Checking if points are contained within a shape

Hi, I am working on an a script which aims to generate opposite points within a shape, from a random starting point (inside the shape). My strategy for generating points is as follows:

1. Choose a random starting point (p_0)
2. Find the boundary point (p_b) closest to p_0. E.g. r = p_0 + t (p_b - p_0)
3. Using the vector generated from the p_b traverse until you reach the opposite point (p_opp) on line r.
4. Choose random direction and repeat from 2. until the required number of points are generated.

My problem is that when I try to traverse the line to find the opposite point I end up exceeding the shape boundary. Is there any other way to check if a point is contained within a shape or force it to stay within the shape? I am currently using inpolygon; Also is it possible to do this in higher dimensions like R^n, n=1,2,3,...,i?

My implementation for finding opposite points on a line:

    % Find the difference between the two points:
    v = p1 - p2;
    t = 1;
    p3 = p1 + t*v;
    while (inpolygon(p3(1),p3(2),b(:,1),b(:,2)))
         p3 = p1 + t*v; % Extrapolate until boundary is reached
         t = t + 1;
    end 
    opp = p1 + (t-2)*v; % Find a point distance t-2 from the boundary. (To make sure its inside the shape)

[Image Analyst]

How are you defining "opposite"? Two points that are on the perimeter and go through some arbitrary interior point are not necessarily on opposite sides of the shape. I think though if the interior point was the centroid, that you could claim that.

[Raazi Rizvi]

I am defining it as diametrically opposed for exampled for point (1,1,1) the opposite would be at (-1,-1,-1).

Answer 1

[Kelly Kearney]

Do you have the Mapping Toolbox? If so, polyxpoly may be helpful to calculate exactly where you'll hit the polygon boundary. The toolbox has several other polygon-related functions that could be useful.