Ok, there's a few things you have to understand about lighting in UDK.
-there's two types of static lighting: lightmapped and per-vertex.
-if the UV channel provided for lightmapping is not valid or the resolution is zero, UDK calculates the light intensity at each vertex. It's good for high vertex densities, but not so great for low vertex densities as above.
-the other type requires an unwrap with no overlapping or tiling UVs (all in the tile) and a fixed square resolution, and saves the lighting data to a (number of) texture. This would probably be better for your model. You need to make an unwrap on a second channel with no overlaps or tiling. UDK has a tool built in to repack your islands but it's not fantastic as none are.
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Are you exporting to the FBX format ? If so there should be an option to export smoothing groups.
Can you post a shot of the model in max ? I presume this is not happening there ?
-there's two types of static lighting: lightmapped and per-vertex.
-if the UV channel provided for lightmapping is not valid or the resolution is zero, UDK calculates the light intensity at each vertex. It's good for high vertex densities, but not so great for low vertex densities as above.
-the other type requires an unwrap with no overlapping or tiling UVs (all in the tile) and a fixed square resolution, and saves the lighting data to a (number of) texture. This would probably be better for your model. You need to make an unwrap on a second channel with no overlaps or tiling. UDK has a tool built in to repack your islands but it's not fantastic as none are.
[ame="http://www.youtube.com/watch?v=bbdOpuKqGaQ"]Creating a lightmap UV channel - YouTube[/ame]