposed frameworks can yield <i>C</i>¹ and <i>C</i>² spline curves that integrate these three abilities. Two concrete applications are provided to demonstrate the effectiveness of the proposed frameworks.</p>