DENVER — Condos and townhouses are rising beside the weedy lots here where Randy Russell once pitched a tent and unrolled a sleeping bag, clustering with other homeless people in camps that were a small haven to him, but an illegal danger in the eyes of city officials.

Living on the streets throws a million problems your way, but finding a place to sleep tops the list. About 32 percent of homeless people have no shelter, according to the federal government, and on Nov. 28, Mr. Russell, 56, was among them. He was sitting in an encampment just north of downtown when the police and city workers arrived to clear it away. A police officer handed Mr. Russell a citation.

“Now I don’t have a place to sleep tonight,” Mr. Russell told the officer in a video. “You’re taking my home away from me.”

Growing numbers of homeless encampments have led to civic soul-searching in cities around the country, from Philadelphia to Chicago to Seattle. Should cities open up public spaces to their poorest residents, or sweep away camps that city leaders, neighbors and business groups see as islands of drugs and crime?

For those on the streets — who have lost their jobs, have suffered from drug addiction, mental illness or disabilities — crackdowns on homeless camps are seen as tantamount to punishing people for being poor.

Activists and homeless residents like Mr. Russell are waging public campaigns and court fights against local laws that ban “urban camping” — prohibitions that activists say are aimed at the homeless. The right to rest, they say, should be a new civil right for the homeless. Many wear buttons that ask, “Move Along to Where?” and are challenging misdemeanor citations and anti-camping ordinances, like Denver’s, in court.

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