A plane through 3 points

Questions
1

I would like to apply this formula equation-of-a-plane-passing-through-3-points to my javascript code.

I have three points p1, p2, p3

  const a1 = p2[0] - p1[0];
  const b1 = p2[1] - p1[1];
  const c1 = p2[2] - p1[2];
  const a2 = p3[0] - p1[0];
  const b2 = p3[1] - p1[1];
  const c2 = p3[2] - p1[2];

    const a = b1 * c2 - b2 * c1;
    const b = a2 * c1 - a1 * c2;
    const c = a1 * b2 - b1 * a2;

    const d = (-a * p1[0] - b * p1[1] - c * p1[2]);

    console.log(p1);
    console.log(p2);
    console.log(p3);
    console.log(" formula π: " + a + "x +" + b + "y + " + c + "z + " + d + "= 0");

Then I get the plane

new THREE.Plane(new THREE.Vector3(a, b, c), d)

It looks nice but…the d value looks bad. As you can see in my attached image the helper of the plane (clipPlanes) used to cut off my object has a gap.

Can you help me to fix it?

Schermata 2020-08-23 alle 17.55.41
Schermata 2020-08-23 alle 17.55.411124×560 37.3 KB

2

Try it with Plane.setFromCoplanarPoints(). Just pass in your three points and let the plane class do the math for you.

2 Likes
3

Thanks a lot!!! It looks much more simple than my formula!! THANKS!

But I got an error, can you help me to use it correctly?

    p1 = [0, h1, l];
    p2 = [0, h1, 0 ];
    p3 = [w, h2, 0];
    let v1 = new THREE.Vector3( p1 );
    let v2 = new THREE.Vector3( p2 );
    let v3 = new THREE.Vector3( p3 );
    let cutPlane = new THREE.Plane();
    const pl = cutPlane.setFromCoplanarPoints(v1,v2,v3);
    //clipPlanes.push(new THREE.Plane(new THREE.Vector3(a, b, c), d));
    console.log(pl)
    clipPlanes.push(pl);

Then I apply the plan to cut the object as

  materialPlanes = new THREE.MeshLambertMaterial({
    color: new THREE.Color().setHSL(0, 0.5, 0.5),
    side: THREE.DoubleSide,
    clippingPlanes: clipPlanes,
    clipIntersection: params.clipIntersection,
  });

I got a generic error but in the console the plane looks missing constant

Plane {normal: Vector3, constant: NaN}

constant: NaN
normal: Vector3

Thanks again!!

4

Set it directly:

    let v1 = new THREE.Vector3( 0, h1, l );
    let v2 = new THREE.Vector3( 0, h1, 0 );
    let v3 = new THREE.Vector3( w, h2, 0 );
1 Like
5

Right!!! Lol!! I’m done!! Thanks!!!

1 Like