Here is an extract from the "Symmetric Multiprocessing Systems: Technical Report", SGI, 1993, which explains in reasonable detail how TLMMI works:
To facilitate high-quality textured imagery, RealityEngine2 employs a technique called MIPmapping. Derived from the Latin phrase, 'multum in parvo', MIPmapping suggests putting "many things in a small space". The process involves the generation of pre-filtered, lower-resolution versions of each texture so that textures applied to a polygon closely approximate its size.
Currently, the highest quality texture mapping in use in the real-time image generation industry is based upon a technique called Tri-linear MIPmapping. This technique has been available on Silicon Graphics IRIS 4D/VGXT series of graphics supercomputers as the highest level of texture quality; the next lower mode, Bi-linear MIPmapping, has the best performance. The RealityEngine2 graphics subsystem is designed as a texture mapping machine, using Tri-linear MIPmapping as the basic level of texture quality and delivering the highest level of performance.
When possible, it is always best to use MIPmapping. By performing much of the texture filtering in advance, MIPmapping provides level-of-detail management in the application of texture to polygons as the polygons vary in scale during dynamic motion of the screen. The new MIPmapping mode added by RealityEngine and RealityEngine2 is Quad-linear MIPmapping, which is used to render 3D textures.
The target quality level and performance mode for RealityEngine2 is 'Tri-linear Interpolation'. This is the highest quality texture function available anywhere and may be found on most of the newer high-end image generators for visual simulation. To simplify the system architecture, all MIPmapping texture modes below Tri-linear Interpolation peform Tri-linear Interpolation while retaining the same calling sequence as before for compatibility.