Visualization of monotonic shaped data by a rational cubic Ball

Abstract

This paper discusses the monotonicity-preserving curve interpolation of 2D monotone data. A piecewise rational cubic Ball function in form of (cubic numerator /cubic denominator), with four shape parameters is presented. The rational cubic Ball spline has four shape parameters in its descriptions where two of them are constrained shape parameters and remaining two of them provide the freedom to user to easily control the shape of the curve by simply changing their values. The sufficient data dependent conditions are derived for two shape parameters to insure the monotonicity everywhere. Numerical results show that the Ball interpolation scheme is quite efficient and well tested for monotone data.