Monotone piecewise rational cubic interpolation

We present a C ¹ interpolating scheme to deal with the problem of monotonicity (that is when data is monotone, the interpolant should also preserve the monotonicity). The scheme uses piecewise rational cubic function, in a most general form which involves four free parameters in its description in each interval. We derive data dependent sufficient conditions on these parameters which ensure the monotonicity of monotone data. These parameters are also used to provide freedom to the user to refine the appearance of the curves interactively.

Keywords:

• rational function
• monotone data
• monotone visual model
• shape parameters
• free parameters

Keywords:

• AMS Subject Classification
• 65D05
• 65D10
• 65D07
• 65D18
• 65U07

Acknowledgements

The authors are pleased to acknowledge the anonymous referees whose valuable comments and suggestion made this manuscript more useful.