PDF功能2型指数插值方程

Question

I'm modifying an application that does PDF manipulation. The function written to interpret functiontype 2s seems to produce a negative value far too frequently. The equation found in the PDF spec is:

yj = C0j + x^N × (C1j − C0j), for 0 ≤ j < n.

Now, I'm getting negative values when I process a function with C0=1 and C1=0. I'm wondering if this is because I'm setting my own x value. What is the x value supposed to be?

Answer 1

The function is computed like this:
1. Input value is cut to function domain:
input = input > domainMax ? domainMax : (input < domainMin ? domainMin : input)
2. Compute inputN = input^N
3. Compute each component of the output value (1 component in your situation) using the formula:
output[j] = C0[j] + inputN * (C1[j] − C0[j]), for 0 ≤ j < n.
4. Cut each output component to function range:
output = output > rangeMax ? rangeMax : (output < rangeMin ? rangeMin : output)

Your function is a linear function (indeed can be used to define a gradient) and returns 0 when input is 1 and 1 when input is 0. Input values greater than 1 are invalid and they are cut to 1 before using them in calculation because the domain is [0, 1].
The application that parses spot color percentages might have to divide that percentage by 100 before feeding it to the function.