I came away from “How to Train Your Dragon 2” not just amused, but impressed.

The computer-animated character and creature designs are sublime. The look (with top cinematographer Roger Deakins as visual consultant) is a ravishing flow teeming with movement, color and form. In the same way that “Finding Nemo” evoked the happy rush of tropical scuba diving, this aerial joyride conjures up the thrill of flight and free fall through cloud formations. There isn’t a single image that looks ordinary or stale.

That’s fine, but it’s the kind of craftsmanship we expect from big-budget entertainment. The impressive part is the storytelling confidence of writer/director Dean DeBlois. He has created a thoughtful tale as meaningful for grown-ups as it is pleasurable for its young primary audience. Like Aesop and the brothers Grimm, he refuses to sugarcoat the story’s bittersweet passages, spinning a fantasy saga with a resonant emotional pull. We know such stories end happily ever after. This one is willing to face a few painful realities on the way.

The Viking dragon-rider Hiccup (voiced with endearing dry humor by Jay Baruchel) is no longer the callow teen from the 2010 original. Now there’s stubble on his jaw and spunky purpose in his manner. In the last film, he put his life on the line to establish peace between his hooligan tribe and the flying fire-breathers. Creating a harmonious new human-dragon ecosystem earned Hiccup the admiration of his chieftain father, Stoick (Gerard Butler), but it also cost him his left foot. His prosthetic is taken in stride here. It’s both a positive message and a thematic point in a film about loss.

In gracefully conceived flight sequences, Hiccup and his dragon Toothless explore the boundaries of their region, searching for new dragon nests. There’s a coterie of the creatures on hand here, each with a distinctive look and personality, and also a slew of new human characters in the form of dragon rustlers. Do-gooding Hiccup hopes to negotiate a truce with the poachers, but the menace won’t be disposed of so easily. They’re capturing a winged air force for cruel Drago Bludvist (Djimon Hounsou), who aims to impose his will on all Norseland.

Of course, the conflict leads to a thrilling, epic showdown. But there’s so much more than pounding Leviathan action to enjoy. The wacky jokes mesh well with the adventure yarn. Poignant story strands from the first film are touchingly explored and elaborated upon. The theme of the movie is what we owe to our families and to ourselves both as parents and children, how doing what appears right can leave your kin feeling alone and lost.

The cast includes Cate Blanchett, Kristen Wiig and Jonah Hill, but the real performing stars are the animators. We’ve reached the point where computer-generated characters can convey subtleties of emotion with a finesse few human performers can equal. Toothless can be cuddly, stubborn, remorseful and abashed in the course of 15 seconds. Hiccup has a scene with Blanchett’s character that is absurdly moving. We may have arrived at a moment when we need not only a best-animated-film Oscar category, but a prize for the best digital performers.