Difference Bounds of 3-Direction Quartic Box Spline Surfaces

The distance from 3-direction quartic box spline surface to the central triangular planar patch of its control net is investigated as well as its bound. Using piecewise expression of 3-direction quartic box spline surface, and the first and second directional differences of the control points, the point wise distance from the surface patch to the central triangular planar patch of its control net is obtained. The bound of the distance is also determined.