inside triangle

%inside_triangle is used to check if a point P is inside
%the triangle P1P2P3 or not.
%
%Inputs: P, P1, P2 and P3 are vectors of length 2 or three of the
% form [x y z] or [x y]
%
%Output: True
%True=1 => P is on or inside P1P2P3
%True=0 => P is outside P1P2P3
%
%Example:
%True=inside_triangle([0.5 0.5],[0 0],[0 2],[2 0]);
%
%The following algorithm is implemented
% If P is ON or INSIDE the triangle
%
% Area(PP1P2) + Area(PP2P3) + Area(PP3P1) = Area(P1P2P3)
%
% If P is OUTSIDE then,
%
% Area(PP1P2) + Area(PP2P3) + Area(PP3P1) > Area(P1P2P3)
%
% Area of a triangle can be found using the determinant:
%
% Area = abs(1/2 * |x1 y1 1| )
% |x2 y2 1|
% |x3 y3 1|
%