Methods and apparatus for cutting a glass sheet along a cutting line into a desired shape. A laser source is configured to apply a laser beam to a beam location on the cutting line of the glass sheet. A source of cooling fluid is configured to apply a cooling fluid to a cooling band on the glass sheet to reduce a temperature of the glass sheet along the cooling path while elevating the temperature of the glass sheet at the beam location with the laser beam. The source of cooling fluid is configured to apply the cooling path as a cooling ring to circumscribe the beam location on the cutting line with the cooling band circumferentially spaced from the beam location while the cooling path and the beam location move simultaneously together in order to propagate a fracture in the glass sheet along the cutting line.