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本文给出一个曲线拟合的方法,此方法的要点如下: 1.设:已知n个型值点A_1,……A_n,并已知每一型值点上的切线位置,则对任意两点Ai,A_(i+1),可定义一个极坐标系S_i,它满足: (1)OA_i与OA_(i+1)之间的夹角等于两切线之间的夹角θ~*(其中O为S_i的原点); (2)|OA_i|=|OA_(i+1)|=R_i。 在S_i中,曲线用三次多项式表达为: r_i(θ)=R_i+a_iθ(θ~*-θ)(1-2·θ/θ~*) 2.本文推导了一个计算切线位置的普遍公式: 对满足足够普遍条件的五个点A_(i-2),A_(i-1),A_i,A_(i+1),A_(i+2),证明A_i处的切线位于A_(i-1)A_i与A_iA_(i+1)的夹角之内,因此,A_i处的切线与A_(i-1)A_i之间的夹角Δβ_i的计算公式为: Δβ_i=γ_i~* (P_(i-1)S_i/(q_iS_(i-1)+P_(i-1)S_i))
In this paper, a method of curve fitting is given. The main points of this method are as follows: 1. Suppose that there are n types of value points A_1, ..., A_n, and knowing the tangent position of each type value point, Point Ai, A_ (i + 1), a polar coordinate system S_i can be defined which satisfies: (1) The angle between OA_i and OA_ (i + 1) is equal to the angle θ ~ * between two tangent lines O is the origin of S_i); (2) | OA_i | = | OA_ (i + 1) | = R_i. In S_i, the curve is expressed by cubic polynomial as: r_i (θ) = R_i + a_iθ (θ ~ * -θ) (1-2 · θ / θ ~ *) 2. This article derives a general formula for calculating the tangent position: For the five points A_ (i-2), A_ (i-1), A_i, A_ (i + 1) and A_ (i + 2) that satisfy the sufficiently general condition, it is proved that the tangent at A_i is located at A_ (i-1 Therefore, the angle Δβ_i between the tangent at A_i and A_i-A_i is calculated as follows: Δβ_i = γ_i ~ * (P_ (i- 1) S_i / (q_iS_ (i-1) + P_ (i-1) S_i))