The 1-2-3’s of Linear Perspective

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Discover the Origins, Methods and Magic of the 3-point Perspective in Artistic Composition

Artists should have fun while painting and drawing. Anxiety shouldn’t be part of that experience, and yet there’s one word in an artist’s vocabulary that can easily strike terror in the heart: perspective. Some artists understand perspective, but most either avoid it in their work or simply guess at it. And while a stigma may exist around one- and two-point perspective, utter panic can set in at the mere mention of three-point perspective.

Considering it took ancient artists centuries to develop the rules for basic perspective, and hundreds more years to understand three-point perspective, modern-day artists shouldn’t judge themselves for any confusion they may feel around the subject. In this lesson, we’ll clarify one- and two-point perspective to shed light on what three-point perspective represents, how its effects are achieved and when it should be utilized. 

Origins of Perspective

All representational art is an attempt to represent, in a drawing or painting, what the human eye observes. Realism had its start with the artists of antiquity, but they soon realized there was a problem with trying to capture on a flat surface what the eye sees through its curved lens. So the Romans simplified that system and introduced art viewed on a flat plane. All later advances in perspective were based on observing scenes through a flat picture plane, a practice that still continues to this day.

In the original formula for both one- and two-point perspective, all vertical lines in a real-life scene remain vertical in a drawing. In other words, all vertical lines in a drawing should be parallel with the left and right sides of the drawing surface. In a way, this replicates actual human vision because our round lenses don’t perceive the convergence of vertical lines when the head is tipped up or down at moderate angles. Vertical lines in our field of vision appear to be parallel with the left and right sides of our sight line because the range of human vision spans nearly 180 degrees. Our eyes can be tipped as much as 30 degrees before we’ll begin to see vertical lines that seem to converge toward a third vanishing point above or below our point of view. By contrast, a flat lens has a smaller range of vision, and vertical lines converge with the slightest tip of the lens. In the early years of art history, however, no flat lenses existed, therefore virtually no three-point art was produced.

It wasn’t until the 1600s that Dutch artist Jan Vredeman de Vries (1527–1609) began to toy with a mathematical approach to finding that mysterious third vanishing point (see Säulengänge in Vogelperspektive). His work on this topic was later continued by German artist Johann Jacob Schübler (1689–1741) (see Perspectiva Pes Picturae). Most pre- and post-Renaissance artists, however, didn’t create images in three-point perspective because they couldn’t personally observe its effects in their daily lives. The 1800s brought about an invention that opened people’s eyes to three-point perspective: photography. When cameras with flat lenses came onto the scene, photographers were baffled by what happened to vertical lines in their photos. In pictures of architecture, for example, buildings looked like they were leaning back into the picture—so much so that, shortly after the invention of the camera, perspective-correcting, or “tilt-shift,” lenses were developed to adjust for defects made by flat camera lenses.

Perspective Methods

The distortion of vertical lines in photographs enlightened artists to what three-point perspective represents. They looked back to Renaissance artist Leon Battista Alberti (Italian; 1404–72) who invented perspective and the idea of a picture plane (or “artist’s window,” as he referred to it). Initially, with Alberti’s formula, artists analyzed horizontal parallel lines that projected into a scene to determine whether an image was in one-point perspective (horizontal lines converging at a central vanishing point) or two-point perspective (horizontal lines converging at two separate vanishing points). Alberti’s picture plane became a new tool to show what happens when vertical lines are observed through a tipped picture plane.

You can witness this effect for yourself by looking through your cell phone camera. Keeping the camera lens perfectly perpendicular to the ground, align the left and rights sides of the screen with any verticals in the view you are aiming the camera at. Once you have all the verticals parallel with the sides of the camera screen, angle the camera’s picture plane up and down and watch how easily the verticals in the scene shift up and down with the camera’s movements. A flat camera lens will distort verticals in a real-life scene with just a slight 1- or 2-degree tilt of the camera.

Now put the camera down and look at the same scene with your eyes. Tilt your head very slightly up and down like you did with the camera. The verticals in your real-life scene will not converge the way they did on the camera screen. This is because you’re looking at the real scene through a curved lens: your eye. The camera is focused on the same scene on a flat lens, thus the convergence of verticals in photographs. This is important information for artists who use photography as reference for their works. The knowledge of this effect is essential, and the correction of any vertical convergence created by a camera is mandatory. These days computer drawing programs can easily tip the angle of a view up or down. While the results may be interesting, it’s crucial that artists are aware of what the program is doing to their picture plane, and whether an angled viewpoint should be incorporated into their art. In other words, is the slant of the picture plane essential to the visual narrative? Is drama the intention for this painting, or is the pushing of verticals being applied for a specific purpose or effect? Whenever digital and photo references are used, artists must always ask these questions—and always be able to answer them.

The Magic of Perspective

After the late-19th-century discovery of three-point perspective, some early 20th-century artists began using it in their work. M.C. Escher (Dutch, 1898–1972) fooled the eye with his well-known three-point perspective illusions, and Howard Cook (American, 1901–80) used a third point to intensify the feeling of height in his urban landscapes of New York City (see Chrysler Building, in Construction). Comic artists of the early 1900s had the most fun with this technique, pushing the viewer’s point of view to extreme heights, depths and angles not seen before in the history of art (see Moon Girl).

Properly applied vertical projections can be seen in the contemporary works of April Flynn Hartzell, Don Taylor, Peter V. Jablokow and Tony Calandra. These artists use three-point perspective to communicate with their viewers. Their inclusion of a third vanishing point isn’t random, nor is it employed due to an unfamiliarity with the premise. Hartzell, for example, intentionally cranes our necks in her House No. 10 as we peer up a steep California hillside at a home surrounded by towering trees. The artist uses three-point perspective to exaggerate the setting, and skillfully portrays what we would see and how we would feel while looking at this view. Inside an Augsburg, Germany, cathedral, Taylor’s Angles, Arches & Light uses forced perspective to enhance the architectural magnificence high above our heads. A traditional one- or two-point perspective painting could never accomplish the majesty and awe Taylor captures in this stunning work. Similarly, Jablokow’s masterfully rendered Calumet River Vertical Lift Bridge stands as testimony to the psychological power three-point perspective can have on a viewer’s sense of scale. And Calandra’s commanding Midtown looks down through a tipped picture plane to take viewers deep into the caverns of the bustling borough of Manhattan.

On the Horizon

It took centuries for artists to discover and formulate the processes for three-point perspective. As modern-day artists, we all need to give ourselves permission to take it slow like our ancestors did. Teach yourself the differences between human vision and camera optics. Study what happens to images in your cell phone camera and how they differ from how you see the world with your eyes. Rest assured, no matter how complicated an image may be, the principles covered here will be at the foundation of every perspective puzzle you encounter.

Three-point perspective can be a potent device for telling your visual story, but when utilized incorrectly, it can cause problems for the uninformed artist. Now that you are better acquainted with the concept—how it works, where it originated, when to use it and when not to—all that remains is to go back to your work and have fun while bringing this information into your creative decisions.

John Roman (johnromanillustration.com) is an award-winning illustrator and the author of The Art of Illustrated Maps: A Complete Guide to Creative Mapmaking’s History, Process and Inspiration (HOW Books). He has taught illustration and perspective drawing at Boston’s Massachusetts College of Art and Design since 1993.

For more about perspective, take a look at these articles below:

• The Beginning Artist’s Guide to Perspective Drawing
• Understanding Perspective and Painting Depth
• All About Perspective Drawing: Linear Perspective in Art

A version of this article first appeared in the May/June 2023 issue of Artists Magazine.