Graphics cards are made for rendering triangles (when you draw a square, you're actually just drawing two triangles), so as far as I know, all real-time terrain systems use triangles for rendering.
Can you tell me some more about TGEA's terrain system?
Horde's terrain system takes in a height-map (a big black/grey/white bitmap) which is then turned into a big model made up of triangles. Several different versions of this model are made with more/less detail, so distant parts of the terrain can use the low-detail versions and closer areas can use the high-detail ones. I think this is sometimes called "chunked lod".
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