Spline Curves and Spline Surfaces

Abstract

In the previous chapter, we used cubic parabolas (Equation 22) to interpolate the line of intersection P₁ P₂ of the graph Γ with a vertical plane ψ. Analogously, a patch Ψ on Γ, which is roughly approximated by two triangles, can be replaced by a cubic graph that consists of all the cubic parabolas we get when we vary the plane ψ. Such a graph is called an “interpolating surface.”