How to get sharp pixel boundaries with Texture? I'd like to have only black/white in the example below, no gray.
a := Image[Table[If[EvenQ[x + y], 1, 0], {x, 50}, {y, 50}]];
Graphics[{Texture[a],
Polygon[{{1, 0}, {0, Sqrt[3]}, {-1, 0}},
VertexTextureCoordinates -> {{1, 0}, {0.5, 1}, {0, 0}}]}, ImageSize -> 200]