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TerrainProviderGetHessian Method

Get the interpolated hessian matrix based on the function of height with respect to the specified longitude and latitude relative to the provider's Shape. This method produces a matrix representing the mixed second order partial derivatives of height in the ShapeFixedFrame.

Note: The direction for the gradient and hessian is defined for use with the directional derivative on the surface. The gradient is defined to be orthogonal to the terrain surface with its surface projection in the direction of the greatest increase in the height. To obtain the second directional derivative for the height (acceleration of height along a particular azimuth), take the negative of the hessian then pre and post multiply it by the velocity vector along the desired azimuth. Then add the negative gradient dotted with the derivative of the velocity vector along the surface.

Namespace:  AGI.Foundation.Terrain
Assembly:  AGI.Foundation.Models (in AGI.Foundation.Models.dll) Version: 19.5.402.0 (19.5.402.0)
Syntax
public Matrix3By3 GetHessian(
	double longitude,
	double latitude
)

Parameters

longitude
Type: SystemDouble
The longitude, in radians. Requesting a gradient for a longitude less than -PI or greater than PI will always return NaN.
latitude
Type: SystemDouble
The latitude, in radians. Requesting a gradient for a latitude less than -PI/2 or greater than PI/2 will always return NaN.

Return Value

Type: Matrix3By3
The hessian matrix expressed in the ShapeFixedFrame at the given location, with units of meters of height per meters of surface distance squared.
See Also