The language of obsession is often dark. Someone in its throes can be described as a victim of mania or addiction. He can be tarred as a fetishist or compulsive. According to Sigmund Freud, who gave it the diagnostic term “fixation,” obsession is an infantile attachment, a snapshot of a moment in the earliest stages of sexual development that persists into adulthood, causing immature and neurotic behavior.

Speaking as an unrepentant obsessive, let me also point out that obsession is the stuff that makes the world go round.

Whatever the reason, human beings fixate — on things, ideas, dreams, people. The question of how a particular seed gets planted, and why we’re receptive to it, is an endlessly fascinating mystery.

Of course, some people have the bug worse than others. And some have the means to pursue their obsessions to the ends of the earth. Case in point, Tim Jenison, a wildly successful high-tech inventor who one day, for whatever reason, woke up with a crazy idea: “I’d like to paint a Vermeer.”

There were two reasons why this should have been a non-starter. Johannes Vermeer, a 17th century Dutch painter known for his photorealistic portraits of domestic scenes, including “Girl with a Pearl Earring” and “The Astronomer,” is considered one of the greatest artists who ever lived. His mastery of the nuances of interior light has never been equalled. His entire creative output amounted to a handful of paintings, each one of which is a priceless masterpiece. And his technique, so different from his contemporaries, has defied centuries of attempts to suss it out.

Setting all of that aside, Mr. Jenison had another minor obstacle to overcome: he’d never painted a painting. Not one.

But the seed of this crazy idea fell on fertile soil, and Mr. Jenison dedicated nearly five years of his life to the pursuit of this impossible goal. At the outset, he had the good sense to approach his old friend Penn Jillette, a showman, magician, and fellow obsessive. Mr. Jillette encouraged him to make a film of the Vermeer project, and offered the services of his magic partner, Teller, as director.

The resulting film, Tim’s Vermeer, which is available on DVD from Netflix or from your local library, is as much a portrait of obsession as it is an exploration of the intersection of art and technology.

One of the great puzzles of Vermeer’s method is that he seems to have worked without sketching. X-rays of his canvases reveal no outlines or preliminary images of any kind underneath the paint. This sets him apart from all of his contemporaries, whose methods can be derived, or at least inferred, from the layers under the varnish. It was as if Vermeer had a photographic ability to look at a scene and render it exactly as it appeared to the eye, without any concession to the constraints of brush and pigment.

Building on the work of British artist David Hockney and physicist Charles Falco, who proposed in 2001 that the Old Masters — including Vermeer — relied heavily on optical devices to create their paintings, Mr. Jenison set out to cast and grind the lenses that Vermeer might have used to project his scenes onto canvas. Using only techniques and materials that were available in Holland in the 17th century, and studying Vermeer’s paintings from the perspective of an inventor of optical devices, Mr. Jenison stumbled on a combination of lenses and mirrors that enabled him, simply by moving his head up and down, or back and forth, to compare a projected scene with the paint he was laying down as he copied it. By focusing on a tiny portion of the canvas at a time, and simply by comparing the tonal values of the laid-on paint to those in the projection, the device enabled anyone, even a complete novice, to act as a kind of human camera.

His first oil painting, a copy of a black and white photograph of his father-in-law, took a mere eight hours. It was virtually perfect. This was an incredible achievement for a man who’d never before lifted a brush or mixed a color.

Having crossed the first hurdle, he set his sights on the summit of Everest: Vermeer’s “The Music Lesson,” a painting of incomparable subtlety and mind-boggling detail.

In order to test his method, Mr. Jenison would have to create a full-scale replica of Vermeer’s studio, with its heavy ceiling beams and geometrically tiled floor, its intricately leaded windows, its precise angle of exposure to the sun — everything down to the last detail. Then he’d have to fill it with exact copies of everything that appears in the painting: the musical instruments (a virginal and a viola da gamba), the elaborately dressed student and music master, the chair with carved lion’s heads, the Oriental rug, whose every knot is visible in Vermeer’s painting…

It took years — years — to build the set. And only then was it time to start painting.

I won’t ruin the film by revealing the result of Mr. Jenison’s gorgeous experiment.

Suffice it to say that with obsession, the journey’s the thing.