The conceptual component of this work is about "reference surfaces'' which are the dual of reference frames often used for shape representation purposes. The theoretical component of this work involves the question of whether one can find a unique (and simple) mapping that aligns two arbitrary perspective views of an opaque textured quadric surface in 3D, given (i) few corresponding points in the two views, or (ii) the outline conic of the surface in one view (only) and few corresponding points in the two views. The practical component of this work is concerned with applying the theoretical results as tools for the task of achieving full correspondence between views of arbitrary objects.