Robust Interval Control Points Computation on Cubic Subdivision Interval Curves for Computer Graphics

This paper presents a method for direct computation of interval points on cubic subdivision curves (interval control polygons). The refinement process for cubic subdivision curves is written in a matrix form which focuses on the action of the refinement on a single interval control point. In this case new interval vertex points and interval edges points are calculated just by applying the refinement matrix to the interval vertex-edge-point vector. In the limit this sequence of interval control points converges to the uniform B-spline curve specified by the original interval control polygon. Simple procedures are formulated using eigenanalysis to calculate directly an interval point on the limit curve. The interval tangent vector on the curve at this limit interval point can also be directly calculated by much the same procedure. A numerical example is provided to demonstrate various aspects of theoretical results