math - Check which side of a plane points are on

Question

I'm trying to take an array of 3D points and a plane and divide the points up into 2 arrays based on which side of the plane they are on. Before I get to heavily into debugging I wanted to post what I'm planning on doing to make sure my understanding of how to do this will work.

Basically I have the plane with 3 points and I use (pseudo code):

var v1 = new vector(plane.b.x-plane.a.x, plane.b.y-plane.a.y, plane.b.z-plane.a.z);
var v2 = new vector(plane.c.x-plane.a.x, plane.c.y-plane.a.y, plane.c.z-plane.a.z);

I take the cross product of these two vectors to get the normal vector.

Then I loop through my array of points and turn them into vectors and calculate the dot product against the normal.

Then i use the dot product to determine the side that the point is on.

Does this sound like it would work?

Answer 1

Let a*x+b*y+c*z+d=0 be the equation determining your plane.

Substitute the [x,y,z] coordinates of a point into the left hand side of the equation (I mean the a*x+b*y+c*z+d) and look at the sign of the result.

The points having the same sign are on the same side of the plane.

Honestly, I did not examine the details of what you wrote. I guess you agree that what I propose is simpler.