Intrinsic representation and shape blending of 3D polygons

The kind of intrinsic representation of a polygon to be considered in this paper comprises a set of parameters that are invariant under Euclidean transformations and determine the shape and size of the polygon uniquely, up to a Euclidean transformation, i.e., rotation and translation. Unlike the case of 2D polygons which essentially has a unique intrinsic representation, 3D polygons allow several variations. We focus on the properties of these intrinsic representations of 3D polygons with regard to their applications to blending the shapes of two 3D polygons. It is shown that only one of these representations, which is a natural extension of the intrinsic functions of a 3D differentiable curve, is suitable for shape blending, and that the other representations lead to discontinuous shape transformation in shape blending. We further study the shape blending method based on the unique suitable intrinsic representation.