Abstract
In this work, we deal with the region control of $$C^2$$ interpolation curves and surfaces using a class of rational interpolation splines in one and two dimensions. Simple sufficient data-dependent constraints are derived on the local control parameters to generate $$C^2$$ interpolation curves lying strictly between two given piecewise linear curves and $$C^2$$ interpolation surfaces lying strictly between two given piecewise bi-liner blending quintic interpolation surfaces. Moreover, we also develop an algorithm concerning the application of the $$C^2$$ rational interpolation spline surfaces on image interpolation.
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