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This article introduces yet another representation of rotations in 3-space.The rotations form a 3-dimensional projective space, which fact has not beenexploited in Computer Science. We use the four affine patches of thisprojective space to parametrize the rotations. This affine patch representationis more compact than quaternions (which require 4 components for calculations),encompasses the entire rotation group without singularities (unlike the Eulerangles and rotation vector approaches), and requires only ratios of linear orquadratic polynomials for basic computations (unlike the Euler angles androtation vector approaches which require transcendental functions).  As an example, we derive the differential equation for the integration ofangular velocity using this affine patch representation of rotations. We remarkthat the complexity of this equation is the same as the correspondingquaternion equation, but has advantages over the quaternion approach e.g.renormalization to unit length is not required, and state space has no deaddirections.

Nonsingular Efficient Modeling of Rotations in 3-space using three components