Point in polygon python3
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point in polygon (pip) tutorial
the point in polygon (pip) problem is a common computational geometry problem that determines whether a given point lies inside, outside, or on the boundary of a polygon. this has various applications in computer graphics, geographic information systems (gis), and game development.
algorithms for pip
there are several algorithms to solve the pip problem. two of the most commonly used are:
1. **ray casting algorithm**: this algorithm counts how many times a ray, starting from the point in question and extending infinitely in one direction, intersects with the edges of the polygon. if the count is odd, the point is inside; if even, the point is outside.
2. **winding number algorithm**: this algorithm calculates the winding number of the point with respect to the polygon. the winding number is the total number of times the polygon winds around the point. if it's non-zero, the point is inside.
implementation of ray casting algorithm
let's implement the ray casting algorithm in python.
step-by-step implementation
1. **define the polygon**: the polygon will be defined as a list of vertices.
2. **define the point**: the point we want to test.
3. **ray casting logic**: implement the logic to count the intersections.
code example
here's a complete python implementation using the ray casting approach:
explanation of the code
1. **function definition**: the function `is_point_in_polygon` takes a `point` and a `polygon` as arguments.
2. **initialization**: the number of vertices `n` is calculated, and a boolean `inside` is initialized to track if the point is inside the polygon.
3. **loop through polygon edges**: the function iterates through each edge of the polygon:
- it checks if the horizontal ray from the point intersects the edge.
- if it does, the `inside` boolean is toggled.
4. **return result**: finally, the function returns whether the point is inside the polygon.
example output
when you ...
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