After abandoning plans in Chicago, Beijing studio MAD has now revealed two new designs for its George Lucas Museum of Narrative Art – one for San Francisco, and a different one for Los Angeles.

Star Wars creator George Lucas was forced to give up plans to build his film museum on the Chicago lakefront after fierce opposition from locals, so is now hedging his bets with two competing California proposals.

The first is for a site on Treasure Island, in San Francisco Bay, while the second is for Exposition Park in Los Angeles, where it would sit near the Natural History Museum and Coliseum.

MAD principal Ma Yansong worked on the two designs simultaneously. Unlike the previous proposal, which comprised an undulating tent-like canopy, both new designs are more sinuous and fluid in form.

Both feature tapered forms that lift the galleries up off the ground, allowing space for pedestrians to walk underneath.

In San Francisco, this would allow for an expansive public space stretching out along the waterfront – connecting with the wider masterplan for Treasure Island, developed by architecture firm SOM.

But in Exposition Park, public spaces would also be located on the building's roof, creating plant- and tree-covered terraces.

On paper, both buildings would create the same amount of gallery space – around 100,000 square feet, which equates to approximately 9,000 square metres.

The LA design also includes an underground car park with room for approximately 1,800 vehicles.

MAD first unveiled its design for the Lucas Museum in late 2014, when it was working with Chicago-based Studio Gang.

Ma – whose best-known projects include the huge Harbin Opera House in China and the curvaceous Absolute Towers in Canada – said at the time that he wanted to make the museum building appear like a "wave" coming out of the ground.

The design proved controversial. Chicago alderman Bob Fioretti described is as "a palace for Jabba the Hut", while local group The Friends of the Parks filed a lawsuit claiming that the site was still a protected waterway.

MAD responded by producing a slimmed-down design, while Chicago mayor Rahm Emanuel suggested a new location, in a bid to keep the project in Illinois. But in the end, Lucas decided to move the proposal to America's West Coast.

According to reports, Lucas is likely to choose between the two locations in the next two to four months.