Odd Results from Barycentric Coordinates and Mesh Normals [4.2 dev6]

chetbeigemeister Geometry3D.get_triangle_barycentric_coords() is a generalized function that doesn't know anything about transformations. It just returns barycentric interpolation coords for a given point in a triangle. It's responsibility of the caller to put all arguments into the same transformations space. Otherwise the results won't be correct if mesh instance have any non-identity transforms.

The original code made a mistake of taking the triangle coordinates in mesh/object space while keeping the interpolated point position (gotten from raycasting) in global space.

If you need the normal in global space you can either:
1) transform the triangle vertices from mesh space to global space prior to passing them to bary function, using mesh instance's global_transform. And then transform vertex normals from mesh space to global space prior to interpolating them to get the final normal.
Or
2) transform the raycast point from global space to mesh space, get barycentric coordinates in the mesh space and interpolate the normal in the mesh space as well. Then transform the final normal from mesh space to global space, again using mesh instance's global_transform.

xyz Hello! I am so sorry to necropost; however, you are the only person I've been able to find giving good advice on this topic.

I'm getting similar results (mainly post 4) as OP using mostly similar code. I've experimented with your answer and I cannot seem to figure out where exactly you would convert between local and global spaces. I've tried to think about it logically, but I can't seem to get it right.

1. Could one just multiply the vertices in the for loop by global_transform and leave it that? For example: var vertices: Array[Vector3] = other.get_vertex_positions_at_face_index(ray_cast.get_collision_face_index()) * global_transform

2. When you say "transform vertex normals from mesh space to global space prior to interpolating them to get the final normal," are you saying that you could do the same thing as the vertices array (multiply the normals during iteration by global_transform)? I think what I'm not understanding is the "prior to interpolation" part - as in, what step in the process that would be. Wouldn't that be when OP calls and passes the normal align_up_direction?

xyz Yes it does!

To give you an idea of what is working, here is the core code. Adapted from OP's code, but I made the global changes.

You can see I multiply by each vertex by GlobalTransform, and I also multiply it to upNormal when I pass it to SetUpDirection().

Vector3[] vertices = new Vector3[3];
Vector3[] normals = new Vector3[3];

for (int i = 0; i < 3; i++)
{
    vertices[i] = meshData.GetVertex(meshData.GetFaceVertex(normRay.GetCollisionFaceIndex(), i)) * GlobalTransform;
    normals[i] = meshData.GetVertexNormal(meshData.GetFaceVertex(normRay.GetCollisionFaceIndex(), i));
}

Vector3 baryCoords = Geometry3D.GetTriangleBarycentricCoords(normRay.GetCollisionPoint(), vertices[0], vertices[1], vertices[2]);

Vector3 upNormal = (normals[0] * baryCoords.X) + (normals[1] * baryCoords.Y) + (normals[2] * baryCoords.Z);
upNormal = upNormal.Normalized();
SetUpDirection(upNormal * GlobalTransform, delta);

In SetUpDirection(), you can see I'm using GlobalTransform as well.

  private void SetUpDirection(Vector3 upNormal, double delta)
  {
      Transform3D normTransform = GlobalTransform;
      normTransform.Basis.Y = upNormal;
      normTransform.Basis.X = -normTransform.Basis.Z.Cross(normTransform.Basis.Y);
      normTransform = normTransform.Orthonormalized();
      GlobalTransform = GlobalTransform.InterpolateWith(normTransform, .5f);
  }

paftdunk Matrix multiplication is not commutative. The order of operands is important. To transform a vertex by a matrix the order should be matrix * vertex. Your code is doing vertex * matrix. This is equivalent to multiplying with a transposed matrix which would result in inverse transformation (if the matrix is orthonormal).

Also to transform a normal properly you need to nullify the translation part of the matrix or use only 3x3 submatrix aka the basis. So you can do matrix.basis * normal_vector. If there is some proportional scaling in the basis you either need to orthonormalize the basis prior to multiplication or normalize the resulting normal vector. If there is non proportional scaling in the matrix, you need to use transposed inverse of the actual matrix. Since Godot's transform class doesn't implement transpose function, you can do normal_vector * matrix.basis.affine_inverse(), which now reverses the operand order to transpose the matrix.

xyz Good point - I did notice that the documentation for getting the barycentric coords mentions that it is already interpolating, so thank you for confirming that. I have removed that - getting SLIGHTLY better looking results.

Could you explain the need for the second cross product?

Here is a video:

Here is the full code:

private void SetUpDirection(Vector3 upNormal, double delta)
{
    Transform3D normTransform = GlobalTransform;
    normTransform.Basis.Y = upNormal;
    normTransform.Basis.X = -normTransform.Basis.Z.Cross(normTransform.Basis.Y);
    normTransform = normTransform.Orthonormalized();
    GlobalTransform = normTransform;
}

public override void _PhysicsProcess(double delta)
{
    if (Input.IsActionPressed("move_test"))
    {
        Vector3 newPos = GlobalPosition;
        newPos.Z -= 6.0f * (float)delta;
        GlobalPosition = newPos;
    }

    if (Input.IsActionPressed("move_test2"))
    {
        Vector3 newPos = GlobalPosition;
        newPos.Z += 6.0f * (float)delta;
        GlobalPosition = newPos;
    }

    if (normRay.IsColliding())
    {

        CollisionObject3D hit = (CollisionObject3D)normRay.GetCollider();

        Vector3 newPos = GlobalPosition;
        newPos.Y = normRay.GetCollisionPoint().Y + .1f;

        GlobalPosition = newPos;

        SetUpDirection(normRay.GetCollisionNormal(), delta);

        if (hit.IsInGroup("AlignmentTest"))
        {
            MeshInstance3D meshInstance = hit.GetNode<MeshInstance3D>("Mesh");
            Mesh mesh = meshInstance.Mesh;

            meshData.CreateFromSurface((ArrayMesh)mesh, 0);

            Vector3[] vertices = new Vector3[3];
            Vector3[] normals = new Vector3[3];

            for (int i = 0; i < 3; i++)
            {
                vertices[i] = GlobalTransform * meshData.GetVertex(meshData.GetFaceVertex(normRay.GetCollisionFaceIndex(), i));
                normals[i] = GlobalTransform.Basis * meshData.GetVertexNormal(meshData.GetFaceVertex(normRay.GetCollisionFaceIndex(), i));
            }

            Vector3 baryCoords = Geometry3D.GetTriangleBarycentricCoords(normRay.GetCollisionPoint(), vertices[0], vertices[1], vertices[2]);

            Vector3 upNormal = (normals[0] * baryCoords.X) + (normals[1] * baryCoords.Y) + (normals[2] * baryCoords.Z);
            upNormal = upNormal.Normalized();

            SetUpDirection(upNormal, delta);
        }
    }
}

paftdunk Could you explain the need for the second cross product?

I explained it. It ensures the orthogonality of the basis vector. orthonormalized() does that as well but it does not guarantee the order in which it does the cross products. So if your basis vectors are not perpendicular when calling orthonormalized() the function will have to change the direction of some of them to make them perpendicular, but you don't know which ones will be changed. It may happen to be y which is your interpolated normal. You don't want that to be changed. So better do it yourself using two cross products so that you end up with the orthogonal vector and use orthonormalized() only to normalize the vector lengths.
So:
y = normal
x = y cross z (or as you've put it -(z cross y)
z = x cross y
orthonormalize

xyz I gotcha now, thank you! I've learned a lot math-wise through you, so I appreciate that and I'm going to continue reading/practicing with it so maybe one day I'll be able to tackle this since I just cannot get it working.

I'm going to go back to the drawing board and figure out a new approach to this problem.

paftdunk Can you post a minimal reproduction project? The whole thing is straightforward, there shouldn't be anything hard or mysterious about it. You likely have a bug somewhere in your transformation calculations.

paftdunk Normals/vertices need to be transformed from collider's space to global space. Not from skate's space which you're currently doing. That doesn't make much sense. So the matrix/basis you're multiplying them with needs to be collider's, not skate's.

You copypasted my pseudocode without thinking. I used GlobalTransform as a generalization, hoping we're understanding that this is GlobalTransform of whichever object triangles belong to.

paftdunk Well you're trying to move the skate only in global horizontal plane. That will seemingly work only when on near horizontal surfaces. The steeper it gets the glitchier it becomes. Since you're changing skate's orientation in 3d space, it needs to move "forward" from its own point of view. This "forward" changes as your rotate the basis. So to go "forward" you need to move it along its z basis vector. Ditto for y when "vertically" constraining to a collider. You need to move along the normal (or y basis), not along global y axis. If done properly the skate should go smoothly around a sphere without glitches.

Hard edges will obviously be a problem that needs some additional care, but that's for another topic.