In early 1980, Aubrey Powell, the then-33-year-old co-founder of the pioneering British design company Hipgnosis, flew to Hawaii to photograph the cover for the British rock band 10cc’s album “Look Hear?”

The shoot involved a specific sheep (only one was available on Oahu, at a university farm) seated on an old-timey psychiatrist’s couch (which had to be constructed by a Honolulu props company) on the island’s North Shore. The sheep, out of its element and skittish from the crashing waves, ruined the first day of the session, so a veterinarian was called in to tranquilize the animal for Day Two. Success.

The final cost of the cover design, including airfare and a sheep wrangler, came to 5,043 pounds — about $26,000 in today’s money and a big sum for the time. (But then again, as Powell, known as Po, said in an interview, back then the music industry “was awash with money.”) In the end, at the behest of Hipgnosis’ other co-founder, Storm Thorgerson, the U.K. version of the LP jacket was dominated by the words “Are You Normal” in large capital letters. The photo of the sheep on the chaise longue was shrunk to about the size of a postage stamp.

In an interview, 10cc singer and bassist Graham Gouldman admitted that although he had had the album art explained to him in the past, he couldn’t recall what it meant. “But I know it’s a brilliant picture,” he said. As for all that pricey effort for such a tiny image? “It doesn’t matter, does it?,” Gouldman said. “It’s art. So it’s got to be done.” He added, “And in Hipgnosis’ case, if you can get the record company to spend the money, then good for them.”

Dutch filmmaker Anton Corbijn, director of “Squaring the Circle (The Story of Hipgnosis),” a documentary on the design firm that opens in New York City on Wednesday, had a slightly different take. “It’s just not normal to fly all the way to Hawaii to do that picture,” he said. “But it makes for a good story.”

“Squaring the Circle” is full of this and other good stories about the oft-absurd lengths London-based Hipgnosis traveled in pursuit of the perfect LP cover in the era before Photoshop. Among the 415 album covers Hipgnosis made between 1968 and 1983 was Pink Floyd’s “Animals” (1977), for which a 40-foot inflatable pig was photographed floating between the chimneys of London’s Battersea Power Station. Unfortunately, the single cable affixed to the pig snapped, and up the balloon went — into the flight zone for Heathrow Airport.

“That was all very exciting, and rather alarming,” recalled Pink Floyd drummer Nick Mason, whose bandmate Roger Waters came up with the idea for the shoot, “because it was obvious that you could have a major disaster for an airline that happened to fly into the escaping pig.”

No planes were harmed in the making of the LP cover, but in the end, Hipgnosis had to resort to a photo collage to achieve the desired effect.

The documentary — shot largely in high-contrast black and white by Corbijn, also a rock photographer and video director known for his work with U2 and Depeche Mode — features new interviews with Powell, plus a number of high-profile former Hipgnosis clients, including all three surviving members of Pink Floyd (David Gilmour, Mason and Waters) and Led Zeppelin’s Robert Plant and Jimmy Page. Paul McCartney, Peter Gabriel and Gouldman are also among the talking heads. Noel Gallagher, a fan, provides some modern-day context and comic relief.

Much of the film focuses on the close working relationship between Powell and Thorgerson, who came up together in the Cambridge, England, art scene of the 1960s, where they were friends with young members of Pink Floyd. (Peter Christopherson, a founding member of British industrial band Throbbing Gristle who died in 2010, became a full partner in Hipgnosis in 1978.)

The design studio would end up doing nearly all of Pink Floyd’s album covers, including “Atom Heart Mother” (1970), which was simply a photograph of a cow in a field, and, most famously, “The Dark Side of the Moon” (1973), with its iconic image of a triangular prism refracting light into a rainbow pattern. (Hipgnosis’ second-best-known cover also came out in 1973: Led Zeppelin’s “Houses of the Holy,” which features a group of naked children scaling basalt columns.)

The “Atom Heart Mother” jacket in particular represented a major departure from the style of the time, which Mason described as putting “a picture of the lovable moptops on the front.”

“We started making demands — which Pink Floyd totally backed us on — saying ‘No title, no name of the band on the cover,’” said Powell, now 76. “This was unheard-of in the world of marketing and record companies.”