  This paper presents some applications using recently developed algorithms for
smooth-continuous data reconstruction based on the digital-discrete method. The
classical discrete method for data reconstruction is based on domain
decomposition according to guiding (or sample) points. Then the Spline method
(for polynomial) or finite elements method (for PDE) is used to fit the data.
Our method is based on the gradually varied function that does not assume the
property of being linearly separable among guiding points, i.e. no domain
decomposition methods are needed. We also demonstrate the flexibility of the
new method and its potential to solve a variety of problems. The examples
include some real data from water well logs and harmonic functions on closed 2D
manifolds. This paper presents the results from six different algorithms. This
method can be easily extended to higher multi-dimensions. We also include an
advanced consideration related to the use of gradually varied mapping.
