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.

中文翻译：

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$$ C ^ 2 $$ C 2带区域控制和图像插值应用的有理插值样条

在这项工作中，我们使用一维和二维有理插值样条来处理\（C ^ 2 \）插值曲线和曲面的区域控制。简单足够的数据依赖性约束派生对本地控制参数以生成\（C ^ 2 \）插补曲线两个给定分段之间严格躺在线性曲线和\（C ^ 2 \）插值曲面躺在严格两个给定分段双之间线性混合五次插值曲面。此外，我们还开发了一种关于\（C ^ 2 \）有理插值样条曲面在图像插值中的应用的算法。