Implicit surface reconstruction based on a new interpolation/approximation radial basis function

•We construct a new representation of CSRBF, which unites interpolation and approximation.•A further adaptive algorithm to determine interpolation and approximation at each point is presented.•We develop the quasi-interpolation method into a method combining interpolation and approximation.•With our multi-level scheme, we can interpolate all the data points and hold a low shape approximation error. Interpolation and approximation radial basis function (RBF) has been widely used in the implicit surface reconstruction. However, a simple interpolation or approximation method may either have unwanted oscillation around the scattered points, or have low accuracy at scattered points. In this paper, we construct a new representation of RBF, which unites interpolation and approximation. A further adaptive algorithm to determine interpolation and approximation is presented. With the new representation, we can develop quasi-interpolation method from an approximation method into a method combining interpolation and approximation. And we can determine interpolation or approximation at each of scattered points without solving large linear systems. Experiments show that the given method is precision-controlled and fast in implicit surface reconstruction.