Test if 2 planes are coplanar

Grasshopper
1

What would be the best way to check if two planes are co-planar?

Would it be enough to check angle between planes normals?

Or there would be more cases when they coplanar?

planariy
planariy.png1096×906 16.3 KB

1 Like
2

Yes, normal angle will be sufficient. Though you’ll have to decide whether anti-parallel normals also count as coplanarity.

Edit: yup, I was confused. Coplanarity requires that the normals are (anti)parallel within tolerance, and that the distance from the origin of each plane to the other plane is within tolerance.

3

Also, depends if you want to test that they are in the same physical plane then you should check origin as well as normals.

4

Parallel normal only means that the planes are parallel. There could be an offset between the planes and therefore not coplanar.

Draw a line between a point on each plane. If the angles between that line and the normal of each plane are 90 degrees, and the angle between the normal is 0 degrees then the planes are coplanar.

1 Like
5

I needed this as well! here is a small definition for checking parallelity and coplanarity!
coplanar.gh (15.6 KB)

coplanar
coplanar1586×630 72.8 KB

6

Yes, yes, there is a simpler way:
coplanar.gh (12.2 KB)

coplanar
coplanar.png1071×460 40.7 KB

1 Like
7

Thanks it seems to work, I was using this for bisectors:

    /// <summary>
    /// Be careful with colinear planes a.XAxis and a.YAxis can change
    /// </summary>
    /// <param name="a"></param>
    /// <param name="b"></param>
    /// <param name="tolerance"></param>
    /// <returns></returns>
    public static Plane BisectorPlane(Plane a, Plane b, double tolerance = 0.01)
    {
        double angle = Vector3d.VectorAngle(a.ZAxis, b.ZAxis);

        if (angle > (1 - tolerance) * Math.PI || angle < tolerance) {
            Plane p = new Plane((a.Origin + b.Origin) * 0.5, a.XAxis, a.YAxis);
            p.Rotate(Math.PI * 0.5, p.XAxis);

            return p;

        }

        Rhino.Geometry.Intersect.Intersection.PlanePlane(a, b, out Line lnA);
        a.Translate(a.ZAxis * 10);
        b.Translate(b.ZAxis * 10);
        Rhino.Geometry.Intersect.Intersection.PlanePlane(a, b, out Line lnB);
        return new Plane(lnA.From, lnA.To, lnB.PointAt(0.5));

    }