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Improve text for aspect that is a cartographical azimuth
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fixes #63
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hugoledoux committed Jan 6, 2025
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9 changes: 4 additions & 5 deletions topofeatures/topofeatures.tex
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Expand Up @@ -98,14 +98,13 @@ \subsection{Slope}%
%%%
\paragraph{Aspect.}
At a given point $p$ on the terrain the gradient can be in any direction, the aspect is this direction projected to the $xy$-plane.
It is basically a 2D vector telling us the direction of the steepest slope at a given point.
It is usually expressed in degrees from an arbitrary direction (most often the north).
It is basically a 2D vector telling us the direction of the steepest slope at a given point; at a given location the aspect will always be perpendicular to the contour line.
Observe that for the parts of the terrain that are horizontal (\eg\ a lake) the value of the aspect is unknown.
Also observe that at a given location the aspect will always be perpendicular to the contour line.


The aspect is usually expressed as a \emph{cartographical azimuth},
\marginnote{cartographical azimuth}
which is expressed in degrees, from the North, clockwise: $0^{\circ}$ means North, $90^{\circ}$ East, $180^{\circ}$ South, and $270^{\circ}$ West.
% GDAL: % https://www.gdal.org/gdaldem.html#gdaldem_aspect
% values between 0° and 360° representing the azimuth that slopes are facing. The definition of the azimuth is such that : 0° means that the slope is facing the North, 90° it's facing the East, 180° it's facing the South and 270° it's facing the West (provided that the top of your input raster is north oriented).



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