The Curvature option enables you to calculate the curvature of a raster at the center of each cell. You can generate three types of curvature grids in MapInfo Pro Advanced.
- Profile curvature - A profile curvature is calculated along the direction of the maximum slope on a surface. You can use profile curvature to calculate the flow of water in a terrain and calculate soil erosion and deposition. In locations where the cell value is negative, the surface is convex at that cell. This indicates erosion of soil. On the other hand, in locations where the cell value is positive, the surface is concave at that cell. This indicates soil deposition on the surface. In locations where the cell value is zero, the surface is flat.
- Plan curvature - A plan curvature is calculated across the direction of the maximum slope. You can use plan curvature to visualize ridges and valleys. A positive cell value indicates the surface is convex. A negative cell value indicates the surface is concave.
- Surface curvature - A surface curvature is calculated as the difference between profile and plan curvatures.
How is Curvature Calculated
A curvature of a surface is calculated for the center cell (Z0) for a 3x3 window, as shown below:
For each cell in the window, the coefficients D through H of the following quadratic equation is calculated.
Z = A*x^2*y^2 + B*x^2*y + C*x*y^2 + D*x^2 + E*y^2 + F*x*y + G*x + H*y + I
Where:
D = [(Z4 + Z5)/2 - Z0] / (Cell_Size)^2
E = [(Z2 + Z7)/2 - Z0] / (Cell_Size)^2
F = (-Z1 + Z3 + Z6 - Z8) / 4 * (Cell_Size)^2
G = (-Z4 + Z5) / 2 * (Cell_Size)
H = (Z2 - Z7) / 2 x (Cell_Size)
The Profile curvature is calculated as:
Profile_Curvature = -2 *[(D*G^2 + E*H^2 + F*G*H) / (G^2 + H^2)]
The Plan curvature is calculated as:
Plan_Curvature = 2 *[(D*H^2 + E*G^2 - F*G*H) / (G^2 + H^2)]
The Surface curvature is calculated as:
Surface_Curvature = -2 *(D + E)