I have a Vector3 represents an Orientation in 3D , how to convert it to the corresponding Quaternion ? Is there any quick way ?

EDIT : I want to add an angular velocity vector to the Orientation Quaternion of the body


1 Answer 1


If your Vector3 stores an euler angle (yaw, pitch, roll) you can use the following static method directly:

Quaternion quaternion = Quaternion.CreateFromYawPitchRoll(vector.X, vector.Y, vector.Z);

On the other hand, if you're not storing an euler angle, but just the direction (or forward vector) of the camera/object, then bear in mind that generally a single 3D vector is not enough to store a complete orientation in 3D space unless you restrict one of the axes of rotation.

A typical case is where your camera/object can't roll or flip around and the Up vector is always pointing in the upper direction, e.g. FPS camera. If that's the case, then you should create a rotation matrix from your forward vector, and then use the following static method:

Quaternion quaternion = Quaternion.CreateFromRotationMatrix(matrix);

As for creating that rotation matrix, I think something like this should work (I hope so, I'm a little rusty with cross products):

Matrix matrix = Matrix.Identity;
matrix.Forward = vector;
matrix.Right = Vector3.Normalize(Vector3.Cross(matrix.Forward, Vector3.Up));
matrix.Up = Vector3.Cross(matrix.Right, matrix.Forward);

I think this may cause problems though if you try to look directly up or down, or close to those orientations, so you may need to handle those cases separatedly.

  • \$\begingroup\$ in my problem i have an angular velocity vector and i want to add it to the quaternion,so i will add the converted vector(quaternion after conversion) to the orientation Quaternion \$\endgroup\$
    – MhdSyrwan
    Jan 7, 2012 at 23:18
  • \$\begingroup\$ Then it's probably represented as an euler angle so just use the first method, and then use Quaternion.Concatenate to add it to the old quaternion (at least it's what I gather from the documentation). But try not to mix up which coordinate corresponds to yaw/pitch/roll. \$\endgroup\$ Jan 7, 2012 at 23:55
  • \$\begingroup\$ but,i think it's Quaternion.CreateFromYawPitchRoll(vector.Y, vector.X, vector.Z); not Quaternion.CreateFromYawPitchRoll(vector.X, vector.Y, vector.Z); isn't that right ? \$\endgroup\$
    – MhdSyrwan
    Jan 8, 2012 at 0:13
  • \$\begingroup\$ Yes it should be since Yaw = Y-axis rotation, Pitch = X-axis rotation, Roll = Z-axis rotation. Depends on how you (or some library you're using) set up those angular velocity values. \$\endgroup\$ Jan 8, 2012 at 0:24
  • 1
    \$\begingroup\$ @MhdSyrwan the velocity-vector may also be an axis-angle vector, which is basically a rotation axis and the angle encoded in the vector-length. Where does the velocity-vector come from? Did you compute it yourself or does it come from any library? \$\endgroup\$ Jan 8, 2012 at 10:39

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