A matter of perspective

Today was supposed to be very hot but it seemed cool and breezy, maybe due to overcast conditions. When the sun popped out it did indeed get toasty out there. I stopped at Beesborough street, an unremarkable suburban street in NDG, that happens to have a good place to stand and paint just beside the Dormez-Vous which you see as the building on the left. The trees were an interesting variety of yellow-greens and chartreuse. 

Perspective is tricky in landscape painting, the scale of things and the shape of linear objects is all affected by distance. The simplest and most widely taught approach is to use a vanishing point, and make all objects scaled or aligned with lines that emanate from the vanishing point. In the painting you can imagine the lines of the road, sidewalk and building converging on a point somewhere in the middle of the scene. The problem with linear perspective is that it only seems to accounts for objects at a certain distance from the viewer. It never seems to work accurately when objects are very close, or very far from your eyes. 

To test perspective, I set up a ruler at a fixed distance from my eye, and then moved an object away from me 1 meter at a time. Then I measured how big the object appeared to be the farther away it got. You can do a simpler version of this by holding your two hands near your face, and moving one hand away until it is about half the size of the other hand. You have to move your hand about 40cm away to have it appear to be half the size of your other hand. Now, try to move your other hand so it is half the size of the hand you moved. It seems like a real stretch now. In fact, in my object test the object had to be about 2.5 meters away to appear one quarter of its original size. 

However I look at it, perspective is not linear, objects that are close to the viewer will loose a lot more of their apparent size than objects that are situated further away. Depth perception is very complex, and I could not find an adequate equation to explain the phenomenon. Perhaps a deceleration curve or inverse log curve. 

What is this to an artist? Sharp angles such as the one you see in the painting above are very hard to get right. I believe the roof line of the building should have been shown as logarithmic, not linear! I was doing a painting of the Lachine Canal a few years ago, in that painting, as I sat quietly, almost meditating, I saw the curvature of the canal wall that I was sitting on. You see in the link, I tried to emulate it by making the straight lines curved. Your brain's visual system is telling you its straight. Anyways, it will take some trigonometry, calculus, and focal point knowledge to figure this one out.   
 

Av. Beesborough View 5 x 7" cold press, watercolour, May 2021 (No. 2644a)