  We present a nodal interpolation method to approximate a subdivision model.
The main application is to model and represent curved geometry without gaps and
preserving the required simulation intent. Accordingly, we devise the technique
to maintain the necessary sharp features and smooth the indicated ones. This
sharp-to-smooth modeling capability handles unstructured configurations of the
simulation points, curves, and surfaces. The surfaces correspond to initial
linear triangulations that determine the sharp point and curve features. The
method automatically suggests a subset of sharp features to smooth which the
user modifies to obtain a limit model preserving the initial points. This model
reconstructs the curvature by subdivision of the initial mesh, with no need of
an underlying curved geometry model. Finally, given a polynomial degree and a
nodal distribution, the method generates a piece-wise polynomial representation
interpolating the limit model. We show numerical evidence that this
approximation, naturally aligned to the subdivision features, converges to the
model geometrically with the polynomial degree for nodal distributions with
sub-optimal Lebesgue constant. We also apply the method to prescribe the curved
boundary of a high-order volume mesh. We conclude that our sharp-to-smooth
modeling capability leads to curved geometry representations with enhanced
preservation of the simulation intent.
