CAD modelling in reverse engineering: Generating C2-continuous planar B-spline curves for free-form shapes

Summary form only given. In Reverse Engineering, the result of surface reconstruction of the scanned objects can neither be recognized nor used for further analysis using the existing CAD system. The surface model needs to be transformed into a CAD model. Generally, conversion of a surface model is done through feature recognition process. For symmetrical shapes of mechanical components such as block, polygon, cylinder, and sphere, the existing CAD software can recognize the shape. While, for asymmetric or free-form shapes the recognition process should be done through curve fitting. Generally, fair interpolatory spline curves and the resulted surfaces encountered in technical design can usually be classified as having to be more aesthetic (e.g. car bodies) or more functional (e.g. airplane fuselages). Interactive techniques are often praised as the optimal tool to achieve aesthetic shapes This paper presents a direct curve-fairing algorithm as an advancement of the conventional curve-fairing method used to optimize curvature plot of a given planar B-spline curves. The direct method determines the region where the curve has imperfections and automatically locates points on a curve that needs to be faired. This method provides flexibility in controlling the typical shape of convex or concave curvature of curves, and can be implemented as an independent system because the modification of a curvature segment does not influence the remaining regions. Therefore, it is regarded more efficient than the method of manipulating a set of control points. It is evident that the application of the direct method can solve geometric constraint problems of planar curves by plotting symmetrically points on the imperfect region in order to fair and derive a C²-continuous curvature. In general, this method is also applicable to solve geometric constraint issues of B-spline curves on Rⁿ Euclidean space.