While it looks like a freeway on-ramp as it hovers over Wilshire Boulevard in the Los Angeles area of Southern California, the people behind the new building anchoring the Los Angeles County Museum of Art (Lacma) define it with aquatic imagery.

The free-flowing sections of the David Geffen Galleries housing the museum’s permanent collection are named after the Pacific, Atlantic and Indian Oceans and the Mediterranean Sea. They are meant to run together physically and culturally as bodies of water do.

Technically, the Geffen Galleries represent the third phase of a two-decade series of renovations. But it is the opening of this space to the public on May 4 that is the truly huge moment of reinvention for Lacma.

The building is a US$724 million, 347,500 sq ft (32,300 square metre) monument designed by Swiss architect Peter Zumthor that gives the museum an entirely new orientation, footprint, feeling and, ideally, an identity that it has largely lacked to the outside world.

The space – all on a single second-storey floor – offers broad-windowed views of the surrounding city. There is no main entrance or central atrium. It is made to wander into, and through, and to encourage accidental interactions with paintings, sculptures and the kinds of work, like ancient pottery or textiles, that visitors often ignore.