Reconstructing B-patch surface from triangular mesh

B-patch is the main block for creating the multivariate B-spline surfaces over triangular parametric domains. It has many interesting properties in the smooth surface construction with arbitrary topology. This paper proposes a new approach for reconstructing B-patch surfaces from triangular mesh based on a local geometric approximation, along with inverse subdivision scheme. The result B-patches with the low degree cross through most of the data points of the original meshes after some steps of the local geometric approximation. The accuracy of result surfaces can be carried out by changing the position of control points and adjusting knotclouds in each of the iterations. Some concrete experimental examples are also provided to demonstrate the effectiveness of the proposed method. Because most of the low degree parametric curves and surfaces are often employed in CAGD, this result has practical significance, especially for mesh compression, inverse engineering, and virtual reality.