How to get plane rotation by known normal vector

Question

I have a FPP quaternion Camera and Plane with known normal vector.

I want to find the orientation of this Plane so I can replace it to the Camera orientation to put the camera forward vector to a plane's normal vector.

• First method I tried, I don't understand RotationAxis and RotationAngle. I built a rotation matrix and applied it to the camera but it didn't behave as I wanted.

• The second method I tried is with method called "from_one_vector_to_another". I don't understand what the "from" vector is in my example; is it the camera's forward vector?

Here is my pseudo code:

Vector3 vector_from = camera->getForwardVector();
Vector3 vector_to = triangle->faceNormal;

Quat cameraQuaternion = camera->getOrientation();

Quat q = vector_from.getRotationTo(vector_to);//The method `getRotationTo` is from Ogre.
camera->setOrientation(cameraQuaternion * q);

Camera does not change their orientation as I expected; it changes its orientation just a little bit.

EDIT:

Maybe I have something wrong with my code:

//Quat xrot = axisToQuat(Vector3(1, 0, 0), vertical);  // disabled for now
Quat yrot = axisToQuat(Vector3(0, 1, 0), horizontal);
rot = rot * yrot;

position += velocity;

Matrix lookAt = Matrix::createLookAt
        (
            Vector3(position.x, position.y, position.z),
            Vector3(position.x, position.y, position.z-1),
            Vector3(0,1,0)
        );

view = rot.toMatrix() * lookAt;

I am only rotating the quaternion. Should I rotate lookAt Matrix too?

Answer 1

So, just to be clear; you want to orient the camera such that it is looking in the direction given by the plane's normal?

The problem with calculating a quaternion for this is that it doesn't usually represent an absolute rotation but rather a rotation through which the initial forward direction of the camera is to be rotated. So what you are looking for is a quaternion that will rotate the initial forward vector of the camera to the normal of the plane. This link will give you that answer:

https://stackoverflow.com/questions/1171849/finding-quaternion-representing-the-rotation-from-one-vector-to-another

However it is common for a camera API to have a function that will take a position and a look at and orient the camera for you. In your case this will be much more simple:

position = whatever you want it to be

look at position = position + normal

Hope I am understanding the question correctly.