How To use Fréchet View

File / Open

• open an input file and display the correspondig Free-space diagram. See File Formats for supported files.

• play with parameter Epsilon and watch the Free-Space diagram change.

• select an algorithm using the panel on the lower left part of the screen:

Curve Algorithm

computes the classical Fréchet Distance for polygonal curves. The answer to the decision problem ("is delta_F <= epsilon ?") is displayed in real-time.

The resulting feasible path is shown as a yellow line inside the free-space diagram. The path may wrap at the right edge of the diagram and continue at the left edge.

Move the mouse pointer over an edge (or a diagonal) to highlight the correspoding parts of the curves.

Show Bounds displays reachable intervals as dotted lines.

Separate Curves moves the input curves apart.

(Optimise und Approximate see below).

Polygon Algorithm

computes the Fréchet distance for simple polygons (i.e. polygons without holes, and without self-intersections).

Decide computes the answer to the decision problem. If successful, the resulting feasible path is shown in the Free-space diagram.

Optimize computes the Fréchet distance (i.e. the smallest possible epsilon) using binary search on a set of critical values.

Approximate computes an approximation result (may sometimes be faster).

k-Fréchet Algorithm

computes the parameter k for the k-Frechet distance.

• the "Greedy" result is shown immediately. Lower and upper bounds for k are shown.

• click "Brute-Force" to compute the exact result; stop the computation if it takes too long.

Connected components are indicated by color.

Click "Show Bounds" to project components to the x- and y-axes. These projected intervals are the basis for the k-Fréchet algorithms.

Print and Save

Curves and the Free-Space diagram can be printed, or saved to disk as a PDF file. (note: saving to an SVG file is available, but may not be accurate. Do prefer PDF).

Command Line

There is a Command Line Interface with some more options.