Both new buildings are striking. The Guardian Art Centre rises above Wangfujing, one of Beijing’s most famous shopping streets, in a series of cubes capped by a large rectangular volume. Duo’s curving towers soar above a half-moon-shaped plaza, their sleek glass facades screened by a lattice of honeycombs. But Scheeren says the motivation behind the two projects was not to create a bold visual statement. “What connects the two projects is a concern for the city and the public domain,” he says.

In Beijing, that meant dealing with a sensitive site that had already been the subject of 30 previous proposals from the city’s planning committee. A stone’s throw from the Forbidden City and across the street from the National Art Museum of China, the site includes an art gallery, an auction house, offices and a 116-room hotel. Its surroundings vary from historic hutongs – narrow streets with low-slung greystone courtyard houses – to bulky 1990s-era edifices.

“We thought, ‘How can we reconcile these two different time zones – the scale of the historic city with the scale of the modern city?’” Scheeren says. What made things even trickier was the ambitious brief, which called for nearly 60,000 square metres (646,000 square feet) of space to be shoehorned into a 6,320-square-metre site. “We had the feeling that we couldn’t plonk a single massive volume into that context.”

Scheeren’s solution was to split the building into “layers like the sediment of the historic city”. Most of the space is underground. On the ground level, a collection of grey basalt stone cubes recalls the form of hutong houses. These are capped by a huge rectangular glass box.

Scheeren used a kind of trompe l’oeil effect on the facade that makes the building seem smaller than it is. The cubes at the base are punctured by circular windows arranged to appear like a traditional Chinese landscape painting. Upstairs, the windows of the rectangular glass box call to mind the greystone bricks that built old Beijing.

“It’s an understated form of monumentality,” Scheeren says.

Although the project was privately funded by China Guardian, the country’s largest auction house, Scheeren says it is “ultimately a building for the public”. That is significant given the epicentre of Beijing’s art world long ago shifted to the city’s periphery, to clusters like the 798 Art Zone and Songzhuang Village.

“This reinserts the art world back into the centre of Beijing,” he says.

Scheeren had similarly grand ambitions for Duo. On paper, the brief was for a mixed-use development like so many others in Singapore, with high-rise apartments, offices and a five-star hotel sitting atop a retail podium. “It [could have been] a plot of land sandwiched between towers that had no accountability to the public spaces of the city,” he says.

He decided to curve the towers so they embraced the space in between them, a design that also channelled the area’s light tropical wind to create a comfortably breezy space. The honeycomb lattice, meanwhile, was conceived as a way to shelter the towers’ facades from the sun, reducing their need for air conditioning.

“The question was, how can we make people feel good in the spaces we create?” Scheeren says.

He adds that the site’s feng shui intrigued him, and that its negative energy may be why it was left undeveloped for so long. The curves and orientation of the two buildings, he explains, were designed with these “esoteric forces” in mind.

“When you go now you can sense a very specific energy, a very positive energy.”

Scheeren says he has been able to think radically in Asia, with the continent now the “creative base for an international scope of work”. But he is turning his attention to three high-rise buildings in Vancouver and Frankfurt – his first major projects outside Asia.

In Frankfurt, Scheeren will chop a 1970s office block into Jenga-like pieces to create 200 luxurious apartments. It is an unusual project that will use huge floor plates to create additional space outside the building’s core structure and allow for some impressive architectural features.

“Imagine if [your apartment] had a 20-metre-wide glass front with no columns to obstruct it,” Scheeren says. “We’re going to turn this into one of the best places to live in Europe.”

He has taken a similar approach with two projects in Vancouver, both of which feature that irregular-stacked-boxed design. He says these extrusions are a way to incorporate spacious outdoor living into a high-rise building, giving apartment dwellers a chance to experience the pleasure of a private garden without needing to live in the suburbs.

It is a technique that has drawn plenty of criticism, especially in Vancouver, where every new project must be vetted stringently by an urban design panel. Local architecture critic Trevor Boddy, for example, has been scathing in his assessment of Scheeren’s work.

He told Surface magazine that it has all the “ham-handedness” of the CCTV tower “with none of its lumpy awe”. He called one of Scheeren’s Vancouver towers “clumsy” and said it would be “our city’s tombstone to the starchitect era”.

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Unflappable as ever, Scheeren takes such criticism in his stride. “We had some pretty intense discussions about it [with the design panel],” he says. “If what you do does not create any sense of friction, you would need to conclude that you’ve done nothing new. What’s new is controversial because it questions a lot of givens.”