Interpolation and Approximation of Surfaces from Three-Dimensional Scattered Data Points

There is a wide range of applications for which surface interpolation or approximation from scattered data points in space is important. Dependent on the field of application and the related properties of the data, many algorithms were developed in the past. This contribution gives a survey of existing algorithms, and identifies basic methods common to independently developed solutions. We distinguish surface construction based on spatial subdivision, distance functions, warping, and incremental surface growing. The systematic analysis of existing approaches leads to several interesting open questions for further research.