Leonardo da Vinci – as portrayed by Peter Capaldi in “Inside the Mind of Leonardo” – is a bit of an odd duck (if “portrayed” is even the right word).

Dressed in contemporary clothing and shot against various deeply shadowed walls of crumbling plaster, the “Doctor Who” actor is shown reciting passages from the Italian artist’s private journals. Capaldi declaims them with such an introspective, almost antisocial intensity (and occasional finger-twitching) that his Leonardo seems, at times, less like the greatest polymathic genius of the Renaissance than an evil genius with Asperger’s syndrome holed up in his lair. Interspersed with these monologues are various visual oddities.

At one point, Capaldi goes off at meticulous length about Leonardo’s famous system for measuring anatomical proportion.

I’m not sure of what general interest this is, except to artists. But it does offer some insight into Leonardo’s peculiarly insatiable way of considering things.

Director Julian Jones also includes a few shots of Capaldi staring directly into the camera, birdlike, as if he were either scrutinizing your face or about to peck at it. (Although some theaters have shown a 3-D version of the film, others will not.)

Among the more interesting passages in the film, which was produced by the History Channel, are those dealing with Leonardo’s sexuality. Widely believed to be gay, the artist wrote about his penis as seeming to have a mind of its own. He also noted, in his journals, that he found the act of heterosexual reproduction “disgusting.”

All of this makes for one eccentric moviegoing experience. Not quite documentary, yet by no means drama, “Inside the Mind of Leonardo” is what might be called poetic biography: maddeningly fragmentary and idiosyncratic, but 100 percent true.

Two stars. Unrated. Contains a tiny bit of crude language. 85 minutes.