Scaling method by using dual point cubic-like slope control ( DPCSC)

An apparatus configured with a scaling function f(x) to scale source data into output data, wherein x is a deviation from a current reference point 0, and two reference data of f(0) and f(1) are used as reference data, the apparatus comprising:

• an initial part to set an initial condition about a slope D with respect to the function f(x) at the point 0, a gain factor G to time the slope D, and f′(0)=f′(1)=DG, wherein the f(x) is a quadratic equation of f(x)=ax2+bx+c, which should pass f(0), f(1), and a middle point f(0.5) by a quantity of f(0.5)=[f(0)+f(1)]/2;
• a calculation part to solve the coefficients of a, b, and, c, in two ranges of 0≦x<0.5 and 0.5≦x<1, so as to obtain the function f(x), with a joint at the middle point;
• and
• a scaling part to scale the source data based on the solved function f(x).

A method for generating destination data samples f(x) in response to two source data samples f(0) and f(1), wherein f(x) is generated for x in a range of 0≦x<1, said method comprising the steps of:

• (a) generating a middle point sample f(0.5) by defining f(0.5)=[f(0)+f(1)]/2;
• (b) fitting a quadratic equation of f(x)=ax2+bx+c to said source data samples f(0) and f(1) and said middle point sample f(0.5);
• and
• (c) generating a resulting equation f(x)=2[f(1)−f(0)−DG]x2+(DG)x+f(0) for one subregion of 0≦x<0.5 and f(x)=2[DG+f(0)−f(1)]x2+[4f(1) −4f(0)−3DG]x+[DG−f(1)+2f(0)] for another subregion of 0.5≦x<1, wherein DG designates a slope at said source data samples f(0) and f(1).