  The I-patch is a multi-sided surface representation, defined as a combination
of implicit ribbon and bounding surfaces, whose pairwise intersections
determine the natural boundaries of the patch. Our goal is to show how a
collection of smoothly connected I-patches can be used to approximate
triangular meshes. We start from a coarse, user-defined vertex graph which
specifies an initial subdivision of the surface. Based on this, we create
ribbons that tightly fit the mesh along its edges in both positional and
tangential sense, then we optimize the free parameters of the patch to better
approximate the interior. If the surfaces are not sufficiently accurate, the
network needs to be refined; here we exploit that the I-patch construction
naturally supports T-nodes. We also describe a normalization method that nicely
approximates the Euclidean distance field, and can be efficiently evaluated.
The capabilities and limitations of the approach are analyzed through several
examples.
