A graph-based method for fitting planar B-spline curves with intersections

A graph-based method for fitting planar B-spline curves with intersections

The problem of fitting B-spline curves to planar point clouds is studied in this paper. A novel method is proposed to deal with the most challenging case where multiple intersecting curves or curves with self-intersection are necessary for shape representation. A method based on Delauney Triangulation of data points is developed to identify connected components which is also capable of removing...

A direct method to solve optimal knots of B-spline curves: An application for non-uniform B-spline curves fitting

B-spline functions are widely used in many industrial applications such as computer graphic representations, computer aided design, computer aided manufacturing, computer numerical control, etc. Recently, there exist some demands, e.g. in reverse engineering (RE) area, to employ B-spline curves for non-trivial cases that include curves with discontinuous points, cusps or turning points from the...

Computing intersections of planar spline curves using knot insertion

We present a new method for computing intersections of two parametric B-Spline curves. We use an intersection of the control polygons as an approximation for an intersection of the curves in combination with knot insertion. The resulting algorithm is asymptotically Newton-like, but without the need of a starting value. Like Newton’s method, it converges quadratically at transversal intersection...

Least-Squares Fitting of Data with B-Spline Curves

Target Curvature Based Automatic Fairing of Planar B-Spline Curves

A new automatic local fairing technique for planar B-spline curves is presented in this paper. According to the design intent, a target curvature plot, which is provided by the designer, is used to identify ‘bad’ points and ‘bad’ curve segments. Then, the corresponding control points are modified in a process of local constrained optimization where the importance of fairness in the sense of ene...