# Given a plane and a point, how can I determine which side of the plane the point is on?

Given the point

Vector pos = new Vector(0.0, 0.20156815648078918, -78.30000305175781, 1.0);


and the plane (triangle)

Vector a = new Vector(-6.599999904632568, 0.0, -78.5, 1.0);
Vector b = new Vector(6.599999904632568, 0.0, -78.5, 1.0);
Vector c = new Vector(6.599999904632568, 4.400000095367432, -78.5, 1.0);


I want to get a plane normal pointing in the direction of pos

//Getting plane normal
Vector ac = Vector.Subtract(a,c);
Vector bc = Vector.Subtract(b,c);
Vector planeNormal = Vector.CrossProduct(bc, ac);

//Testing which side of the plane the point is on
double dprod = Vector.DotProduct(planeNormal, pos);
if (dprod < 0)
{
planeNormal.Negate();
}


But this method is wrong. The resulting planeNormal points in the negative Z direction, so it should not be negated. Is there a best practise for this? Please help me, I fail massively @ math :)

• I'd normalize the normal, if you're using a similar method for lighting calculations. – Ray Dey Apr 23 '11 at 2:18