Merrell, in his analysis of semiosis as a process of progressive acquisition of meaning of signs, has made a significant step in the direction of the definition of three-dimensional signs: 
 

"The products of three-dimensional semiotics from within human bio temporality can be related to... 'homeomorphic' (iconic) models.... 'Homeomorphic' models are intuited, developed, and perceived chiefly  from within the domain of secondary qualities, of what is on the surface to be seen and sensed in terms of  relatively immediate and less immediated sensations. These items of experience, rather than mere two-dimensional surfaces, are actually three-dimensional entities the intuition, conception, creation and perception of which move along one-dimensional trajectories 'world lines' in three dimensional space."(1)

As an example we can take any detail of a product such as a lid, a hinge, a knob, a handle, a ventilation opening, a display, etc. The relative area's are sets of points with a common functional goal but with infinite feasible formal variations. It is this freedom that makes design altogether possible. The three-dimensional surface is created by sets of points organized along 'lines' that reveal preferences. These can be, for example, a predilection of symmetrical motives or geometric solids, patterns of growth in nature or any others. A classification of these patterns is possible by analyzing the principles of their topological formation. Actually a whole new section of topology is under construction as 'chaos theory' in which giant (perhaps sometimes overvalued) steps has been made, in the wake of Bénoit Mandelson, in the revelation of mechanisms, fractals, that underlie dynamic systems such as the living organism or the turbulence of gases or liquids. Essentially it proves that any process, even seemingly random ones, can be described by mathematical algorithms, that in reiterated application are capable to generate  complexity as two-dimensional combinations of intrinsically simple, one-dimensional, classifiers, or selective 'if...then' strings. (5)
In our case we talk about the creation of surface area's, or membranes, containing myriad's of points that follow certain patterns of common similar, if not identical, 'behavior' that are, in other words, subject to 'attractors', such as concaving or convexing, protruding or penetrating, deviding or connecting, bending or undulating, stretching or contracting following the concept of the designer. Any of these and many other verbs that describe actions in space, or gestures, are descriptive of the grammar of design language and, in accordance to chaos theory, combinations of relatively simple linear sets of points, or lines. 

Moreover these lines and the membranes that they describe, being signs or combinations of signs, do have meanings. But these meanings are completely different from the more evident meanings concerning products as protheses and area's of products as expression of functions. They belong, as I see it, rather to forgotten archaic languages, as Ur-omens, in use by man since primordial times, long before invention of written language. as we can see from archeological reperts and as remnants of so-called primitive languages. 
Line segments, straight or bend, either horizontal, vertical or inclined, single or in repetition, circles, crosses, chevrons, serpentines, spirals: they all were actually signs in this original sacred language, that were materialized during the Antique Neolithic Era (VIIth - IIIrd millennium b.C.) onwards, both as in- scriptions on all kinds of surfaces, precursors of our characters and numerals, and as manufacts that were called by the ancient greeks 'xoanon', figurines. Marija Gimbutas, in the wake of Johann J. Bachofen traces these artifacts back into even earlier archaic times and suggests that they represent mostly a female life giving and life taking bird goddess, source of all life and of the entire universe. 

 statuine of a neolythic goddess (from the cover of Gimbutas' book)

This suggests a the existence of a common source of divine representations, artifacts and  even written language. It is in these remote origins that lies, in my opinion, the secret of our esthetic feeling, maybe scattered in incongruous bits, broken vessels, but still powerful in its subconscious presence; perhaps even because of this. 
Design morphology seems to lead us back through Euclidean geometry past a variant of biological taxonomy adapted to artifacts, toward the deeper nature of art as a manifestation of the eternal human need for transcendence. 

Perhaps we can say of design what Baudelaire said of temples: 

Where man passes through forests of symbols 
That observe him with familiar looks.

2.   Walter Benjamin, Erkenntniskritische Vorrede, Gesammelte  Schriften I-1, p.208, (1925), Suhrkamp, Frankfurt a.M.,  1991 (back)

3.   René Thom,  Stabilité Structurelle et Morphogénèse, (1972), IIme ed., InterEditions, Paris, 1977 (back) 

4.   Wentworth D'Arcy Thompson, On Growth and Form (1917), An Abridged Edition, Cambridge UP, 1961, back

5.    M. Mitchell Waldrop,  Complexity. The emerging science at the edge of order and chaos  (1992), Pinguin Books, 1994, p.183 ff. (back) 

6.   Johann Jakob Bachofen, Das Mutterrecht,  (1861), (back) 

7.    Marija Gimbutas,  The Language of the Goddess,  (1989), 
ISBN 88-304-0982-0,  it.ed.1997, Neri Pozza, Vicenza, (back)

8.     Significant investigations on the possibility of visual language have been made; as for example (in the wider contest of cultural semiotics) by  Göran Sonesson whose site furnishes also a generous list of links to other sites:

http://www.arthist.lu.se/kultsem/semiotics/kult_sem_eng.html

9. A different approach, mainly dedicated to the 'iconic' language of publicity is suggested by Claude Cossette. You can find excerpts from it (in French) on the following site: 

http://dionysos.ulaval.ca/ikon/finaux/1-texque/imadem/IMADEM.HTML