square.dat $-$ Notepad hyp$-$veh$-$cross$-$sect$.$dat $-$ Notepad

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$-0\mathrm{.}14843-0\mathrm{.}017512$Define a class called Boundary to represent a polygonal domain with temperature values at the polygon vertices. Implement two methods: $\_\_$init$\_\_$ and distance$\_$to$\_$closest$\_$edge. The points of the polygon and temperatures are supplied in a text file. The $\_\_$init$\_\_$ method should read that file and store values in a manner of your choosing. Here is an example file that corresponds to an square domain, note that the final line repeats the first point. This was a deliberate choice in the file representation. Other representations are possible but this one makes coding convenient when treating consecutive points as defining edges. In this file column $1$ is x position of a point, column $2$ is y position and column $3$ is the temperature value. Each row represents a point plus its temperature.

$0\mathrm{.}00\mathrm{.}0600\mathrm{.}0$

$1\mathrm{.}00\mathrm{.}0700\mathrm{.}0$

$1\mathrm{.}01\mathrm{.}01000\mathrm{.}0$

$0\mathrm{.}01\mathrm{.}0850\mathrm{.}0$

$0\mathrm{.}00\mathrm{.}0600\mathrm{.}0$

The other method to write is distance$\_$to$\_$closest$\_$edge. For a given point interior to the polygon, this method should locate the closest edge and find the distance to the closest point on the line segment of that closest edge. You should make use of the function you built earlier: closest$\_$point$\_$on$\_$line$\_$segment. You will need to treat every edge of the polygon as a line segment and test all edges in turn to find the closest. When you have found the closest, return a tuple of form $($edge$\_$index, distance$).$ The

edge$\_$index $($integer$)$ is defined as the index of the first point on the segment. The distance is the closest distance to the closest edge that you located.

The code snippet below shows the skeleton of what is required for the Boundary class in this task.

class Boundary$()$:

def $\_\_$init$\_\_($self$,$ filename$)$:

$"""$Reads filename and stores points and temperature values for later use."""

def distance$\_$to$\_$closest$\_$edge$($self$,$ p$)$:

$"""$Given point p$,$ return $($edge$\_$index, distance$)$ of closest edge and distance to

$,->$ that edge."""

We can test this code using a square. The file is square.dat.

$>>>$ square $=$ Boundary$("$square$.$dat"$)$

$>>>$ square.distance$\_$to$\_$closest$\_$edge