Question

I am creating a java application. I need to calculate the determinant of three point. I have calculated it:

     static int determinant(Point point1, Point point2, Point point3) {
    int x1 = point1.x;
    int x2 = point2.x;
    int x3 = point3.x;
    int y1 = point1.y;
    int y2 = point2.y;
    int y3 = point3.y;
    return (x1 * y2) + (x3 * y1) + (x2 * y3) - (x3 * y2) - (x2 * y1)
            - (x1 * y3);
}

(I am not good in math)But, I found the following when I searched about it:

public int ccw(int p1, int p2, int p3)
{
return (xPoints[p2] - xPoints[p1])*(yPoints[p3] - yPoints[p1]) - (yPoints[p2] -    yPoints[p1])*(xPoints[p3] - xPoints[p1]);
}

which one is the correct method? If the first method is the correct one, what does the second method do?

Answer 1

both equations are the same. there is no mathematical difference between the two.

someone better at math than I could probably give you the mathematic proof. I chose to go the practical route, implemented in python, because I can

def fun1(p1,p2,p3) :
   print (p1[0]*p2[1])+(p3[0]*p1[1])+(p2[0]*p3[1]) - (p3[0]*p2[1]) - (p2[0]*
   p1[1]) - (p1[0]*p3[1])

def fun2(p1,p2,p3) :
   print (p2[0]-p1[0])*(p3[1]-p1[1])-(p2[1] - p1[1])*(p3[0]-p1[0])

>>> fun1((0,0),(9,1),(3,2))
15
>>> fun2((0,0),(9,1),(3,2))
15
>>> fun2((33,5),(4,6),(8,1))
141
>>> fun1((33,5),(4,6),(8,1))
141

for any 3 points, fun1 and fun2 will yield the same result.