I am trying to make a globe (a sphere with maps on it) with OpenGL ES 1.1 on iOS.
I can draw a sphere and draw borders, but with one problem: lines that are not facing my view are also drawn on the screen . Like this:

The picture shows that America looks great, but you can see Australia on its back. It should not be displayed because it is at the back of the globe, and the BLACK and PURPLE bands in the globe are not transparent.
Any ideas on what options should be tuned in order to get the right globe?
If this helps, I can post the relevant parts of the code . Just ask in which part, and I will update the question.
Thank you very much in advance.
: , Sphere:
glEnableClientState(GL_VERTEX_ARRAY);
glPolygonOffset(-1.0f, -1.0f);
glColorMask(GL_FALSE, GL_FALSE, GL_FALSE, GL_FALSE);
int x, y;
GLfloat curR, curG, curB;
curR = curG = curB = 0.15f;
for (y=0; y<EARTH_LAT_RES; y++) {
if (y%10 == 0) {
glColor4f(curR, curG, curB, 1.0f);
curR = curR == 0.15f ? 0.6f : 0.15f;
curB = curB == 0.15f ? 0.6f : 0.15f;
}
for (x=0; x<EARTH_LON_RES; x++) {
Vertex3D vs[4];
vs[1] = vertices[x][y];
vs[0] = vertices[x][y+1];
vs[3] = vertices[x+1][y];
vs[2] = vertices[x+1][y+1];
glVertexPointer(3, GL_FLOAT, 0, vs);
glDrawArrays(GL_TRIANGLE_STRIP, 0, 4);
}
}
glColorMask(GL_TRUE, GL_TRUE, GL_TRUE, GL_TRUE);
glDisable(GL_POLYGON_OFFSET_FILL);
glDisableClientState(GL_VERTEX_ARRAY);
, :
int i;
glEnable(GL_BLEND);
glBlendFunc(GL_SRC_ALPHA, GL_ONE_MINUS_SRC_ALPHA);
glEnableClientState(GL_VERTEX_ARRAY);
for (i=0; i<vxp->nFeatures; i++)
{
glVertexPointer(3, GL_FLOAT, 0, vxp->pFeatures[i].pVerts);
glDrawArrays(GL_LINE_STRIP, 0, vxp->pFeatures[i].nVerts);
}
glDisableClientState(GL_VERTEX_ARRAY);
glDisable(GL_BLEND);
, :
glMatrixMode(GL_PROJECTION);
glLoadIdentity();
glEnable(GL_DEPTH_TEST);
glEnable(GL_CULL_FACE);
glCullFace(GL_BACK);
glOrthof(-1.0f, 1.0f, -1.5f, 1.5f, -1.0f, 1.0f);
glFrustumf (-1.0, 1.0, -1.5, 1.5, -1.0, 1.0);
glMatrixMode(GL_MODELVIEW);
glLoadIdentity();