1. A method for rendering a plurality of objects, the method comprising: receiving ray differential information associated with a ray; determining a first ray differential based on at least information associated with the ray and a first surface patch; processing information associated with the first ray differential and the first surface patch; determining a first resolution based on at least information associated with the first ray differential and the first surface patch; obtaining a first geometry representation based on at least information associated with the first surface patch and the first resolution; obtaining a second geometry representation associated with a second surface patch tessellated at a second resolution, the second surface patch being adjacent to the first surface patch; determining whether there is at least one patch crack between the first geometry representation and the second geometry representation; if there is the at least one patch crack, performing a stitching process to the first geometry representation and the second geometry representation; determining whether the ray and the first surface patch intersect based on at least information associated with the ray and the first geometry representation.