Spiral Tree on Polyhedron

In previous chapters we established the planar model for our spiral treeslittreespiral tree (based on convex hulls)convex hull and the extensions to convex polyhedra of the planar notions of convex hull/minimal-length enclosing polygon.polygonminimal length enclosing In this chapter we continue our pursuit by proving that the spiraling idea works as well for vertex-mergingvertex-merging in polyhedral half-surfaceshalf-surface bounded by simple closed quasigeodesics,quasigeodesicsimple closed with respect to the relative version of either convex hull or enclosing geodesic polygon.