Local Convexity-Preserving 𝐶² Rational Cubic Spline for Convex Data

Figure 1

Convexity- and nonconvexity-preserving curves.

(a) Cubic Hermite spline curve

(b) PCHIP curve

(c) Convexity-preserving rational cubic curve with 𝑢_𝑖=0.25, 𝑣_𝑖=0.25

(d) Convexity-preserving rational cubic curve with 𝑢_𝑖=1.5, 𝑣_𝑖=1.5