Reconstructing B-patch Surfaces Using Inverse Loop Subdivision Scheme

B-patch surface is the main block to construct the triangular B-spline surfaces and has many interesting properties of the surfaces over a triangular parametric domain. This paper proposes a new method for reconstructing the low-degree B-patch surfaces using inverse Loop subdivision scheme, along with geometric approximation algorithm. The obtained surfaces are the low-degree B-patches over the triangular domain and almost cross through the data points of the original triangular meshes after several steps of the geometric approximating. Comparing with techniques use the original mesh as the surface control polyhedron, our method reconstructed B-patches with the degree reduces to 2 ⁱ times after i steps of the inverse. The accuracy of the result B-patches can be improved by adjusting the location of control points and knot vectors in each step of iterations. Some experimental results demonstrate the efficacy of the proposed approach. Because most the low-degree parametric surfaces are often employed in CAGD, mesh compression, inverse engineering, and virtual reality, this result has practical significance.