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OpenGL: Triangles with Infinite Points

I am trying to make a two-dimensional half-plane in OpenGL with the following code:

void renderHalfplane(double *x, double *n)
{
  glPushMatrix();
  double theta = -360.0 * atan2(n[0], n[1])/(2.0*PI);

  glTranslated(x[0], x[1], 0);
  glRotated(theta, 0, 0, 1.0);

  glBegin(GL_TRIANGLES);
  glVertex4d(0.0, 0.0, 0.0, 1.0);
  glVertex4d(1.0, 0.0, 0.0, 0.0);
  glVertex4d(0.0,-1.0, 0.0, 0.0);
  glVertex4d(0.0, 0.0, 0.0, 1,0);
  glVertex4d(-1.0,0.0, 0.0, 0.0);
  glVertex4d(0.0,-1.0, 0.0, 0.0);
  glEnd();

  glPopMatrix();
}

Here I use homogeneous coordinates to draw triangles with two vertices at “infinity”.

This code works like a charm on my computer, but the user reports that he does not correctly display them: instead of an infinite half-plane, they see two (final) triangles.

Am I using the w coordinate 0 undefined behavior? Is this something that only works on some versions of OpenGL? I tried to look at the Hronos OpenGL specifications, but could not find a section in which rendering of primitives with a w-coordinate of 0 was processed.

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(nVidia Quadro), . ( ), W , .

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