DETROIT — ONE of the biggest coups of the recent North American International Auto Show in Detroit was Ford’s new GT, a sleek supercar that was developed in secret and revealed to a surprised audience.

The car, with a body made of carbon fiber, takes all of 3.2 seconds to reach 60 miles an hour. It is aimed at giving Ford a showpiece of style and engineering that it hopes will bathe its lower-end cars in panache — the so-called halo effect.

But the GT also is something of a first in the auto industry. At the same time that Ford engineers were developing the sports car for the real world, software engineers were working to build a digital version of the GT to star in the latest version of the Xbox racing video game, Forza Motorsport.

While video game developers have worked with automakers for years, it is rare for the two to partner from the start of a car’s development — and it meant that Ford had to invite the game developers into its inner circle at a time when few people, even at Ford, knew of the GT’s existence.