Is it in the polygon? The challenge
Given point and a path of points, say whether or not the point is in the polygon that is created by the path.
Also return true if the point is on an edge of the polygon.
Input
A list of pairs of integers.
The first 2 integers represent the point.
The remaining pairs (3rd and 4th, 5th and 6th etc.) represent the vertices of the polygon.
The edges are in the order of the input pairs.
The path is assumed to loop back to the first point of the path.
The input is assumed to be valid.
No three points in the path are collinear.
ex. 123 82 84 01 83 42
Output
A truthy/falsy value.
Test cases
Input -&gt; Output
0 0 10 10 10 -1 -5 0 -&gt; true
5 5 10 10 10 50 50 20 -&gt; false
5 5 0 0 0 10 1 20 6 30 10 -40 -&gt; true
This is code-golf. Shortest answer in bytes wins.
Charcoal, 52 50 bytes
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Try it online! Link is to verbose version of code. Explanation:
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Split the input into pairs of coordinates.
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Calculate the area of three polygons: the one formed by taking the last, first and second points; the one formed from all of the points (including the test point); the one formed from all of the points except the test point.
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Use the shoelace formula to calculate the area of that polygon.
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Check whether the last area equals the sum of the first two. If this is the case, then the point lies within the polygon.