G^2 blending of cubic Pythagorean hodograph curves with prescribed total arc length
Received:July 13, 2020  Revised:October 26, 2020
Key Word: Pythagorean-hodograph curve   G^2 blending   Prescribed arc length   Nonlinear equations  
Fund ProjectL:National Natural Science Foundation of China
Author NameAffiliationAddress
Yong-Xia Hao Jiangsu University Jiangsu University
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      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.
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