Shape Blending between 3-d Triangular Meshes Based on Their Intrinsic Variables

Shape blending determines the in-between shapes that provide the gradual transformation of one shape into another. It is usually considered a two-step problem: the correspondence problem and the interpolation problem. This paper presents a solution to the interpolation of transforming one triangular mesh model into another triangular mesh based on their intrinsic definitions. Rather than considering a triangular mesh as a set of independent points, the solution treats a triangular mesh as a set of intrinsic variables which describes the basic geometric nature of the triangular mesh. The correspondent intrinsic variables of the initial and the final meshes are interpolated to determine the intermediate shapes. This approach is easy and fast enough in fully interactive time and can avoid the shrinkage and kinks because all the variables change monotonically. The approach produces satisfactory results and is translation and rotation invariant. It is also useful for the shape blending between free-form surfaces as they can be approximated by triangular mesh using triangulation techniques.