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# FAQ: What is the difference between the main output of the CURVATURE function and the optional outputs {out_profile_curve} and {out_plan_curve}?

## Question

What is the difference between the main output of the CURVATURE function and the optional outputs {out_profile_curve} and {out_plan_curve}?

## Answer

The Grid CURVATURE expression is a function of direction, or angle. This means that the value of the curvature varies as the direction changes.

The two main directions of interest are:
1) the direction of maximum slope,
2) the perpendicular to the direction of maximum slope.

The direction of maximum slope is called the 'profile curvature', and its output is generated when naming the out_profile_curve parameter. The perpendicular to the direction of maximum slope is called the 'planform curvature', and its output is generated when naming the out_plan_curve parameter.

The primary output of the CURVATURE expression is an overall curvature of the surface fitted through all 9 cells that compose the immediate 3by3 cell neighbourhood. The formula for CURVATURE is:

curvature = (out_plan_curve) - (out_profile_curve)