True=inside_triangle(P,P1,P2,P3);

function True=inside_triangle(P,P1,P2,P3);
%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|
%

%Written by: Nassim Khaled-July 2009
x1=P1(1);
y1=P1(2);

x2=P2(1);
y2=P2(2);

x3=P3(1);
y3=P3(2);

x=P(1);
y=P(2);

Area_PP1P2 = 1/2. *abs(det([x y 1;x1 y1 1;x2 y2 1]));
Area_PP2P3 = 1/2. *abs(det([x y 1;x2 y2 1;x3 y3 1]));
Area_PP3P1 = 1/2. *abs(det([x y 1;x3 y3 1;x1 y1 1]));
Area_P1P2P3 = 1/2. *abs(det([x1 y1 1;x2 y2 1;x3 y3 1]));
Sum=(Area_PP1P2 + Area_PP2P3 + Area_PP3P1);
True=isequal(Sum, Area_P1P2P3);