In this work we show an approach to find an interpolant surface for a point cloud consisting of thousands of 3D scattered points. The interpolant implicit surface is represented as a combination of compactly supported radial basis functions, so that the problem can be reduced to solving an SPD sparse linear system. We carried out numerical experiments with several benchmarks data sets and compare computational efficiency of iterative versus direct methods. The rendering of the reconstructed surface is implemented by a ray tracing algorithm and we evaluate the relation between the precision of the numerical solution and the quality of the obtained surface.