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What do I do to a projection transformation to ensure that a single billboard quad always takes up the entire projection window?

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This is an OpenGL or DirectX question. Use 2D perspective:
glViewport(*rect)
glMatrixMode(GL_PROJECTION)
glLoadIdentity()
gluOrtho2D(rect[0],rect[0]+rect[2],rect[1],rect[1]+rect[3])
glMatrixMode(GL_MODELVIEW)
glLoadIdentity()

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