A novel method which entirely resides inside conformal geometric algebra (CGA) is presented estimating the pose of a camera from one image of a known object. At first, subproblems covering only three feature points are solved and globally assessed. The object model is accordingly pruned and rigidly fitted to corresponding projection rays by evaluating a succinct CGA expression which emerged from a purely geometric approach. It results a set of 3-point poses each given by a motor. These spinor elements of CGA embody rigid body motions from the manifold SE(3). The poses are then to be averaged according to their quality. This is the second aspect of this work as the respective motors do not come from a linear space and averaging must be carried out appropriately. For this purpose, a technique called weighted intrinsic mean is used.