NURBS Curve Shape Modification and Fairness Evaluation

摘要

For the purpose of evaluation, a NURBS curve is used, because it is commonly used in the areas of CAD/CAM and Computer Graphics. A curve with a monotone radius of curvature distribution is considered as a fair curve in the area of Computer Aided Aesthetic Design (CAAD). But no official standards have been established. Therefore, a criterion for a fair curve is proposed. A quintic NURBS curve, the first derivative of a quintic NURBS curve, curvature vector, curvature, and radius of curvature are expressed. The concept of radius of curvature specification to modify the shape of a NURBS curve is illustrated. The difference between the NURBS curve radius of curvature and the specified radius of curvature is minimized by introducing the least-squares method to modify the shape of the NURBS curve. As curve fairness evaluation, radius of curvature distribution is used as an alternative characteristic of a curve. Algebraic functions such as linear, quadratic, cubic, quartic, quintic, and six degrees are applied to the radius of curvature distribution of the designed curve to specify the radius of curvature. Then, the shape of the curve is modified according to the specified radius of curvature distribution. In this manner, six NURBS curves whose radius of curvature are these algebraic functions are generated, and are predefined. Using the correlation matching, the similarity is evaluated by comparing the radius of curvature distribution of the designed curve with those of six NURBS curves predefined. The highest similarity curve to the designed curve among these predefined curves is selected. The similarity evaluated of the selected curve is determined as fairness of the designed curve.