Curve Shape Modification and Similarity Evaluation

In computer aided aesthetic design, designers evaluate the quality of a designed curve by looking at its curvature or radius of curvature plots. If the quality of a designed curve does not meet a designer´s demand, they usually modify the control points of the curve interactively. But the definition of the quality of a designed curve is ambiguous and no official standards are given. Therefore, in this paper, a criterion of a fair curve is established. A five degree B-spline curve and curvature are expressed. Feature of curvature distribution and radius of curvature distribution are discussed. The radius of curvature specification to modify the shape of a B-spline curve is described. To modify the shape of the B-spline curve, the least-squares method is introduced to minimize the difference between the B-spline curve radius of curvature and the specified radius of curvature. Correlation matching for similarity evaluation is described. The discrete values of radius of curvature are considered as the components of a multi dimensional vector for the curve. Similarity between two curves is calculated by normalizing the dot product of the vectors. Curve shape similarity evaluation is tried by giving examples. Examples show the numerical similarity evaluation matches our visual recognition of curve shape similarity. Assuming a curve with constant variation of radius of curvature distribution is fair, the similarity of the designed curve to a fair curve is evaluated.