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Abstract
The aesthetic curves include the logarithmic (equiangular) spiral, clothoid, and involute curves. Although most of them are expressed only by an integral form of the tangent vector, it is possible to interactively generate and deform them and they are expected to be utilized for practical use of industrial and graphical design. However, the curvature of a log-aesthetic curve segment must be monotonically increasing or decreasing and a strong constraint as a function of arc length is imposed on its curvature. For geometrical design, it is desirable not to impose strong constraints on the designer’s activity, to let him/her design freely and to embed the properties of the log-aesthetic curves for complicated curves with both increasing and decreasing curvature. Hence we develop discrete filters named discrete log-aesthetic filters to fair a sequence of points with noises and to fit it locally to log-aesthetic curves. Furthermore we extend them for surfaces.