关键词: PH空间曲线, 曲线拟合, G1 Hermite插值, Bernstein基函数

Abstract: To construct a G1 continuity spatial quintic Pythagorean-hodograph fitted curve for the reconstruction of spatial curve, through adding some intermediate conditions into the space sampling points to determine endpoints’ dates, it interpolates these spatial discrete data with G1 Hermite to construct spatial PH fitted curve. According to the sufficient and necessary conditions of PH space curve, the quartic derived vector composed of four quadratic polynomials is given. Its coefficients in Bernstein basis are compared with coefficients of Bézier curve’s derived vector to compose a system of equations. Following it compares Bézier curve’s derived vector coefficients with the control points of Bézier curve, by adding some free parameters to build their equal relationships. Then it composes a system of equations with aforementioned equations and equal relationships. By solving them, a G1 continuity spatial quintic Pythagorean-hodograph fitted curve is producted with G1 Hermite interpolation, which satisfies?the data of endpoints determined by intermediate conditions, and some numerical examples are presented. This construction method is intuitive, it includes multiple free parameters to control the shape of curve fitting effect.

Key words: Pythagorean-Hodograph（PH） spatial curve, curve fitting, G1 Hermite interpolation, Bernstein basis function