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Curvilinear Perspective Part 2: Spherical Perspective

If you heard a lot of artists talk about perspective on the internet, chances are that you have heard people talking about fish eye lens, or 5 or 6 point perspective. I’ve seen many people use slightly different methods for drawing them, but at the end of the day, they are all different variations of the same thing, orthographic spherical perspective. To break down what this term means, let’s start with spherical perspective.

Spherical perspective is when, instead of using a flat picture plane, you use a spherical one. The basic principles of spherical perspective are very similar to cylindrical perspective, which I have already covered. The biggest difference is that the surface of a sphere is way harder to project onto a flat drawing than that of a cylinder. There have been some people who have skipped that process by just drawing straight on a sphere.

Image by Daisuke Samejima

There are also people who will use map projections, giving us things like azimuthal spherical perspective.

azimuthal perspective grid by David Chelsea

I you’re interested in spherical perspective that use map projections, I’d direct you towards the works of António Bandeira Araújo

The orthographic part of orthographic spherical perspective means that it is being projected orthographically. Orthographic projection is simply a way of projecting an environment so that things don't appear to change in size as they move closer or further away from the camera. The most famous form of it is isometric. Basically, instead of trying to project the entire surface of the sphere onto our canvas, we are simply trying to render the sphere as we would see it sitting in front of us, using a simple projection method.

The first thing you need to keep in mind when drawing spherical perspective is that every straight line will be drawn as portions of great circles, the largest circles that can be drawn around a sphere.

To draw a great circle in orthographic projection, all you need to do is make sure that the center of the ellipse (our circle) is at the center of the circle (our sphere).

Since the picture plane is completely encompassing the station point, every set of parallel lines will require two vanishing points. And since we usually work with three sets of parallel lines, we are going to need six vanishing points.

To draw parallel lines converging towards vanishing points, you simply rotate the circles so that they overlap at the same points

The easiest setup for orthographic spherical perspective is what a lot of people call five point perspective. It’s a circle with one vanishing point at the center and four around the edge. The vanishing points around the edge are connected to their opposites with ellipsis, whereas the one at the center just has straight lines moving away from it.

Even though people call this five point perspective, it still technically has six vanishing points. Two of them are just overlapping.

To find the vanishing points for other setups, we would do what I did in the animation above. Draw three great circles that are all 90 degrees apart from each other, and see where they cross each other. If you feel confident in your ability to free hand it, then it should be easy. But if you don't feel confident, or if you just want more precision, then you can use the following method.

This method requires you to know how to rotate things, and how to draw circles in orthographic projection. I’ve already written two posts on those topics that I recommend that you read first. (1, 2)

First, we draw a horizon. This will simply be a horizontal great circle.

Next, we’ll need to find four vanishing points on this horizon that are 90 degrees apart from each other. To do this, we can use the technique that I talked about in “understanding spheres”. Draw a birds eye view of the sphere above your drawing with four dots around its edge. Now draw vertical lines downwards from each of these dots until they cross the horizon.

Now we need to find the other two great circles. To do this, we simply need to draw ellipses that cross two vanishing points on opposite ends, whilst making sure that its minor axis is pointing towards the other two vanishing points.

Once you have all three great circles, just look at where they intersect, and you’ll have all six vanishing points

Considering the shape of the lines that you have to draw, I’d recommend that you try to set up a simple perspective grid. If the vanishing points are on the edge of the circle, You’d simply position the ends of the ellipsis major axis at them, and change its width a bunch, like I did with the five point perspective grid. If the vanishing points are not around the edge, you’ll need to rotate the ellipses as well to get a proper grid.

Do this with every set vanishing points, and you will have a simple spherical perspective grid. From there on out, everything else follows the same rules as standard perspective.

#perspective #curvilinear perspective #art advice #drawing #art

Added some more detail in the background.

For a little while I was unsure if I should draw this as if it was its own globe. Similare to a lot of the drawings I have seen using curvilinear perspective.

However I think that would feel a bit off. I also do like that we are seeing this in not just the point of what the raven see, but we see it in the perspective that the raven would see it.

I have also put the young girl away from now because I have some additional ideas to make this piece more story oriented. So for now I will focus on getting the full piece together with lines and some base colours around.

#curvilinear perspective #the hangingtree #sketches #concept sketch

Curvilinear Perspective and The Hanging tree.

I am not used to draw in perspective so jumping on to curvilinear perspective might have been quite the jump, but it has made the process very interesting and I have to use techniques that are new, fun and challanging.

I found a grid online and put that in the background and started to draw ontop of that. I had a few trials and fails! first I did try to draw the image in a full perspective. seeing both the view of the little girl and the raven. But it was a lot more challanging then expected.

I saw so many drawings of cities drawn in this perspective from an above angle. and i used that as reference for my new attempt at souly the raven point of view.

I am also sketching out how the girls is going to be posed in the image and might do more sketches of that. I want her to look scared, uncomfortable or even curious. I did a quick sketch as reference in the top right corner.

I am happy with the tree. Maybe make it a bit larger in the image because right now the top right-ish corner is very dull and “naked”. So pushing everything up might be the way to go.

#curvilinear perspective #concept sketch #sketches #sketch #the hangingtree