In two-point perspective, we draw our vertical lines, vertical. In three-point perspective, our vertical lines are at an angle, converging on our third vanishing point above or below. 

The simplest way to experience third-point perspective is to stand at the corner of a tall building like a church tower and look up. Not only will the sides of the church converge to vanishing points to either side, but the parallel vertical lines of the tower will appear to converge at some point high in the sky—our third vanishing point.

Three-point perspective makes for a more realistic scene but only becomes apparent when there's enough vertical relief, either up to the sky or below, in what we're viewing. As a result, we most commonly see it in views of downtown skyscrapers, perhaps with a caped or swinging superhero.

Also see One-point perspective and Two-point perspective.

Three-point perspective

Perspective can be tricky to get your head around. In drawing and art, using perspective creates the illusion of three-dimensional space on a flat surface. The simplest form to understand is one-point perspective. You will have experienced one-point perspective when standing in a corridor or looking down the center of a street. If you continue the parallel lines of the walls and ground toward the center, they would appear to converge at a central point in front of you at eye level, known as the vanishing point. When real-life features are parallel like this, you can use a central vanishing point as a guide to help capture the scene accurately.

The simplicity of one-point perspective makes it impactful. Leonardo Da Vinci, a personal hero of mine, famously employed one-point perspective in his painting of the Last Supper in the Santa Maria delle Grazie monastery in Milan. The vanishing point, carefully placed behind Jesus' head, draws the viewer's attention to the main subject of the scene.

Turns out Kubrick is pretty handy at one-point perspective.

One-point perspective

Lines converge to two points on a horizon.

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Two-point perspective