How do I make an object's y-axis align with a Vector3?

Question

I have a golf ball on the ground, and from a raycast, I have the normal which gives me the slope of the ground by the ball.

I have an object which is rendered on the HUD to show that slope to the player.

I have a parent object rotated -90 degrees around X, so that the indicator's Z-axis points up. This way I can do this:

Quaternion yRot = Quaternion.Euler(0, -CameraController.Instance.CachedTransform.eulerAngles.y, 0);
Vector3 displayGroundNormal = yRot * _groundNormal;
_lieIndicator3DParentCachedTransform.rotation = Quaternion.LookRotation(displayGroundNormal);

This, as far as I can tell, takes the ground normal, rotates it around the y-axis so that it shows the proper perspective given the camera's facing. Then it tells that parent object to look in that direction, which aligns its z-axis with the rotated ground normal.

This works, except the object I have also rotates around the y-axis depending on the orientation of the camera. I thought that I was throwing that information away in the second step by keeping only a Vector3 aligned with the ground normal rotated for the camera position.

So I want this:

Not this:

Answer 1

Construct the normal relative to the camera:

Quaternion yRot = Quaternion.Euler(0, -CameraController.Instance.CachedTransform.eulerAngles.y, 0); Vector3 displayGroundNormal = yRot * _groundNormal;

Get the yz-plane projection of the adjusted ground normal:

Vector3 yzNormalComponents = new Vector3(0, displayGroundNormal.y, displayGroundNormal.z);

Get the angle between the yz-plane projection and the y-axis:

float zAngle = Vector3.Angle(yzNormalComponents, Vector3.up) * Mathf.Sign(displayGroundNormal.z);

Now rotate the z-axis toward the negative y-axis by that angle:

Vector3 zDir = Vector3.RotateTowards(Vector3.forward, Vector3.down, zAngle * Mathf.Deg2Rad, 3);

Use Quaternion.LookRotation to look in the calculated z direction, with the adjusted ground normal as up:

_lieIndicator3DParentCachedTransform.rotation = Quaternion.LookRotation(zDir, displayGroundNormal);