One looks like a futuristic bicycle helmet stretched across its Tokyo site in an aerodynamic sweep. The other has been said to resemble a woman's private parts.
Both are in fact sinuous sporting stadiums by the London-based Iraqi architect Zaha Hadid, who is facing calls for her exuberant designs to be scaled back.
This week Japanese sports officials finally bowed to criticism that Hadid's scheme for the Tokyo 2020 Olympic stadium was too big and expensive, saying they would shrink the design by a quarter.
The 80,000-seat venue, planned for the site of the current 48,000-seat national stadium, built in 1958, is described by Hadid as "light and cohesive", its structure forming a dynamic bridge that "creates an exciting new journey for visitors".
But the design has been met with fury by Japanese architects, who have complained that it is grossly insensitive to its context, looming 70 metres above the area of low-rise buildings and parks in the west of the city, close to the Meiji shrine, where a 15-metre height limit is in force.
The 100-strong group, led by Pritzker prize winner Fumihiko Maki, 85, filed a petition against the project earlier this month.
They protested that the stadium was two to three times the size of its equivalents in London and Athens, and, at 300 billion yen (HK$22.7 billion), would cost more than three times as much as either of them to build.
In response to mounting pressure, the Japan Sport Council has now announced it will scale back the floor space by a quarter to 220,000 square metres, and reduce the budget to 180 billion yen - still nearly 40 per cent higher than the government's initial estimates for a new stadium.
With its ambitious scale, the project has echoes of Hadid's plans for the aquatics centre for the London Olympics last year, which were originally intended to comprise two buildings rippling along the edge of the Olympic park like a pair of stingrays. But the realities of a budget got in the way and the scheme was cut in half.
The Tokyo news comes as Hadid has been forced to bat off claims that her design for Qatar's Al-Wakrah stadium, for the 2022 soccer World Cup, is based on the female genitalia, after images of the "vagina stadium" went viral last week.
The architect insists that the building's swollen covers, which part along the roof to frame a central ovoid opening, were inspired by the sails of local dhow sailing boats, but others have ridiculed their labial similarities.
The Daily Show ran images of the stadium sprouting a forest of pubic hair.
As the feminist website Jezebel put it: "Any discerning human will be quick to recognise that the building looks exactly like an enormous vagina."
"Seriously though, why criticise," the website continued. "Every city's skyline looks like a row of shadowy phalli glinting in the urban smog. It's about time that we pay some architectural respect to the yoni."
However, Hadid has little time for such lewd comparisons.
"It's really embarrassing that they come up with nonsense like this," she told Time this week. "What are they saying? Everything with a hole in it is a vagina? That's ridiculous."
Queen of the curve and conjuror of otherworldly forms, Zaha Hadid has become a sought-after global brand, dotting the world with her rippling white structures, from Abu Dhabi to Azerbaijan.
She has turned her hand to everything from swirling urban plans and challenging footwear to jagged jewellery and garish superyachts. But success hasn't always come easy.
Born in Baghdad in 1950, Hadid studied mathematics in Beirut, before training as an architect at the Architectural Association in London. Her first building was a small fire station in Germany, built in 1994, whose tilting walls and angled stairs proved too much for the firefighters to stand.
But since the mid-2000s commissions have flooded in, from the BMW headquarters in Leipzig, Germany, to the Guangzhou Opera House.
Her first and only work in Hong Kong is the Innovation Tower at the Hong Kong Polytechnic University.
Hadid was the first woman to win the Pritzker Prize (architecture's equivalent of a Nobel Prize) in 2004, and is two-time winner of the RIBA Stirling Prize, for the Maxxi Art Centre in Rome and the Evelyn Grace Academy in London. Her 400 staff are working on projects in more than 40 countries through her company Zaha Hadid Architects.