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Fix a few cosmetic things I saw
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hugoledoux committed Nov 9, 2020
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3 changes: 2 additions & 1 deletion conversion/conversion.tex
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Expand Up @@ -74,6 +74,7 @@ \section{Conversion to isolines}%
The resulting set of segment lines forms an approximation of the isoline.
This process is then repeated for every level value.
Notice that an isoline can have several \emph{components}, for instance when the terrain has more than one peak.
\marginnote{isoline component}\index{isoline component}

Therefore the number and size of the line segments in the resulting isoline are dependent on the resolution of the data representation.
% Consequently by refining that data representation, \eg\ by performing interpolation, the resolution of the contour lines is improved.
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%

As shown in Figure~\ref{fig:isoline2}b, another solution is to find \emph{one} cell \(\tau_0\)intersecting the isoline at a given elevation, `tracing' the isoline by navigating from \(\tau_0\)to the adjacent cell, and continuing until \(\tau_0\)is visited again (or the border of the dataset is reached).
As shown in Figure~\ref{fig:isoline2}b, another solution is to find \emph{one} cell \(\tau_0\) intersecting the isoline at a given elevation, `tracing' the isoline by navigating from \(\tau_0\)to the adjacent cell, and continuing until \(\tau_0\) is visited again (or the border of the dataset is reached).
To navigate to the adjacent cell, it suffices to identify the edge \(\epsilon\) intersecting the isoline, and then navigating to the triangle/cell that is incident to \(\epsilon\).
It is possible that there is no adjacent cell, if the boundary of the convex hull is reached in a TIN for instance.
This requires that the TIN be stored in a topological data structure in which the adjacency between the triangles is available (for a grid this is implied).
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2 changes: 1 addition & 1 deletion topofeatures/topofeatures.tex
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Expand Up @@ -31,7 +31,7 @@ \section{Slope}
\end{figure}

The slope at a given location $p$ on a terrain is defined by the plane $H$ that is tangent at $p$ to the surface representing the terrain (see Figure~\ref{fig:slope_concept}).
What we casually refer to as ``slope'' has actually two components: (1) gradient; (2) aspect (see Figure~\ref{fig:slope_aspect}).
What we casually refer to as `slope' has actually two components: (1) gradient; (2) aspect (see Figure~\ref{fig:slope_aspect}).
\begin{figure}
\centering
\includegraphics[width=\linewidth]{figs/slope_aspect}
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