When you say profound and obnoxious, is it mainly the intensity or the size of the highlight which is unpleasant?
The intensity ought to be lowered if you lower the intensity of the light source(s) affecting the entity. For example, a light which is coloured 255,255,255 could become 100,100,100, although this will obviously affect lighting in other ways and on other meshes.
The size of the specular highlight is going to depend on the distance between vertices, because B3D only does per-vertex lighting. In other words, your highlight will be at least the size of the distance between the nearest vertex to the light and the closest vertex to that first vertex. So if your mesh has just a few vertices, widely spaced, the highlight will be huge. The only way I can think of to deal with that would be to subdivide the mesh a few times to create a better spacing of vertices across the surface.
To be honest, Blitz3D's EntityShininess is a tough beast to tame, so if neither of those work, you might want to consider a sphere map or a cube map applied with additive blending, which should create a pleasing shine to the object if you paint the map quite smooth and subtle. I did that to create the shiny balls in Kick Shot Pool, and although they were pretty intense, that's only because the maps were painted that way.
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