“From Up on Poppy Hill” is frankly stunning, as beautiful a hand-drawn animated feature as you are likely to see. It’s a time-machine dream of a not-so-distant past, a sweet and honestly sentimental story that also represents a collaboration between the greatest of Japanese animators and his up-and-coming son.

“Poppy Hill” is directed by Goro Miyazaki, whose father, the Oscar-winning Hayao Miyazaki (“Spirited Away”), wrote the screenplay based on a graphic novel.

The year is 1963 in Yokohama, when all of Japan was gearing up for the 1964 Tokyo Olympics. With her father lost at sea during the Korean War and her mother studying in America, high-school-junior Umi (voiced by Sarah Bolger of TV’s “The Tudors”) has to keep an eye on her two younger siblings while doing a lot of the cooking and cleaning in the boardinghouse run by her grandmother.

Each morning, Umi runs two signal flags up the pole facing the harbor outside her hillside home. Why she does this is one of the plot’s gentle mysteries.

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As it turns out, one of Umi’s classmates has noticed the flags and written a poetic question in the school newspaper: “Fair Girl, why do you send your thoughts to the sky?” While Umi tries to figure out who that classmate might be, she becomes captivated by a jump a young man makes from the roof of an enormous but dilapidated old building called the Latin Quarter that the boys in the school use as a clubhouse. That young man, Shun (Anton Yelchin), jumps into a pool to protest that the school wants to raze the Latin Quarter and put a spanking new building in its place.

It will shock no one that Umi and Shun feel a strong, albeit demure, attraction to each other, but, surprising for a movie as genteel as this one, a very real-world obstacle is thrust in the path of their relationship.