The Flying Triangle

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Ancient Cuneiform depended the incisions of little “v” corners, modified triangles pressed into clay.  In art the triangle is fundamental.  It can be foreshortened, extended, overlapped, made to appear ascending or descending or turning.  Example one presents a series of diagrams illustrating these different systems for building space using the triangle.

Example 1.  Triangle Diagrams,

My first triangle demonstration addresses an aerial view of NYC along with its respective diagram (examples 3 and 4). The triangle drives toward the beholder but, appears to slide under the beholder’s vantage point.  I exaggerated the effect by squeezing the triangular image into a tight square.  You see how I reconstructed the image by looking at the original unedited photo (example 2). In the diagram (example 3) I demonstrate two-point perspective with the vanishing points set on the far right and far left on the eye level. Their two respective receding triangles leave an advancing triangle (in red) in the center.

Example 2. Original unedited photo.

Example 2. Diagram for painting.

Example 3. Painting of NYC from an aerial perspective.

A more straightforward single point perspective design can be seen in examples 4 and 5. The image derived from the observation deck at Rockefeller Center looking north to Central Park. Example 4 presents a triangle whose recessional lines converge on the eyelevel horizon at a central vanishing point.  This creates a feeling of movement which helps to give movement to the overly rigid linear perspective grid. The painted example uses a mix of vanishing points which all roughly gather around the central vanishing point.  The beholder has  a vantage point about 60 stories above Manhattan looking north to Central Park with the Hudson River on our left.

Example 4.  Triangle diagram with single vanishing point.

Example 6. Painting with many slightly askew variations on the single vanishing point.

Like Example 2, Examples 7 and 8 use a two point perspective system. One is far left and the other is farther right.  The difference is, here you can see lines above the eyelevel which descend to the far right vanishing point.  These lines indicate the location of building lines. The crosswalk lines are indicated in red. The painting (example 8) is still underway.

Example 7. The diagram with ascending and descending recessional lines.

Example 8. The painting, a street scene.

The next examples (9, 10 and 11) add some new complications. In the diagram we see three vanishing points. The principle vanishing point controls the direction of the primary triangle (representing ascending sea grasses). But, these sea grasses level off and turn to the left. They are illustrated with red lines in the diagram.  In the original photo there is no clear descending triangle above the horizon. I applied  this above the eyelevel to the diagram.  It solved a problem for me. I needed to have beholder see into infinite space so; I created the triangle above the eyelevel with its viewing notch of the distant water. Example 11 presents the painting, a 36×48” image on brushed silver enameled laminated aluminum.

Example 9, original photo without distant viewing notch.

Example 10. Diagram.

Example 11.  Painting of ascending, turning sea grass with distant viewing notch.

Lastly, is a bridge and canal painting in examples 12 and 13.  The underside of the bridge has recessional lines that converge down into a triangle. The pylons supporting the bridge converge to the far right creating a series of right-flanked triangles with the exception of the wall on the far right.  There we see the left flank of the supporting structure.  The colors are set in  both high value and color contrasts.  Shapes slightly overlap and appear to vibrate ( a surrogate for our  parallax stereoptic vision).  Apart from the structural design I enjoyed painting the industrial surfaces and the textured vibrating watery surface.

Example 12. Diagram of Bridge and Canal image.

Example 13. Painting, Bridges and Canals, 24×48, on enameled aluminum,

I invite you to join me this April 20-23, 2017 (Thursday through Sunday) the Cultural Center at Ponte Vedra Beach sponsors of workshop with me; two days on location and two days in the studio. Call Sara Bass at 904-280-0614 x 204 or register at .







  1. Agnes Wnuk

    Dear David, These diagrams and examples are both instructive. Thank you for sharing your expertise with us students. Will be studying carefully before designing my next painting.

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