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André Nusser 2024-06-18 18:09:24 +02:00
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Frechet_distance/doc/Frechet_distance/Frechet_distance.txt
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@ -12,18 +12,24 @@ namespace CGAL {
<img src="FrechetTeaser.jpg" style="max-width:70%;"/>
</center>
This package provides functions for computing the Fréchet distance of polylines in any dimension under Euclidean metric.
This package provides functions for computing the Fréchet distance of polylines in any dimension under the Euclidean metric.
\section secFrechetDistanceIntroduction Introdution
The Fréchet distance .....
The Fréchet distance is a classical dissimilarity measure between polylines.
Its advantages over other measures is that it consideres the polylines as a continuous objects and that it takes into account the order of the points.
Intuitively, the Fréchet distance is commonly explained as follows: Imagine a human walking on one polyline while a dog walks on the other polyline, they are connected by a leash, and they are only allowed to walk forward. The Fréchet distance is the shortest leash length that allows both the human and dog walk from start to end on their respective trajectories.
\cgalFigureBegin{figRefId,pdist-pkg-small.png}
Here you can put the caption
\cgalFigureEnd
The Fréchet distance is a metric and hence two polylines that are equal (disregarding consecutive colinear points) have a distance of zero.
\section secFrechetDistanceAPI API
The package provides one function to approximate the Fréchet distance and one function to decide whether the Fréchet distance is at most a given value.
The function `continuous_Frechet_distance()` computes an approximation of the Fréchet distance between two polylines,
up to a given approximation error. It returns an interval.
The function `continuous_Frechet_distance_less_than()` decides if the Fréchet distance
@ -44,13 +50,13 @@ the algorithm switches to the usage of square root extensions.
\subsection subsecFrechetDistanceFirstExample Decision for 2D Polylines
The following example shows ...
The following example shows how we can use `continuous_Frechet_distance_less_than()` to decide whether the Fréchet distance between two polylines in the Euclidean plane is at most a given value.
\cgalExample{Frechet_distance/Frechet_distance_2.cpp}
\subsection subsecFrechetDistanceSecondExample Distance Computation for 3D Polylines
The following example shows ...
The following example shows how we can compute the Fréchet distance up to a given precision on two polylines in 3-dimensional Euclidean space using `continuous_Frechet_distance()`.
\cgalExample{Frechet_distance/Frechet_distance_3.cpp}
@ -58,7 +64,7 @@ The following example shows ...
\subsection subsecFrechetDistanceImplementation Implementation History
An intial version using floating point arithmetic was developed by the authors
while working at the Max-Planck Institute of Computer Science in Saarbrücken.
while working at the Max Planck Institute for Informatics in Saarbrücken, Germany.
André Nusser, together with Sebastien Loriot and Andreas Fabri, introduced
the usage of interval arithmetic and square root extensions to achieve a certified result.