Fairing with neighbourhood LOD filtering to upgrade interactively B-Spline into Class-A curve

Class-A curves show very appreciable features in terms of smoothness and curvature trend that is commonly perceived as high quality profiles. These curves are commonly sketched by experienced operators, but at the present day no tools are available to transform a B-spline into a Class-A curve. The k-neigh-fast is an improved version of k-neighbours algorithm, described in Amati et al. (Comput Graph 30(3):345–352, 2006), aiming to transform a B-spline non-Class-A slope into a B-spline Class-A curve by manipulating a group of k geometric coefficients. Once the level of detail (LOD) representation of a curve has been computed, the k-neigh-fast algorithm, detects those control points representing non-Class-A imperfections. At each LOD, the algorithm individuates the detail coefficient maximizing the internal functional. Then k-neighbours has been modified applying filtering criteria. A control step starts to verify the transformation from a non-Class-A curve into a Class-A shape. This process is repeated until the chosen stopping condition is satisfied. The final shape with improved smoothness and monotonic curvature is achieved through manual procedure. This paper reports results dealing on an improved and faster wavelet-based LOD filtering implementation used to generate very smooth set of profiles that own to Class-A set. The LODs representation allows to divide curves into their coarser least-square approximations and details coefficients. The extraction and manipulation of details with multi-level filtering, allows to determine geometric imperfections. This method has been tested to the smoothing of the hull profile of ships: results are good since the non-A-curve are well converted in smoother lines. A more efficient implementation, based on a flexible LOD representation led to prove many benefits of this techniques; the tests performed exploiting a computer program implementation have demonstrated very good results in most of simulations considered.

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