Symmetric smooth interpolation on triangles

Rational and polynomial 'smooth' interpolation schemes are derived which interpolate a function and its derivatives along the boundary of a triangle. The interpolation schemes are symmetric and affine invariant on the triangle and can be used to construct a piecewise defined function which is CN(Ω) over a triangular subdivision of a polygonal region Ω

Non-uniform corner cutting

The convergence of a non-uniform corner cutting process is investigated. It is shown that the limit curve will be differentiable provided the proportions of the corner cuts are kept within appropriate constraints. Keywords Subdivision, corner cuttin

A rational cubic spline with tension

A rational cubic spline curve is described which has tension control parameters for manipulating the shape of the curve. The spline is presented in both interpolatory and rational B-spline forms, and the behaviour of the resulting representations is analysed with respect to variation of the control parameters