A
one-dimensional monotone interpolation method based on interface reconstruction
with partial volumes in the slope-space utilizing the Hermite cubic-spline, is
proposed. The new method is only quartic, however is C2 and unconditionally monotone. A set of control points is employed to
constrain the curvature of the interpolation function and to eliminate possible
nonphysical oscillations in the slope space. An extension of this method in
two-dimensions is also discussed.
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