Part of the reason the Chinese artist Ai Weiwei — the subject of a current exhibition at the Brooklyn Museum and of Danish filmmaker Andreas Johnsen’s new documentary, “The Fake Case” — is such an intriguing figure is that his recent career feels like the latest battle in the very old war between the imagination and the state.

Especially since 2008, when the aftermath of the Chengdu earthquake in China awakened his conscience and made him a determined critic of his government, Ai has taunted, mocked and passionately denounced the authoritarianism, corruption and incompetence that he sees around him. He has made more-or-less conventional works of art reflecting these concerns, and made deft use of social media and his own celebrity.

The essential cinematic introduction to Ai remains Alison Klayman’s 2012 documentary, “Ai Weiwei: Never Sorry.”Johnsen’s film is an interesting addendum and no doubt a harbinger of more sequels to come. It takes up the story in 2011, after Ai had been detained for nearly three months and found himself under virtual house arrest.

Charged with tax violations and forbidden to leave the country or speak to the press, he spends his days in the Beijing complex that serves as his home, studio and quasi-corporate headquarters.

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Under constant surveillance, he goes for walks with his young son, talks with lawyers and foreign journalists, and supervises the making of new work. Some of the film reflects directly on his confrontations with the authorities.

Though his impish sense of humor is still intact, he also seems tired and melancholy.

Throughout “Ai Weiwei: The Fake Case,” Johnsen’s camera never leaves Ai’s side, giving the film an informal intimacy. Critical and contextual perspectives will have to be sought elsewhere. Johnsen offers viewers the challenge and pleasure of an important artist’s company, and a chance to appreciate anew his wisdom, his wit and his bravery.