LONDON — Three figures sit round a clover-shape table: a bearded and slippered Chinese sage, a periwigged European, and a Japanese aristocrat whose kimono bears his ancient family crest. The sage, arms crossed, gazes impassively into space; the samurai is cuddled up close to the Westerner, casting a guarded glance at his Asian neighbor. You could say it has been like that ever since.

“A Meeting of Japan, China and the West,” painted by Japanese artist Shiba Kokan in the late 18th century, neatly symbolizes one of the “encounters” that are the subject of the Victoria & Albert Museum’s winter blockbuster, “Encounters: The Meeting of Asia and Europe, 1500-1800.” As Kokan’s painting suggests, these early centuries of contact laid the foundations for trade alignments and political alliances that persist to this day.

As organizing conceits go, “Encounters” is a roomy one: It could be (and is) used to justify the inclusion of just about anything. The “Asia” of the title sprawls from India to Japan via Siam (modern-day Thailand), Sri Lanka and China, each of which would merit an exhibition of its own. In short, this is just the kind of showcase “big exhibition” beloved of Japanese museums. Perhaps that’s why “Encounters” has found a Japanese sponsor, the Nomura group, and why the show is proving popular with Japanese visitors.

Nonetheless, it’s hard not to get swept up in this beautifully presented show. The curators have not only cherry-picked the V&A’s own collection, but also the holdings of institutions worldwide. There’s a three-legged stool like you’ve never seen — constructed of elephant femurs and made for an Austrian emperor. Elephants to thank, too, for the Robinson Casket, a masterpiece of Indian craftsmanship carved in ivory and inset with sapphires. Two jeweled and enameled Japanese telescopes are triumphs of art as much as science. “Encounters” is one of the loveliest exhibitions in London this winter.

The geographical promiscuity of this haul of treasures reflects the haphazard nature of the European trading project of the time. Trade items and profits were sought wherever they might be found, and merchants made whatever accommodations were necessary to get their hands on luxury goods that fetched a fortune back home.

Thus, while the Portuguese in Molacca and the British in Calcutta and Madras built elegant European-style settlements, the Dutch in Japan were confined to Dejima, a nubbin of land offshore in Nagasaki harbor. Holland was the only European power with trading access to Japan — a prize worth the discomfort and tedium of life on Dejima. It wasn’t until the show of force by U.S. Commodore Matthew Perry’s black ships in 1854 that the West was able to dictate terms to Japan; the Unequal Treaties that were subsequently imposed contributed significantly to the rise of Japanese nationalism and expansionism, and ultimately to the country’s disastrous involvement in World War II.

With so much to cram in, it’s to the curators’ credit that they’ve attempted to show the exchange wasn’t all one-sided.

The late Edward Said, author of “Orientalism,” would surely have been pleased at the inclusion of a Chinese scroll depicting a procession of English visitors bearing staggering scientific gadgets — astrolabes and optical instruments — annotated with a deprecatingly magnanimous little poem by the Qianlong Emperor. “Their gifts are not precious,” wrote the emperor, “but curiosities, whose subtleties have been exaggerated. Still, in cherishing men from afar, no matter how meager their offerings, we treat them with generosity.”

Elsewhere, the show modulates into the personal — a good reminder that even clashes of civilizations are enacted by individuals. Fans of British author William Dalrymple’s writings on India will be delighted by the section titled “Personal Encounters: Europeans in South East Asia,” which features a number of tender paintings of the Anglo-Indian families explored in Dalrymple’s most recent book, “White Mughals.”

Indeed, Dalrymple contributes an essay to the exhibition’s handsome catalog, which also contains such scholarly big names as London University Japanologist Timon Screech. Here he writes on the impact of Western art and technology in Japan, the subject of his groundbreaking 2002 study, “The Lens With the Heart: The Western Scientific Gaze and Popular Imagery in Later Edo Japan.”

The process begun by scholars such as Screech reached its logical conclusion in last year’s funky study “Occidentalism” — A robust riposte to Said’s “Orientalism” — authored by Ian Buruma and Avishai Margalit.

“Occidentalism” examines ways the East has (mis)interpreted, stereotyped and fantasized the West, and perhaps inspired the V&A curators to add an intriguing epilogue to this exhibition, featuring Indian, Chinese and Japanese fantasies of Europe.

We are treated to such visions as Utagawa Toyoharu’s ukiyo-e print of the Roman Forum. It’s not that the print is architecturally inaccurate, it is just that all the buildings are rendered in the lacquered red of a Shinto shrine gate. (The one shunga [erotic woodblock] in the exhibition, showing an eye-poppingly well-endowed Dutchman mounting a Japanese courtesan, is not located in the fantasies section — one doesn’t know whether to applaud the curators’ good taste or deplore their lack of humor.)

Some, wealthy and eccentric enough, lived out their fantasies, like the Europhile Yongzhen Emperor of Qing China (ruled 1723-35). A portrait here shows him resplendent in a periwig, with a pussy-bow neckcloth and fashionably patterned waistcoat. A celebrated painting on silk (not showing here, but reproduced in the catalog) depicts the emperor cornering a tiger with a pitchfork, clad in the knickerbockers and dressing gown of the European dandy.

The irony of that painting is that the tiger was perhaps the most celebrated symbol of the East during these years of encounter. The tiger-skin rugs prized by Western traders and imperialists were more than just furry floor coverings, they represented Western ascendancy — the superior European technology of guns, with which tigers were easily hunted; and the superior European wealth, able to buy up tiger skins cheaply from native peoples.

Fitting, then, that the exhibition concludes with the marvelous Tippoos Tiger. This automaton takes the shape of a tiger crouched on — and devouring — a British soldier. The internal mechanism moves the tiger and its victim, and powers an organ that simulates the roar of the animal and the screams of the soldier. It was commissioned by the Tipu Sultan, at the end of the 18th century, and reflects both his hatred of the British and his fascination with Western technology. It’s a love-hate relationship of mutual fascination that underlies many of the works in this exhibition.

Just whisper quietly the ultimate fate of Tippoos Tiger. It fell into British hands at the fall of Seringapatam in 1799, then found its way first into the museum of that British colonial powerhouse, the East India Company, and finally into the holdings of the British colonial treasure house that is the V&A itself.

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