A Surface Reconstruction Algorithm Based on Implicit T-Spline Surfaces

In this paper,we introduce the implicit T-spline surfaces,generalize the definition of T-meshes from2D to3D,and construct the T-meshes from the unorganized collection of sampling points based on the octrees and subdivision.By exploiting the surface fitting models,we transform the problem of surface reconstruction to an optimization problem.Then based on the implicit T-spline surfaces,we describe the optimization problem in the matrix forms,and convert it to a linear system by the theory of optimization.By solving the linear system,we get the unknown coefficients and the reconstructed surfaces.Finally,we conclude the paper with some illustrating examples and conclusion remarks.Our method can solve the surface reconstruction problems well；ad hoc it can effectively reduce the unknown coefficients compared with the implicit tensor product B-spline functions.