Metamorphosis: Titian 2012, National Gallery, London

What do the Ancient Greek Games have to do with an exhibition in the year of London 2012? Screw up your eyes, and it all becomes wonderfully clear

Question: How will the London Olympics resemble those held in Greece from 766BC to AD394? Answer: They won't. All right, that's not fair: there will be running, jumping and javelin-throwing. But the differences between London's £12bn media-fest and the ancient Games – always held in Olympia, and restricted to Greek-speaking men – so heavily outweigh the similarities as to make their coincidence of name seem bogus.

Oddly, one way in which the new Olympics will genuinely echo the old is in their inspiring of art. Myron sculpted Timanthes, champion of the 456BC Olympics; Polykleitos made his javelin-toting Doryphoros after a later Games; Phidias carved the Olympian deity, Zeus. In place of this trio, the London Cultural Olympiad offers us Mark Wallinger, Conrad Shawcross and Chris Ofili, in a show at the National Gallery called Metamorphosis: Titian 2012.

Now, you're probably thinking: Titian? Wasn't he Venetian? Well, yes. But like any sensible artist, Titian pitched his work at rich clients, and those clients had a yen for Ovid. Now, you're probably thinking: Ovid? Wasn't he Roman? Well, yes. But his best-known poem elided Latin history with Greek mythology, its subject, as its title, being Metamorphoses – myth made real, gods become bulls or horseflies, Attic antiquity magicked into Roman modernity. These transformations bewitched Renaissance patrons, living through a cultural metamorphosis of their own. A result of this fascination is the three great Titians in the National Gallery, all scenes from Ovid: Diana and Actæon, The Death of Actæon and Diana and Callisto.

For the Olympiad, Wallinger, Shawcross and Ofili were invited to make works which respond to these pictures: if you screw up your eyes, you can see the logic. They have produced sets for new ballets at the Royal Opera House, but have also made artworks which respond to Titian directly, and it is these that are on show in the National Gallery.

Mark Wallinger's Diana is customarily wonderful. In a darkened room, he has built a sub-room into which we cannot quite look through a louvred door and frosted window. It seems to be a bathroom: blurred shampoo bottles stand on the window's sill. As you ponder these, something moves. It is a woman, seemingly naked – one of seven chosen by Wallinger, all genuinely called Diana, who will occupy the room in turn throughout the show.

This Diana is washing her hair. You can tell that it is long and dark – she tosses it to flick off the water. It is impossible not to look, to make sense of what you are seeing. In the next room, Titian's Actæon is struggling with the same impulse. You feel as momentarily aghast as he is, and as fearful of humiliation – if not "Peeping Tom hunter turned into stag", then "Pervy art critic arrested in gallery". One aim of a good historical-response show must be to unlock something of the original work, to take it from Greece to Rome, Rome to Venice, Venice to London 2012. Wallinger's Diana does that brilliantly.

As often with Greek myths, the story of Diana and Actæon seems cruelly capricious. Sartre saw it as a parable of rape: but did Actæon really need to be torn apart by his own hounds? Conrad Shawcross's Trophy asks this question.

In a Hirst-esque glass tank, the proboscis of an industrial robot slowly traces the outline of a single stag's horn carved in wood. Or, rather, in woods. The work's wall-label lists sapele, afzelia, American black walnut, African walnut, oak, teak, apple, mahogany, afromosia, pear, iroko, utile. This is a battle of cold steel and warm nature, of law and compassion, poetry and prose. Shawcross's cleverness lies in his talent for instilling his machines with feeling. This one, his Diana, seems to view the antler it has made with curiosity, although whether it is admiring the sensuousness of its creation or sizing it up as food is impossible to say.

And then there is Chris Ofili's Metamorphoses, a suite of seven paintings related to his set design for Diana and Actæon, the ballet.

What to say about these? Since he moved to Trinidad, Ofili appears to be undergoing a metamorphosis of his own. Alas, this is a transformation into a pale shadow of Peter Doig, a friend, fellow resident of the island and much better painter. Ovid – Bather, Ovid – Stag and the rest unnecessarily spell out the sexuality of Ovid's story, rendering it in a tangle of Art Nouveau-ish phalluses and breasts. Not good. Still, Shawcross and Wallinger are well worth seeing, as, of course, is Titian. So do.

To 23 Sep (020-7747 2885)

Critic's Choice

The Royal Academy in London showcases items from the private collection of Sterling Clark in From Paris: A Taste for Impressionism. Taken from the Sterling and Francine Clark Institute in Massachusetts, the 70 artworks include Impressionist paintings never seen before in the UK (till 23 Sep). On a similar theme, Tate Liverpool is offering Turner, Monet, Twombly: Later Paintings, where the artists complement rather than compete with each other (till 28 Oct).