Chart 5, page 48 in NACA Report 1135 is an example of this and as you say method of characteristics is needed for something other than a point source. You see the simple equation sin =1/M in a lot of introductory books and it is good for learning the concept but is only good for a point source.Shock angle is a non-simple analytical function of wedge angle (or nose angle for bullets) and mach number. For more complex shapes such as bullets ogives with bearing surface