My first real “ahhh” moment on the world’s newest cruise ship came as I eased myself into a “martini-glass” hot tub, a mere wrist-stretch from a piña colada.

Having clocked up more than eight miles (almost 14,000 steps) during my two-day run around Celebrity Edge it was a blissful juncture heightened not only by the pressure jets pummeling my feet, and the punch of the rum, but the unobstructed view of the penny-slot-drop sunset over the Caribbean Sea.

The most hotly anticipated cruise ship of the year arrived at her home in Florida’s Port Everglades earlier this week – ahead of her christening on Tuesday by Nobel laureate Malala Yousafzai. Although Malala won’t be setting sail (she has to be at Harvard the following day to receive an activist of the year award) her role as godmother to the 2,918-passenger ship is a massive coup for Celebrity Cruises.

As I wallowed in the tub I recalled that morning’s architectural insight tour. Tom Wright (the W in WKK Architects), whose other projects include the Burj Al Arab hotel, had explained how his vision for two bowl-like tubs perched on a stem had come to fruition.

Nothing is simple when it comes to cruise-ship design. Constraints include motion, load distribution and the small matter of where to hide unsightly things like cooling systems and plumbing.

The much-anticipated Magic Carpet doesn't disappoint

Celebrity’s break-the-mould $1 billion ship is the culmination of four years’ to-ing and fro-ing between cruise-line execs, the blue-sky thinking of a stellar team of designers and worker bees at STX shipyard in France.

“You want to put a hot tub on a stick? Forget it!” was more or less the response to Wright’s idea. “Luckily for us,” he continued, “STX had an engineer with exemplary talent for this type of structure. He decided it was possible and ran with it.”

“We’ve got store rooms of brilliant ideas,” added Wright. “It’s just a case of marrying the right ideas with the right ship.”

Relax in the ship's spectacular roof-top garden

And how. This is the first time a ship has set sail with a tennis-court-sized room cantilevered off one side. The “Magic Carpet” can be lowered, raised and used in various ways – from a posh tender-boarding platform that hovers at sea level to a restaurant, bar and live music venue on deck 13.

I loved seeing it dangle, mid-air, when one half of it did a fly-by past my room.

The rule book has also been ripped up in Eden, a three-storey glass-walled bubble of a lounge-cum-restaurant-cum-performance space where Patricia Urquiola has gone all out with a retro-cool pistachio-hued carpet, acres of hanging plants, toffee-coloured sofas, “tree-trunk” pillars and a herb wall behind the bar that doubles as a store for cocktail garnishes. All around are cosy seating nooks to lose yourself in.

Culinary wows on board Celebrity Edge Credit: Teresa Machan

In the two-storey Edge Villas, which house a sea-view plunge pool, Kelly Hoppen has infused warm and neutral tones with pops of “Hoppen green”. There are plantation rockers, beaded stools and New York-style subway tiles in the dining room.

“It screams ‘woman’,” said Yolanda, the suite guide-cum-realtor, who was doing a great job of justifying the £24,300-per-week price tag.

For better views than the captain book one of the two-bedroom, two-bathroom Iconic Suites, which sit above the “wings” that extend from the bridge. The whopping 2,500 sq ft suites spill on to a vast veranda with a hot tub and a shaded cabana. Inside there’s a butler’s pantry for entertaining and a rugby-team-sized bathtub with more jets than a geyser.

Work off any excess calories consumed, with a walk around the main pool Credit: Teresa Machan

Stairs are notable by their absence. In Eden you perambulate to a mezzanine level via a spiralling ramp; on the pool deck a gently sloping jogging track-cum-walkway leads to the 14th deck, where Wright has conjured a Zen-like rooftop garden.

Curvilinear seating, hand-carved screens and treetop sculptures that provide wind protection, as well as shelter from the sun, are used to great effect. Planters of salt-resistant shrubs are tended by a resident horticulturalist.

Prior to boarding I had heard much about Edge being the first ship to be designed entirely in 3D. What did it mean?

Edge also features two martini glass-shaped hot tubs Credit: Teresa Machan

I dismissed it as a load of old waffle. For the architects, who had spent thousands of hours immersed in a “3D cave” reviewing, fine-tuning and perfecting every single detail it was nothing short of revolutionary. “This is probably the 30th iteration,” said Wright, of the garden. “We were able to put the entire deck in a wind tunnel.”

Instagram positively purred. A post of the garden with its white sofa seating, tropical cushions, carved trees and plants received 88 likes and garnered comments including, “That’s not a cruise ship!” and, “This is a ship?”. My mum nailed it: “It looks like a ‘room-’ at Chelsea Flower Show… and then you see the sea.”

Back in the martini glass, I wondered whether my 360-degree view of the now redolent, tangerine horizon could be improved.

Probably not.