US Patent 7143127 Scaling method by using symmetrical middle-point slope control (SMSC)

A method is for scaling data from a source data to a destination data, wherein a function f(x) is determined to describe the destination data, in which x is a deviation from a current reference point 0. Two source data of f(0) and f(1) with respect to the point 0 and the point 1 are used as reference data. The method is performed by setting an initial condition about a primary slope D =f(1)−f(0), f(0.5)=[f(1)+f(0)]/2, a gain factor G>1, and f′(0.5)=DG=[f(1)−f(0)]G The f(x) is taken by a quadratic equation of f(x)=ax2+bx+c, which should pass f(0), f(1), f(0.5) and satisfy the slope of f′(0.5). Coefficients of a, b, and, c, are respectively solved in two ranges of 0≦x<0.5 and 0.5≦x<1, so as to obtain the function f(x) being about symmetric to the middle point at 0.5. The same procedure is applied for a next source data. Preferably, the function is symmetric to the middle point at (0.5, f(0.5)). Also and, a Z transformation of Z(z)=X(x)−0.5 is applied to reduce the calculation load by mapping the one range to the other one range.