1. A computer-implemented method for converting a nonresident mipmap level of a texture map into a resident mipmap level of the texture map, comprising: receiving a request to convert the nonresident mipmap level into a resident mipmap level for use in rendering an image for display, wherein the resident mipmap level is stored in a physical memory accessible by a processing unit and the nonresident mipmap level is stored in a portion of virtual memory that is paged out of the physical memory; initiating a copy of the nonresident mipmap level from a nonresident memory storage to a resident memory storage; and updating an extrapolation threshold level of detail (LOD) value that is used by the processing unit to produce filtered texel values of the image when the copy of the nonresident mipmap level is complete.