In this paper we treat the problem of smoothing a user input in form of a stroke consisting of line elements. We pose the problem as a minimization problem for the Dirichlet energy of the resulting spline under the constraint that it must lie inside the offset of the input. We present an approximation solution that works with three steps, namely simplification, regularization and smooth rendering. The simplification step is described in more detail in our paper, we will only recall the most important facts and use the algorithm as it is. In the regularization step we subdivide the simplified spline into equidistant segments and then apply the Savitzky Golay filter to it. One must take special care to ensure that the regularized spline lies inside the offset of the input. We describe a heuristics that guarantees it. The smooth rendering step consists in using the nodes of the regularized spline as control points of a B Spline. We discuss the quality and outcome of this approach and give a few examples.
Line smoothing · Dirichlet Energy · Savitzky-Golay filter
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