A Strategy for the Interpolation of Surfaces through the Use of Basis Functions

Abstract. For the construction of digital terrain models based on surface interpolation, it is defined a bivariate function that interpolates a finite set of sample points, , such that, . In this work, it is presented a strategy for the generation of interpolation surfaces through the use of basis functions. This methodology is based on a work by Chaturvedi and Piegl, where improvements related to the construction of the basis functions were made. The proposed strategy allows a larger expansion of the basis function’s support region, represented by the interior of a trajectory curve, composed of quadratic rational Bézier segments and reduces the approximation error between the reference surface and the interpolation surface.