Abstract: Multidimensional projection has become a standard tool for visual analysis of multidimensional data sets, as the 2D representation of multidimensional instances gives an important and informative panorama of the data. Recently, research in this topic has been steered towards methods that permit user intervention and interactivity. One of such methods is inverse projection, a recently proposed resampling mechanism that allows users to generate new multidimensional instances by creating reference 2D points in the projection space. Given an m-dimensional data set and its 2D projection, inverse projection transforms a user-defined 2D point into an m-dimensional point by means of a mapping function. In this work, we propose a novel inverse projection technique based on Radial Basis Functions interpolation. Our technique provides a smooth and global mapping from low to high dimensions, in contrast with the former technique (iLAMP) which is local and piecewise continuous. In order to demonstrate the potential of our technique, we use a 3D human-faces data set and a procedure to interactively reconstruct and generate new 3D faces. The results demonstrate the simplicity, robustness and efficiency of our approach to create new face models from a structured data set, a task that would typically require the manipulation of hundreds of parameters.