Given a 3x3 fixed grid of surface coordinates (the center points of the cells of an elevation raster), is it possible to estimate the Gaussian curvature for the center point of this grid without parameterizing all 9 points into an equation?
Asked
Active
Viewed 56 times
1 Answers
0
It's unclear what your data exactly mean. If they somehow relate to a surface $z=f(x,y)$ the Gaussian curvature computes to $$\kappa={f_{xx}f_{yy}-f_{xy}^2\over(1+f_x^2+f_y^2)^2}\ .$$ Try to estimate this quantity from your data. I don't think that a mere nine points will give a reasonably precise approximation.
Christian Blatter
- 226,825
The thing I want to avoid is parameterizing the points into a function $z=f(x,y)$ since it might get computationally intensive for many points. So I guess, I am looking for a numerical solution to estimating curvature for the center point in the grid.
– TimB Nov 08 '18 at 13:47