A selective eraser of curvature extrema for B-spline curves

• We extend the standard B-spline least squares method for approximating a series of points in the plane.
• The extension allows specifying the location of curvature extrema.
• The primal-dual interior point method is used to solve the constrained optimization problem.
• We use B-spline symbolic operators to provide the gradient of constraints to the optimization method.
• The application examples consist in producing fair curves from measured points over airfoils.

This paper provides a selective eraser of curvature extrema for B-spline curves. It is introduced as an extension to the standard least squares method for approximating a series of points using a B-spline. The extension consists in adding constraints to produce segments of curve with monotone increase or decrease of curvature. The primal-dual interior point method is used to solve the constrained optimization problem. The method requires gradients that are computed using B-spline symbolic operators. Therefore, the algorithm relies on the arithmetic and differential properties of B-splines. The variation-diminishing property of B-splines is also exploited to apply the constraints.The application examples consist in producing fair curves from measured points over airfoils. The data come from the publicly available UIUC database. The data contains a fair amount of noise for some airfoils. Especially in these circumstances, a fixed number of segments with monotonic variation of curvature hold great promise to produce curves that are, at once, very general and uncompromising over oscillations.

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