Now, think about this:

What about when we have lines which are neither orthogonal to the picture plane nor parallel to it? Do they have vanishing points, or not? And if so, where are they?

• Draw at least 3 views of this situation: the usual view where you can see all three axes and the line, along with a top view (with the y-axis invisible) and the side view (with the x-axis invisible). Remember to place the viewer's eye on the z axis, and to draw a line that is neither orthogonal nor parallel to the picture plane. Then sketch in lines of sight from the viewer's eye to the line.
• What can you say about how equally spaced points on the line will appear to the viewer?
• Will the line ever "vanish" to the viewer? If so, in what direction will the viewer be looking when the line vanishes?
• What about a second line, parallel to the first. Will its perspective image be parallel to the first? If not, where will they intersect?
• What about the specific situation when the lines are "horizontal", that is parallel to the "floor" (the xz plane)? Do these lines have vanishing points? If, so can you say something more specific about where they are?
• What about the different situation when the lines are parallel to the "side wall" (the yz plane)? Do these lines have vanishing points? If so, where are they?

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