There are many methods based on optimization technique for resolving the problem of deformation-minimization in texture mapping. Recently, a new optimization-based method for parameterizing polygonal meshes with minimum deformation has been developed to specifically address the problem of feature matching in texture mapping. However, these optimization-based methods achieve the result of high quality at the expense of long computation time. In this paper, we present a fast analytic texture mapping method based on radial basis function (RBF) interpolation to solve the problem of constrained texture mapping. The users control the mapping process by interactively defining and editing a set of constraints consisting of 3D points picked on the surface and the corresponding 2D points of the texture. RBF is invoked to interpolate the user-defined constraints to provide an analytic parameterization of the surface. The energy-minimization characteristic of RBF also ensures that the mapping function smoothly interpolates the constraints with satisfying non-deformation properties. This method has been applied to several data sets and excellent results have been produced. Our method is much faster than the optimization-based method for texture mapping with the same good effect achieved.