本文選題：PH空間曲線 + 曲線擬合��； 參考：《計(jì)算機(jī)工程與應(yīng)用》2017年20期

【摘要】：為了構(gòu)造一種空間五次Pythagorean-hodograph G~1連續(xù)擬合曲線以重建空間曲線,對已知空間采樣點(diǎn)數(shù)據(jù)加入中間條件確定首末端點(diǎn)數(shù)據(jù),對其進(jìn)行G~1Hermite插值構(gòu)造擬合PH曲線。根據(jù)空間PH曲線的充分必要條件,給出由四個(gè)二次多項(xiàng)式組成的四次導(dǎo)函數(shù),比對其與空間五次Bézier曲線的導(dǎo)函數(shù)在Bernstein基下分別對應(yīng)的向量型系數(shù),形成向量等式,再根據(jù)Bézier曲線導(dǎo)函數(shù)的系數(shù)與其控制多邊形頂點(diǎn)的關(guān)系,引入自由參數(shù)建立五次Bézier曲線導(dǎo)函數(shù)的系數(shù)與首末端點(diǎn)的等量關(guān)系,并與前述向量等式組成方程組。通過求解方程組可得一段由G~1Hermite插值構(gòu)造出的滿足由中間條件給出的首末端點(diǎn)數(shù)據(jù)且G~1連續(xù)的PH擬合曲線,并給出了數(shù)值實(shí)例。此構(gòu)造方法直觀,有多個(gè)自由參數(shù)可對曲線進(jìn)行擬合效果的形狀控制,且通過數(shù)值實(shí)驗(yàn)擬合效果較好。
[Abstract]:In order to construct a space quintic Pythagorean-hodograph continuous fitting curve to reconstruct the spatial curve, the first and last terminal point data are determined by adding intermediate conditions to the known spatial sampling point data, and the fitting PH curve is constructed by GG 1Hermite interpolation. According to the necessary and sufficient conditions of the spatial PH curve, the fourth derivative function composed of four quadratic polynomials is given. The vector equation is formed by comparing the vector type coefficients corresponding to the derivative function of the spatial quintic B 茅 zier curve under the Bernstein basis. According to the relation between the coefficient of derivative function of B 茅 zier curve and the vertex of its control polygon, the free parameter is introduced to establish the isometric relation between the coefficient of derivative function of B 茅 zier curve and the first and end point of the derivative function of B 茅 zier curve, and the equations are formed with the vector equation mentioned above. By solving the equations, we can obtain a continuous PH fitting curve which satisfies the first and last endpoints data given by the intermediate condition and the GQ 1 continuous PH fitting curve, which is constructed by the GQ 1Hermite interpolation, and a numerical example is given. This method is intuitionistic and has many free parameters to control the shape of the curve fitting effect, and the fitting effect is better by numerical experiment.
【作者單位】： 桂林電子科技大學(xué)數(shù)學(xué)與計(jì)算科學(xué)學(xué)院廣西高校數(shù)據(jù)分析與計(jì)算重點(diǎn)實(shí)驗(yàn)室;桂林電子科技大學(xué)數(shù)學(xué)與計(jì)算科學(xué)學(xué)院;
【基金】：廣西自然科學(xué)基金(No.2015GXNSFAA139014)
【分類號(hào)】：O186.11

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