Particle simulations in space plasma physics community usually use the Cartesian coordinate system, which is suitable for the simple configuration considered there. In tokamak physics community, curvlinear coordinates are usually used because of the toroidal configuration. (Another difference is that the kinetic equation solved is usually the gyrokinetic one rather than the primitive Vlasov equation.) Since my research interests are in tokamak plasma, I will primarily use general curvilinear coordinate system in presenting the PIC method. Specificly, the Jacobian of the coordinate system will be explicitly shown in the formulas.