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## QuaternionQuaternions are like complex numbers. The number of dimensions in a quaternion number is 4. Multiplication over quaternions is NOT commutative. Multiplication over quaternions is associative. Representation for example: Where i is the complex root, j is another basis root and k is yet another basis root. ## RotationsIf we have an axis angle representation consisting of an angle and an axis represented by a vector (a_x,a_y,a_z) of unit length, the equivilant quaternion representation is: where the axis is normalized so that . where the quaternion is normalised so that . let's say that is: . Then follows by taking the square root: ## Apply rotation to a pointTo apply rotation to a point, represent the point as i, j and k factors (the real part is 0), then the new point P is, given the old point p and a rotation quaternion q: ... where conj is the conjugate operator, flipping the signs of all the non-real components of the quaternion. Author: Danny (remove the ".nospam" to send) Last modification on: Sat, 04 May 2024 . |