Three-dimensional shape blending: intrinsic solutions to spatial interpolation problems
This paper presents an efficient algorithm for shape blending between 3-D polylines and between 3-D polyhedral objects based on their intrinsic definitions. Rather than interpolating the vertex locations explicitly, our algorithms determine the intermediate shapes by interpolating the intrinsic variables of the initial and the final shapes. Our algorithms are easy and fast enough in fully interactive time. The generated intermediate shapes are independent of the locations and orientations of the two key frame shapes and all intrinsic variables (the edge lengths and the directed angles) change monotonically. An optimization algorithm is performed for closed requirement. We then generalize our method to shape blending between triangular meshes with arbitrary topology and between freeform curves/surfaces and our results are satisfactory.
shape blending interpolation intrinsic variables computer animation msi algorithm