\(G^2\) blending of cubic Pythagorean hodograph curves with prescribed total arc length. (English) Zbl 1499.65057
Summary: Pythagorean-hodograph (PH) curve is widely used in curve modeling because of its advantages in arc length and equidistant curve calculation. This paper discusses the \(G^2\) continuous blending of cubic PH curves under total arc length constraint. Given three points including two end control points and a joint point, construct two cubic PH curves such that they interpolate the end control points and are \(G^2\) continuous at joint point with prescribed total arc length. It can also be regarded as a curve extension problem. According to the arc length formula of cubic PH curve and the condition of \(G^2\) blending, the problem is transformed into a constrained minimization problem. Several examples are served to illustrate our method.
MSC:
| 65D17 | Computer-aided design (modeling of curves and surfaces) |
| 68U07 | Computer science aspects of computer-aided design |
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