[GRASS-user] [GRASSLIST:1160] RE: Surface area of a DEM

[Hamish]

> Jonathan Greenberg wrote:
> 
> > I was thinking this, but does the fact that a DEM grid cell is
> > square cause complications in this formulation?  A 45 degree slope
> > to the west would have a different surface area than a 45 degree
> > slope to the southwest.  I've come across some solutions that use a
> > set of 8 triangles created by the lines between the center cell and
> > each of its 8 neighbors to help in the calculation, but I was hoping
> > this ability might be buried in a GRASS command someplace.
> 
me:
> think of each cell as a spinning dinner plate on a stick.
> 
> you can rotate each cell in the direction of the aspect, and the
> slope->projected area will be the same.

that is all wrong of course.


take a cube of side "1", apply a plane in it of 45 degrees (W aspect)
to cut the cube in two parts. (each shaped like a monopoly-house roof)

one side is unit length of 1, the other sqrt(2). area=sqrt(2).


take the same cube, this time with an aspect of SW. when you cut the
cube this time you get two 4-sided pyramids. area of the plane is
sqrt(2)*sqrt(2) = 2.



Hamish