It sounds like you are trying to understand how a bilinear interpolation method was used to transform one set of points (the right figure) to another set of points (the left figure), but you are not sure how to express the equation algebraically. Here is an explanation that may help:
- Bilinear interpolation is a method for estimating values between two points in a two-dimensional space. In this case, the two points are the four corners of a square or rectangle that contains the point of interest. The method works by fitting a bilinear function to the four points and using this function to estimate the value at the point of interest.
- In your case, it sounds like the bilinear interpolation method was used to transform the points of the right figure to the points of the left figure. To do this, you would need to define a transformation function that maps each point in the right figure to its corresponding point in the left figure.
- One way to do this is to use a biharmonic spline method, which is a type of smoothing function that can be used to interpolate values between data points. The biharmonic spline method fits a function to the data points that minimizes the curvature of the function, which helps to reduce errors and produce a smooth transformation.
When you use the cftool function in MATLAB, it fits a curve or surface to your data using various interpolation and smoothing techniques. The details of how the curve or surface is fitted depend on the options you select in cftool and the type of data you are working with.
