P-Bézier and P-Bspline curves - new representations with proximity control

Our current paper takes a different approach: the basis functions are calculated by a much simpler algebra that is capable to reproduce standard formulations like Bézier and B-splines curves, and can maintain Cn end constraints. We introduce the Proximity-Bézier, shortly P-Bézier, and P-Bspline curves, including the construction of basis functions and the most important mathematical properties. A general control point insertion algorithm is also described. Several examples are shown to compare the classical and the new representations. A tensor product generalization of the scheme is also demonstrated.