Point-normal subdivision curves and surfaces

Subdivision Curves and Surfaces

Although curves can be generally described by using concepts such as NURBS, we will introduce subdivision curves as a lead-in to the more general concept of subdivision surfaces. Suppose we wanted to perform knot-insertion in the middle of a B-spline curve defined by four control points, p0 through p3. Using the blossoming technique, we would determine the control point to be as in Figure 1. Th...

Adaptive Subdivision Curves and Surfaces

Well-known schemes of subdivision curves and surfaces are modified so that they allow an adaptive refinement. Adaptation is controlled by an error measure which indicates for the vertices of a mesh whether the approximation is sufficient. The adaptive constructions are based on local operations of refining or coarsening. They allow to reach all other subdivisions, in particular the non-adaptive...

Creating and Editing Curves on Subdivision Surfaces

Subdivision Curves on Surfaces and Applications

Subdivision curves have great importance for many CAD/CAM applications. In this paper we propose a simple method to define subdivision schemes on triangulations. It works by translating to the triangulation a perturbation of a planar binary subdivision. To reproduce this perturbation in the surface we use both, shortest and straightest geodesics, so we call this strategy intrinsic projection me...

Ringing subdivision of curves and surfaces

Split&Tweak subdivisions iteratively refine a polygon by inserting a vertex in the middle of each edge (Split) and then moving each vertex to an affine combination of five consecutive vertices (Tweak). Special cases include Dyn, Gregory, and Levin’s fourpoint subdivision, Lane and Riesenfeld’s cubic and quintic B-spline subdivision, Rossignac’s subdivision which produces C curves, and Maillot a...