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Generalized Cubic DP Curve

Zhu Xiu-yun

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Abstract

A set of cubic polynomial function with two shape parameters was presented as an extension of cubic DP basis functions.The properties of the new basis were analyzed.The generalized cubic DP curve with two shape parameters was defined using the new basis.The new curve not only retains many properties of cubic DP curve,but also can adjust the shape by moderating shape parameters λ or μ.Based on the some given condition,the two section curves can be G2 or C2-continuous between adjacent generalized cubic DP curves,which is useful for free curve and surface design.

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What this paper is about

A set of cubic polynomial function with two shape parameters was presented as an extension of cubic DP basis functions.The properties of the new basis were analyzed.The generalized cubic DP curve with two shape parameters was defined using the new basis.The new curve not only retains many properties of cubic DP curve,but also can adjust the shape by moderating shape parameters λ or μ.Based on the some given condition,the two section curves can be G2 or C2-continuous between adjacent generalized cubic DP curves,which is useful for free curve and surface design.

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Available abstract

A set of cubic polynomial function with two shape parameters was presented as an extension of cubic DP basis functions.The properties of the new basis were analyzed.The generalized cubic DP curve with two shape parameters was defined using the new basis.The new curve not only retains many properties of cubic DP curve,but also can adjust the shape by moderating shape parameters λ or μ.Based on the some given condition,the two section curves can be G2 or C2-continuous between adjacent generalized cubic DP curves,which is useful for free curve and surface design.

Key concepts: Cubic function, Cubic form, Basis (linear algebra), Basis function, Shape parameter, Function (biology), Cubic crystal system, Curve fitting

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