Planar cubic Pythagorean-hodograph hyperbolic curves
Received:March 02, 2021  Revised:August 04, 2021
Key Word: Pythagorean-hodograph curve  Algebraic hyperbolic Bézier curve   G^1 Hermite interpolation  
Fund ProjectL:The National Natural Science Foundation of China (General Program, Key Program, Major Research Plan)
Author NameAffiliationAddress
Yong-Xia Hao Jiangsu University Jiangsu University
Lianxing Liao Jiangsu University Jiangsu University
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      The purpose of this paper is to develop a method to construct the Pythagorean-hodograph hyperbolic (PH-H) curves based on the good geometric properties of PH curves and algebraic hyperbolic curves. The definition of Pythagorean-hodograph hyperbolic curves is given and their properties are examined. By using hyperbolic basis functions and algebraic Bézier basis functions respectively, two different necessary and sufficient conditions for a planar cubic algebraic hyperbolic Bézier curve to be a PH curve are obtained. Moreover, cubic PH-H curves are applied in the problem of G^1 Hermite interpolation with determined closed form solutions. Several examples are served to illustrate our method.
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