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projecting 2d-triangles into 3d-objects (made of triangles, too)??

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do you guys know any good tutorials or tricks how to project a bunch of 2d-triangles into 3d-objects? i''m working on a 3d-terrain engine. i have generated triangles from 2d-curves (fields, lakes, shores, etc, 2d-map data). the terrain is 3d triangles and now i''d like to cover it with area geometry. the problem is that the terrain and the areas don''t share vertices so i somehow need to project the fields into the terrain. anyone knows how to do this fast (or how to do it at all)? currently i render the area polygons into textures and cover the terrain with them, but that eats a lot of memory and doesn''t look very good...

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