You could almost do this by adding an Array modifier to your plane. Add an Empty to your scene, and use it as the Object Offset of the modifier:

Translate and rotate the Empty to control where copies of your plane will be generated.

Of course, you'll have to manually move the Empty around until it looks good.. I'm not sure how you could automatically detect the amount of offset required.

1. Add an Array modifier to your plane
2. Add an Empty to your scene
3. Set the Object Offset of the modifier to the new Empty:
4. Move the Emtpy up along Z, and rotate it 90 degrees.

Of course, you'll have to manually move the Empty up and down until it looks good.. I'm not sure how you could automatically detect the amount of offset required.

When you click "Apply" on the Array modifier, both planes will exist as a single object.