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How do you know if a point is inside a polyhedron?
Typically this involves casting a ray in any direction and counting the number of intersections. If the point is inside the polygon it will only intersect once (regular polyhedrons are not concave), and if its outside it will intersect zero or twice.
How do you find out if a point is inside a polygon?
One simple way of finding whether the point is inside or outside a simple polygon is to test how many times a ray, starting from the point and going in any fixed direction, intersects the edges of the polygon. If the point is on the outside of the polygon the ray will intersect its edge an even number of times.
Does the point lie on the circle?
If the distance is greater than the radius, the point lies outside. If it’s equal to the radius, the point lies on the circle. And if it’s less than the radius, you guessed it right, the point will lie inside the circle. As simple as that!
How do you find a point in a polyhedron?
As a first step, find the point on the surface of the mesh closest to the point. You need to keep track the location, and specific feature: whether the closest point is in the middle of face, on the edge of the mesh, or one of the vertices of the mesh.
When do you know if a point is inside a mesh?
When at some point the face index returns -1, you know there are no more faces between the checked point and the end point, then you add up the total number of intersections. If that number is even, it went in and out, and is currently out.
How to determine the interior of a polygon?
Another solution forwarded by Philippe Reverdy is to compute the sum of the angles made between the test point and each pair of points making up the polygon. If this sum is 2pi then the point is an interior point, if 0 then the point is an exterior point.
How to determine the status of a point in a polygon?
To determine the status of a point (x p,y p) consider a horizontal ray emanating from (x p,y p) and to the right. If the number of times this ray intersects the line segments making up the polygon is even then the point is outside the polygon. Whereas if the number of intersections is odd then the point (x p,y p) lies inside the polygon.