| 摘要 |
A scaling method is to scale source data to destination data, wherein three reference points of the source data denoted as -1, 0, and 1. Function f(x)=ax<2>+bx+c are used to describe the destination data within 0 and 1. The method includes setting a midpoint 0.5 with a quantity of f(0.5)=[f(0)+f(1)]/2 and f'(0)=f'(1)=DG, wherein D is a slope of [2f(0)-f(-1)-f(1)], and G is a gain factor to adjust the slope. Curve f(x) passes through the points of 0, 0.5, and 1. The coefficients of a, b, and c for f(x) are solved by a range of 0<=x<0.5 and a range of 0.5<=x<1, so that the f(x) is symmetric or substantially symmetric to the midpoint. Curve is set to have: f(x)=2[f(1)-f(0)-DG]x<2>+(DG)x+f(0) for 0<=x<0.5; and f(x)=2[DG+f(0)-f(1)]x<2>+[4f(1)-4f(0)-3DG]x+[DG-f(1)+2f(0)] for 0.5<=x<1.
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