At the heart of Barra is a symbol of Rio’s profligate spending and class divisions, a new arts center, the City of Music, designed by the French architect Christian de Portzamparc, across from a giant mall with a replica of the Statue of Liberty out front. A project started under the previous mayor, twice over budget at $250 million and marooned in the middle of a highway, the place has provoked angry complaints that it is out of touch with both the city’s culture and its real needs.

A concrete complex of theaters, raised sky high on giant piers, the center may be the most absurd new building in years. It can bring to mind that famous Stonehenge gag from the film “This Is Spinal Tap,” in which a design for a rock concert stage-set mislabeled feet as inches — except the proportions here are reversed. People in charge complained to me about whole sections of unusable seats without views, ineptly designed stages, halls without dressing rooms, windswept plazas and staircases going nowhere.

Farther west, the Olympic Village, accelerating urban sprawl, rises on a site that will become yet more luxury housing after the Games. The development threatens to dislodge Vila Autódromo, a longtime favela. I walked the favela’s quiet, rutted streets. Children bounced on a broken trampoline; music wafted from a church; a family took me onto its rooftop terrace with a view over mango and guava trees onto the bay. Altair Guimaraes, the head of the residents’ association, roused from his nap in a hammock after working the night shift, shook his head. “You don’t need to massacre the people to do mega-events,” he said.

The story isn’t that simple. In the working-class areas to the city’s north, like Méier and Madureira, the city has been providing new clinics, running new bus lines, building schools. I visited Madureira Park, a mile-and-a-half-long, $50 million concrete and green swath with a giant samba stage and water feature, built on land freed up by relocating high-voltage electric lines. The place has been a game changer for residents of a crowded district with precious little open space.

In Méier, I toured an old movie palace where Bob Dylan and Brazil’s Dylan, Tom Jobim, once performed, lately reborn as the João Nogueira Cultural Center, with a multiplex, exhibition space and a rooftop terrace. Old men sunbathed and teenagers flirted in the shade of a concrete trellis.

But alongside those upgrades, other public projects make no sense: the Minha Casa Minha Vida (My House My Life) projects are glum new housing blocks for the poor, cheaply made, proliferating around the city, many far out west, a long distance from where resettled residents used to live. Morar Carioca, a public program to bring architects together with favela residents and public officials, promised collaborative solutions to redevelopment. Residents in Providência, consulted as part of the program, said they wanted clean streets and paved roads.