BALTIMORE — National Guard troops fanned out through the city, shield-bearing police officers blocked the streets and firefighters doused still-simmering blazes early Tuesday as a growing area of Baltimore shuddered from riots following the funeral of a black man who died in police custody. The violence that started in West Baltimore on Monday afternoon — within a mile of where Freddie Gray was arrested and placed into a police van earlier this month — had by midnight spread to East Baltimore and neighborhoods close to downtown and near the baseball stadium. It was one of the most volatile outbreaks of violence prompted by a police-involved death since the days of protests that followed the death of Michael Brown, an unarmed black man who was shot and killed during a confrontation with a white police officer in Ferguson, Missouri, last summer. At least 15 officers were hurt, including six who remained hospitalized late Monday, police said.