Abstract: To reconstruct curves and surfaces robustly from scattered data,an implicit progressive-iterative algo-rithm with compactly supported radial basis functions based on the variational quasi-interpolation method is pro-posed.Firstly,the non-zero constraint of the implicit function is constructed using normal vectors at the given points,an iterative scheme for calculating coefficients of the implicit function is developed and its convergence is discussed.Secondly,by introducing an acceleration factor,the implicit progressive-iteration algorithm is sped up,and the convergence is analyzed.Finally,the accelerated algorithm is modified to decrease the space and time complexity.Numerical experiments show that the algorithm is effective for curve and surface reconstruction,and it also achieves good results for reconstructing from data with missing samples,non-uniform distribution,and noises.Moreover,it is simple to implement and easy to process in parallel.