City officials and planners will hold a public meeting on Tuesday to discuss the James Edgar Park redevelopment project. The meeting has been called by Mayor Linda M. Balzotti, Ward 2 City Councilor Tom Monahan, the Brockton Redevelopment Authority, and the city’s Planning and Parks departments. It will be held at George’s Café, 228 Belmont St. Refreshments will be served. Work to revamp the historic park bordered by Brook, Dover, South Fuller, and Winthrop streets is to be funded by a $400,000 grant from the state Office of Energy and Environmental Affairs. It will go toward new playground equipment, new volleyball and basketball courts, parking areas, storage and bathroom facilities, benches, and drainage for the field where American Legion games are played.