- #1
Saladsamurai
- 3,020
- 7
So I have this surface that I am trying to make approximations on. Now I have values for [itex]f(x_1,y_1)[/itex] and [itex]f(x_2,y_2)[/itex]. I want to find the value of [itex]f(x,y)[/itex] where x and y lie between (x1, x2) and (y1, y2). I am willing to assume that f changes linearly in both x and y for this small interval. Would the appropriate interpolation function then be
[tex]f(x,y)=f(x_1,y_1) + \frac{f(x_2,y_2) - f(x_1,y_1)}{x_2 - x_1} *(x - x_1) + \frac{f(x_2,y_2) - f(x_1,y_1)}{y_2 - y_1} *(y - y_1)[/tex]
?
I feel like it would be ... but I also feel like it could be
[tex]
f(x,y)=
f(x_1,y_1) +
\sqrt{
[\frac{f(x_2,y_2) - f(x_1,y_1)}{x_2 - x_1} *(x - x_1)]^2
+
[\frac{f(x_2,y_2) - f(x_1,y_1)}{y_2 - y_1} *(y - y_1)]^2
}
[/tex]What do you think? I am really confusing myself here First or second one?
[tex]f(x,y)=f(x_1,y_1) + \frac{f(x_2,y_2) - f(x_1,y_1)}{x_2 - x_1} *(x - x_1) + \frac{f(x_2,y_2) - f(x_1,y_1)}{y_2 - y_1} *(y - y_1)[/tex]
?
I feel like it would be ... but I also feel like it could be
[tex]
f(x,y)=
f(x_1,y_1) +
\sqrt{
[\frac{f(x_2,y_2) - f(x_1,y_1)}{x_2 - x_1} *(x - x_1)]^2
+
[\frac{f(x_2,y_2) - f(x_1,y_1)}{y_2 - y_1} *(y - y_1)]^2
}
[/tex]What do you think? I am really confusing myself here First or second one?