This contribution addresses the problem of curve and surface evolution. We explain a general framework for the evolution-based approximation of a given set of points by a curve.

Then we apply this method to surfaces. We show the sequential evolution of curves and surfaces on some concrete examples.

We apply the curve evolution as a solving method in statistical data analysis. Our aim is to use closed B-spline curves for the description of data sets related to the local density of the data sample.

The result is a contour fulfilling some predefined statistical criterion. We also explain the notion of data depth.

We also use the surface evolution for the surface reconstruction from point clouds. We describe the digital reconstruction problem and the methods of surface reconstruction.

For the implementation of evolution algorithms we use the interactive environment MATLAB.