Problem with transform.InverseTransformDirection and non-uniform scale

Questions & Answers
1

I made the plane to work with mesh vertices

var plane = new Plane(
     hit.transform.InverseTransformDirection(normal),
     hit.transform.InverseTransformPoint(position)
);

If the object has the uniform scale then all looks good

alt text

but otherwise the plane normal has weird angle and I don’t understand why.

alt text

with.InverseTransformVector even worser. The angle goes 2 times bigger

alt text

Blue line - my plane

Green spheres - plane intersections

white sphere - plane center

UPDATE

There is code to reproduce

Place component to default cube in zero position, rotate it with Y != 0, scale ONE horizontal dimesion. You will see onesided plane.

using UnityEngine;

public class PlaceOnCube : MonoBehaviour
{
public Vector3 PlaneOrigin = new Vector3(0, 0, 0);
public Vector3 PlaneNormal = new Vector3(1, 0, 0);

private void OnDrawGizmos()
{
    Gizmos.DrawSphere(PlaneOrigin, .03f);

    var plane = new Plane(
           transform.InverseTransformDirection(PlaneNormal),
           transform.InverseTransformPoint(PlaneOrigin)
           );

    ReGeneratePlane(plane);
}

private void ReGeneratePlane(Plane plane)
{
    var meshfilter = transform.GetComponent<MeshFilter>();
    var mesh = meshfilter.mesh;
    var tris = mesh.triangles;
    var verts = mesh.vertices;
    var newTris = new int[36 + 6];
    var newVerts = new Vector3[24 + 4];

    for (int j = 0; j < verts.Length; j++)
        newVerts[j] = verts[j];

    newVerts[24] = plane.ClosestPointOnPlane(new Vector3(-2, -1, 0));
    newVerts[25] = plane.ClosestPointOnPlane(new Vector3(2, -1, 0));
    newVerts[26] = plane.ClosestPointOnPlane(new Vector3(-2, 1, 0));
    newVerts[27] = plane.ClosestPointOnPlane(new Vector3(2, 1, 0));

    for (int j = 0; j < tris.Length; j++)
        newTris[j] = tris[j];

    newTris[36] = 24;
    newTris[37] = 26;
    newTris[38] = 25;
    newTris[39] = 26;
    newTris[40] = 27;
    newTris[41] = 25;

    mesh.vertices = newVerts;
    mesh.triangles = newTris;

    meshfilter.mesh = mesh;
}
}
2

What’s happening is that your plane’s normal vector is being scaled with the object’s transformation. In this case vector magnitude doesn’t matter, however if it was you would also notice that the vector grows and shrinks. The solution for this is to essentially ‘invert’ the scale that’s being applied.

Your line

transform.InverseTransformDirection(PlaneNormal)

is doing this behind the scenes;

transform.worldToLocalMatrix.MultiplyVector (PlaneNormal)

To fix the scaling, we instead need to transform the vector by the inverse-transpose of the same matrix;

transform.worldToLocalMatrix.inverse.transpose.MultiplyVector (PlaneNormal)

The inverse of the worldToLocalMatrix is just the opposite transformation, so we can use this instead;

transform.localToWorldMatrix.transpose.MultiplyVector (PlaneNormal)

If you want to read more, this article has a good explanation;

https://paroj.github.io/gltut/Illumination/Tut09%20Normal%20Transformation.html