Art Companion, Chapter 28, Triangulation: When Guessing Fails

The Art Studio Companion: A Master Class for Artists

Note: This chapter was a transcript from my YouTube video:

In this study, we examined triangulation, one of the most advanced methods of organizing visual perception.

Triangulation is an essential and exciting technique in visual arts that enhances the accuracy and realism of compositions. It helps artists place objects in their true relationships, create accurate proportions, and convey believable perspective. With practice, triangulation trains the hand to capture what the eye sees. It is a fantastic process that will take your drawings to the next level.[1]

199 Demo with my markup.

In demo 199, triangulation involves marking two points (landmarks), such as the left and right sides of a bank of grass with a slight downward slope to the right side. To find the axis line of the slope, you align your finger, pen, or brush with the bank's edge and draw that axis line in your artwork. Next, you find the third point by using the same method to align the axis lines from point 1 to the object (center palm) and from point 2 to the object. The point where those two axis lines meet is the third point, creating a triangulated point. This method provides an excellent location for the object, such as the circular center of the palm.

200 Demo of pencil against glass plane.

When you want to triangulate something you see, imagine there is a glass window between you and the object. The idea is to lay your pencil against the imaginary glass plane and tilt the pencil between the two points. In this demonstration, I used my Idyllwild studio window on a cold February day. Point 1 is a small clump of wood, and Point 2 is the base of a pine tree. By placing my pencil against the glass, I demonstrate the axis lines formed between the two points. Normally we don't have a window between us and what we are drawing. But do your best to imagine it.

An intuitive mistake, which is common, is to turn the pencil towards the furthest object, as if you were pointing at it. Unfortunately, that does not give us the right axis line for the drawing. Imagining the glass window between you and the object, helps prevent you from pointing the pencil, and provides you with the right axis line for your drawing.

201 Demo: Do not point the pencil towards or away from the points.

202 Demo: Pencil flat against imaginary glass plane.

In demo 201, I incorrectly angle the pencil. However, demo 202 demonstrates the correct angling of the pencil between two corners of the box, keeping the pencil flat against the imaginary glass window.

Clock Face

203 Demo of a clockface.

The drawing on the right of the box illustrates the orientation of the axis lines on your paper, like a clock face. When aligning the angle of the pencil, envision it as one of the hands of the clock face. For example, as shown by the drawn clock face centered on the front corner of the box, I angled my pencil and found it would be directed towards a little after "2."

In demo 204, my second point (landmark) was the bottom front corner of the box. Again, envision a clock face at the second point. This provides the two main points from which you can triangulate the third points.

204 Demo of 2nd point of triangulation.

205 Demo of 3rd point of triangulation.

Training Your Hand

This technique of aligning axis lines trains your hand to draw what your eye sees. It's similar to learning techniques in a sport, where the goal is that with more practice, your body becomes coordinated and responds automatically. Initially, you may find yourself way off, as it's demanding work that requires refining. But with practice your estimations will improve exponentially.

After establishing a few points, you can use any two of them to find the next third point of the triangle.

In demo 206, all the outside edges of the box are drawn. Now it's time to erase all the guides and clock faces.

Pro Tip: When working on a canvas, I use vine charcoal and erase it with a kneaded eraser. This method can also be used on a painted surface.

206 Demo of triangulation continued.

In demo 207, noticed that the finished contour lines of the box are drawn in dynamic perspective. The top of the box has expanded as it gets closer to the viewer, while the bottom of the box appears smaller as it recedes into the distance. Yet, the perspective does not feel over-exaggerated; rather, it feels natural and realistic.

207 Demo of completion of triangulation demo.

Another important aspect of using triangulation is that it allows for objects to be drawn in correct proportions within the context of perspective. In painting and drawing, objects appear larger the closer they are to the viewer. For example, in figure drawing, if a model is reaching towards the viewer with one hand while the other hand is further away, the size of the hands will be different, with the closer hand appearing larger and the farther hand appearing smaller. Triangulation allows for the truest proportions to be integrated within the perspective, resulting in more accurate and realistic drawings.

By locating and marking points on the subject, triangulation can be used to draw even the most complex objects, such as feet and hands. For example, in demo 208, marking the knuckles' landmarks and connecting their axis lines results in natural-looking hands. Without this technique, drawing hands intuitively often feels unnatural and awkward.

Triangulation can be used in both general and/or highly detailed ways. But, if a high level of detail is desired, it may take many hours to simply mark all the necessary points.

208 Newberry, Creation, detail, 2022, graphite. Triangulating landmarks.

Triangulation is one of the most advanced techniques there is. It will elevate our drawings to a high level of realism and naturalism. Mastering this technique requires hard work and dedication, but the payoff is immense. By employing triangulation, subjects come alive, gain substance, and convey effortless naturalism.

Practice #1

As always, it is crucial to reinforce your understanding through practice. With a pencil and eraser, draw a contour line drawing of a simple still-life featuring three objects, such as a fruit, cup, and book. Dedicate 3-9 hours to complete the drawing, allowing ample time for lots of axis lines and lots of erasing! The idea is to do a kind of mechanical drawing that, with erasing, ends up looking completely natural.

Pro Tip: Don’t rush to finish, rather enjoy each little landmark that falls into place.

Practice #2

As always, it is crucial to reinforce your understanding through practice. Using pencil and eraser create a line drawing of your hand from life. Think of each knuckle as a planet, and that you are aligning the cosmos within your hand. That has a nice symbolism to it. Like with the still-life, give yourself 3-9 hours.

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[1] This chapter is based on my online video tutorial, Triangulation in Drawing on YouTube. I am shocked that such a nerdy tutorial has garnered more than 13K views.

The Art Studio Companion: A Master Class for Artists will be available in May, 2024 via Amazon.