Is a Point Inside or Outside a Complex Shape Using the Odd-Even Rule?

[sachinism]

how do we tell whether a point is inside a given surface or outside a given surface?

p.s: the shape i am talking about is complicated and is not necessarily represented by a equation

 

[HallsofIvy]

All of that will depend upon how you are "given" the surface and what you mean by "inside" and "outside". Are you assuming that this is a closed surface so that it separates three dimensional space into an "inside" and an "outside"? If so then the "outside" is the set that contains points "at infinity". No matter how complicated a closed surface is, you can always determine whether a point is "inside" or "outside" by looking at a line from that point to infinity. The point is inside the surface if and only if such a line crosses the surface in an odd number of points and is outside the surface if and only if it crosses the surface in an even number of points (which would include 0 points).

 

[sachinism]

thx

the odd even rule helped