The Convex Hull of Two Closed Implicit Surfaces

This chapter presents a method of computing the convex hull surface of genus-0 freeform surfaces defined with implicit form (or computing the developable transition surface of two genus-0 freeform surfaces). The issue is reduced to compute a curve in higher dimensional space R⁶. Using the techniques of classical differential geometry, we derive a system of differential equations governing the curves. The curves are then obtained numerically solving the initial-value problem for a system of first-order ordinary differential equations. Based on this, we finally construct the transition surface and hence the convex hull of the two freeform surfaces.