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# Quaternion to Matrix, Matrix to Quaternion

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### Quaternion to Matrix, Matrix to Quaternion

1. 1. Melody Cariaga<br />Diana Delgado<br />Aila Feliciano<br />Angelica Pontejos<br />Quaternion to Matrix<br />
2. 2. What is a Quaternion?<br /> provide a convenient mathematical notation for representing orientations and rotations of objects<br /> in three dimensions. <br />compared to Euler angles they are simpler to compose and avoid the problem of gimbal lock.<br />compared to rotation matrices they are more numerically stable and may be more efficient.<br />
3. 3. Format<br />a + bi + cj +dk<br />
4. 4. Formula<br />
5. 5. Example<br />7 + 9i + 5j + 1k<br />
6. 6.
7. 7. Matrix to Quaternion<br />
8. 8. Trace<br />sum of the main diagonal of a matrix<br />
9. 9. Robust Method<br /><ul><li>to choose the diagonal element with the largest absolute value</li></li></ul><li>A matrix can be numerically unstable if its trace is zero or very small.<br />If r is zero the matrix is the identity matrix, and the quaternion must be the identity quaternion (1, 0, 0, 0).<br />
10. 10. Formula<br />
11. 11. http://en.wikipedia.org/wiki/Quaternions_and_spatial_rotation#Conversion_to_and_from_the_matrix_representation<br />http://www.euclideanspace.com/maths/geometry/rotations/conversions/quaternionToMatrix/index.htm<br />http://www.euclideanspace.com/maths/geometry/rotations/conversions/matrixToQuaternion/index.htm<br />References:<br />