# [Gdal-dev] RE: shaded relief utility (DIY)

Charles Wivell Charles.Wivell at dnr.state.mn.us
Mon Nov 6 09:21:37 EST 2006

```Hi George;

The equation you have is the gradient of z in either the x or y
direction (the matrix can also be used to calculate an edge image (Sobal
edge image)).

The equation will give you elevation between postings. However, to
create a shaded relief, you need to calculate the illumination angles.
To do that you first need to find the normal vector to the elevation
surface = tangent at a point. You then need to create a vector from your
point to your light source (the Sun?). The angle between these two
vectors is the zenith angle. A brightness value can then be calculated
using B = Acos(zenith_angle). Where A is just a scalar to get your
brightness in the range you want.

You could use the gradient equation to find the tangent vector in the x
direction and the tangent vector in the y direction and then cross the
two vectors to get the normal vector at that point.

Usually a shaded relief is just a qualitative thing, so a good
approximation is just to create two vectors between one positing (the
posting of interest) and the next posting in the x direction and the
next posting in the y direction. If you then cross these two vectors,
you get the approximate normal at the posting of interest.

Chuck

=====================================
Charles Wivell
MN DNR Forestry/Resource Assessment
413 SE 13th Street
Grand Rapids, MN 55744
218-327-4449 x 233
=====================================

>>> odhiambo george <odhiambogeorge at yahoo.com> 11/1/2006 5:38 AM >>>
Dear Sir,

I'm trying to write a MATLAB program for calculating or creating
shaded relief from a DEM. I have come across the equation attached to
this e-mail which i believe represents calculation of the cell values
heights.

What I don't undersyand is how to handle the DEM, for example, how do
I use the DEM together with the equation  ?

Kindly assist by shedding some light on the procedure used

Kind regards,
George

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