luquinhas0021
31st May 2017, 15:32
Be an 1 x [p + 1] data grid, which generates a pth degree interpolation polynomial.
Consider the (x,y) point, and we want know what is the (x + a,y) point value. So, instead we put f(x + 0.5) in the respective pth degree interpolation polynomial, we put intermediate values, the closest as possible to last first interpolation node, and make a new interpolation polynomial with this value.
Example:
An 1 x 4 data grid, with (0,0), (0,1), (0,2) and (0,3) points.. We want interpolate the (0,0.5) point. Instead we put 0.5 replacing x in f(x) = ax^3 + bx^2 + c function interpolation, we put, for example, 0.05 and discover how many is f(0.05). Then, we make a new polynomial with the (0,0.5), (0,1), (0,2) and (0,3) points, and discover the value of the point (0,0.1) point. We catch this value and make a new interpolation polynomial, and so on, still find the (0,0.5) point value.
Sure must have something that seems with it. I wrote it for know your opinion: do you guess that it interpolation method is good for images (Generate better results than the "direct" method)? Logically, it must be adapted for two dimensional case, or, in worst case, the interpolation to be done in x then in y dimension.
Consider the (x,y) point, and we want know what is the (x + a,y) point value. So, instead we put f(x + 0.5) in the respective pth degree interpolation polynomial, we put intermediate values, the closest as possible to last first interpolation node, and make a new interpolation polynomial with this value.
Example:
An 1 x 4 data grid, with (0,0), (0,1), (0,2) and (0,3) points.. We want interpolate the (0,0.5) point. Instead we put 0.5 replacing x in f(x) = ax^3 + bx^2 + c function interpolation, we put, for example, 0.05 and discover how many is f(0.05). Then, we make a new polynomial with the (0,0.5), (0,1), (0,2) and (0,3) points, and discover the value of the point (0,0.1) point. We catch this value and make a new interpolation polynomial, and so on, still find the (0,0.5) point value.
Sure must have something that seems with it. I wrote it for know your opinion: do you guess that it interpolation method is good for images (Generate better results than the "direct" method)? Logically, it must be adapted for two dimensional case, or, in worst case, the interpolation to be done in x then in y dimension.