An algorithm for fairing of ordered points using local interpolation

We present an algorithm for faring of data point set using the local interpolation. This approach takes three steps. First, we need to compute the tangent vector and discrete curvature of each data points. The next step is to indentify `bad´ points and `good´ points according to the given rules. The algorithms finally adjust the `bad´ points by local fitting based on minimizing the strain energy of the fitting curve. Local fitting curve is a Bezier segment interpolating the `good´ points and their tangents, then we will generate new points on this segment to replace the `bad´ points. The algorithm can adjust points as many as possible within a given accuracy in one fairing step, but the traditional faring algorithm can adjust the given number of `bad´ points. Finally, some examples of this algorithm demonstrate its usefulness and quality. This method will be widely used to preprocess data point set in reversing engineering.