Application of Perspective

Some might find it weird to start with perspective, they'll say it's an advanced technique. But I think it's better to teach people techniques that are recreatable, factual, and rely on instinct as little as possible.

Perspective just seems like a more complex concept to some artists because they can actually list the steps, wheras they might have a habit of creating an image in two steps "sketch" and "paint", even though there's much much more to it than that for new artists.

The "Point" approach

Foreshortening is a optical illusion that distorts an object's scale based on the angle of the viewer.

Using Point Perspective is a basic way to emulate foreshortening, which typically describes the way that one end of an object seems to get smaller as it moves away from the viewer. Generally you can make use of one, two, or three-point perspective.

A Vanishing Point is a point, typically on a horizon line, where multiple lines converge / terminate. Parallel lines will always share the same vanishing point.

It's often said that the "number" of the perspective points refers to how many vanishing points there are in a scene. In actuality you can have many vanishing points in one image depending on the subject(s) and setting. But for the following, and most examples, we'll set up scenes that use primarily one or two.

There is a difference between what you see and what you know. The opposite edges of a square may be parallel, but when you tilt it they suddenly appear as if they are going to meet.

Like all drawing and painting techniques, the point of perspective points is not to recreate the physical world, but to fake it. For instance the definition of parallel lines is that they never intersect. But to create foreshortening within most artistic works it will be required that parallel lines appear to intersect at points of convergence, or vanishing points.

art info
As the object turns, the direction of the top and bottom sides intersect closer and closer. This intersection is our vanishing point.

1 Point Perspective

As the name would suggest, one point perspective involves making use of one point of convergence within our canvas to dictate the foreshortening of the image. All other lines are traditionally parallel to the edges of the paper / screen.

The secret to completing a one point perspective image is to remember that the lines that meet at that single vanishing point should be thought of as parallel not within your image but within the scene you are drawing. In other words the edges of a square wall along the ceiling and along the floor are parallel in real life but on the canvas will appear to lead to a single vanishing point.

1 Point Perspective: Construction

Unlike a cube which has equally sized sides, a Cuboid is a six sided object with an irregular length, width, or height.

The simplest form to create in perspective exercises is the cuboid. The most direct way to create an interior space is to choose a single point in the center of a page (you may draw a horizon line first if you wish), mark it, and then extend from there all the corners of the walls, floor and ceiling that lead to it.

For an object you are seeing the outer surface of, simply draw the edges you *can* see to the vanishing point.

Software Specific: Photoshop

When constructing perspectives in photoshop specifically I recommend artists use the shape tool for the simple reason that the lines can be seen even when they go off the canvas (wheras with a pixel line, the pixels will stop at the canvas border). You'll find that the most visually pleasing images usually don't having more than one of their vanishing points fall within the canvas border. There are some things to keep in mind about using the shape tool however.

  1. Make sure the shape tool is set to "shapes" in the first drop down of the tool option bar. If it is set to "paths" or "pixels", you will not see all of the line it makes.
  2. Make sure to set "combine shapes" in the shape tool options bar so that each line doesn't appear on its own layer. These will quickly add up.
  3. I do still recommend using some layers so that you can hide them when needed. Either use one layer for each object, or one for each vanishing point, it is up to you. Consider that a single 3 point box shape will have 12 lines and you see how they can add up.
  4. Change the color of a line by either the "fill" dropdown in the tool option bar or by just double clicking the shape layer preview in the layer browser.

Distortion with perspective

One way of illustrating the differences and uses of 1 and 2 point perspective is an exercise involving distorting a flat image using 1 point perspective, and then adding depth to it using 2 point perspective.

Let's start with a simple 2D image. This image could be a logo, icon, emblem, or any design that appears to be facing directly towards the viewer (this one is a dog).

If we want to apply a distortion to this image we place a grid over it. Since the image may not be perfectly square we can't rely on just measuring out a square grid - so we make our own using the diagonal line method to find mid points.

Below is the original image on the left and step 1 of our grid on the right.

1
2
3
4

In the 3rd image, on the left, we've divided the image even more by adding one horizontal and one vertical line to the image, each crossing over the center intersection of the grid. We are not basing the new horizontal and vertical lines on the mid point of the outer edge.

Now we have a good, evenly spaced, grid-divided image from which to transcribe a copy.

We start by choosing a vanishing point from which we bring out two lines at arbitrary angles. These lines can go up, or down, or as in this example, to the side. It also depends on how you want the final image to appear to recede from the viewer.

Just always remember this golden rule:

The farther away your vanishing point is from your drawing the LESS distortion you will see in it.

This rule will becoome more apparent as you work with perspective. It's basically the obeservation that the closer to the vanishing point you place your image the more the image boundries must distort to point towards that vanishing point. Because of this, especially since in computer graphics we have access to the amazing ability to change our canvas size at any time, don't be afraid to create vanishing points that are *very* far away from your image. It's perfectly common to place the vanishing point outside the canvas or bounds of where the final composition will be.

Once you've established these two sides of your image boundary you can decide on the other two. Remember, for less distortion place the cross lines further away from the vanishing point. For more distortion place it near.

We're not going to go into whether or not less or more distortion is a good thing on this page. For thoe most part this will be a completely stylistic decision on the part of the artist. You may want more distortion to make an object appear closer, or perhaps just to give the image more "energy", there are multiple reasons that are purely up to you.

What is important now is the basic steps involved. You can see in the image above the new lines are numbered. This is the order in which you should add them. The most important step here is the last (number 5). This middle line that extends form the vanishing point to the cross section of the new, distorted, grid must be drawn from the vanishing point and to the interescting diagonal lines in your grid. Drawing it any other way will result in incorrect perspective in your grid.

Here we've simply added more divisions to the existing lines just as we did with the original grid. A vertical line was added to finish dividing the grid into four pieces, and then a new, smaller, diagonal lines have been added to connect the middle horizontal and vertical lines to one another to create new mid-points within the quad.

Once done we will have a grid of 16 divisions. We could add more if we really wanted to (you can continue dividing the grid with diagonal lines as many times as you want) but 16 is typically a good density of grid squares for most images.

We are now prepared to actually transcribe the image. This is the most time consuming step in the process as it will involve us utilizing our ability to read proportions when copying the lines, shapes, and colors of the original image.

If a particular point or curve of a line ends on or near a certain spot on the original grid we now have a better idea where that same point or curve should appear on our distorted grid.

Now that we have transcribed a distorted version of our original image we have successfully created a 1 point perspective distortion.

But so far we have only reproduced a surface that exists on a single plane in space. If we want to give the object the appearance of actual depth then we will need to add thickness to it with lines that do not point towards an existing vanishing point.

In other words, we need....

2 Point Perspective

It should be no surprise that if "1" point perspective makes use of a single vanishing point then "2" point perspective will utilize a second vanishing point.

In the next image you'll see that we've added another vanishing point, in red, and have already drawn lines from that point to various points on the drawing.

The targets of these lines can vary from image to image. Obvious targets will be sharp points produced by the lines of the design. Less obvious will be the curves of the design where the "depth" of the object thickness will begin and end. These areas are generally the furthest reach of a possible line from the second vanishing point before the lines misses the object and continues on into nothingness. In other words if the second vanishing point can see a point on surface shape outline then a line can be drawn to it.

Unless we intended to work with a wedge-shaped object like a knife or ramp then the second vanishing point in almost all projects will appear on the opposite side of your object. This will produce an image seen from an angle as you can see for yourself.

Also keep in mind that, while it will be done regularly on this page, the second perspective point does NOT have to fall upon a horizon line. Neither of the points do. It simply makes the process of learning about them and relating to them as real world objects a little easier.

Once the appropriate lines have been drawn to create thickness in our now mutli-dimensional object we can finish it by drawing the edges of the surface that is facing away from us.

Only here and now can we add the final lines that will denote "thickness" on our object. In the example above they are the green lines that lead towards the red convergence / vanishing point. This is another step that will rely on the creativity of the artist. But generally you want to copy the nearest outer curve of the original image while scaling down the new lines fit within the projected lines of the new vanishing point.

Don't think that all of your new linework will always be visible. It's perfectly normal for some lines to be hidden behind the original image (for instance the single green line under the "neck" of the dog head in our example image).

Upon removing the original lines (it is recommended that you keep all "construction lines" within a folder in your chosen art program's layer browser to simply hide them) we can see the final product.

Below you can see the it side by side with the original. Notice how it is not just a matter of adding "thichkness" lines to the image but how the shape of the surface itself is slightly distorted. It is BOTH of these qualities, the thickness lines and the distortion, that gives it the impression of being and actual object turned slightly in 3d space.

Let's look at some general properties of 2 point perspective.

Unlike a cube which has equally sized sides, a Cuboid is a six sided object with an irregular length, width, or height.

Perspective using two points of course means any given object will have at least two sets of vanishing points. Imagine again a box, where two opposite sides have edges which lead in a completely different direction than the other two sides. But in this case, instead of being parallel to the edges of the paper or screen, these sides will lead to their own vanishing point.

It helps to imagine an axis (though unlike the figure image here they do not always have to be at 90 degrees to each other).

There are a few things to keep in mind about perspective using more than one point.

  • The Vanishing points do not have to fall within the canvas. In fact the most natural images will come from placing them outside the canvas.
  • The closer together two vanishing points are, the more distorted the image will appear as the angles increase. Objects will then start to look either closer or larger depending on other factors that represent their scale.

    Consider the images to the right. Notice how moving the vanishing points around can completely change the look of an object, even though the "position" of the object isn't changing at all.
  • Not all objects in a scene will make use of the same vanishing points. Only objects that share parallel directions will project to the same point.

    For instance, in the following image, the red box has been turned by only 9 degrees compared to the blue box, yet you can see this results in a very different set of vanishing points.
Here we have 3 renders of the exact same scene but with different locations for the vanishing points.
The 1st has the vainishing points for each object far apart.
In the 2nd the vanishing points are moved closer together, making the image noticeably skewed.
In the 3rd, both vanishing points have been moved closer again, increasing the distortion even further.
You could add other boxes that share these vanishing points, but they must face the exact same direction as the box they share points with.

2 Point Perspective: Construction

There are a few different approaches to constructing a 2 point perspective image. It's important to have one because if you try drawing all the lines leading to one vanishing points first before adding the vertical lines, chances are you'll get a misalignment somewhere and lines that were supposed to make one corner of your cuboid, won't. There are two approaches that will prevent this.

  1. Start with three vertical lines first, denoting the edges of the visible sides, and leave the edge furthest away to be drawn after the vanishing point lines.
  2. Build the box from the bottom up, which may make more "logical" sense.
    • Put down two lines from the left point and two lines from the right point to make the foundation quad (the "floor" of the box).
    • Draw all four vertical lines straight up from the intersections (the "wall" of the box).
    • Again draw two lines from the left point and two from the right point, having them cross over / end on the vertical lines (the "lid" of the box).
The order of the "ground up" method.

3-Point Perspective

The only way that 3 point perspective differs from 2 point perspective is that the set of lines that were previously parallel to each other now lead to a 3rd vanishing point.

The construction of a 3 point image is also very similar. Using the diagram above, the green vertical lines are simple drawn to a point above or below the image

Let's look again at the way point position distorts an object. The 1st is a fairly regular image where the vertical vanishing point is far below the canvas.
In the 2nd the vertical vanishing point has been moved into the frame, making the image noticeably skewed. increasing the distortion.
In the 3rd, all vanishing points have been moved closer, increasing the distortion even further.

0 point and parallel projections

It is possible for an object to have no vanishing points at which perspective lines converge. In other words, in a simple cuboid example, each set of lines is completely parallel to the others of a similar direction.

Orthographic projection is a parallel view where the view direction is perpendicular to [one of] the project planes.

You might hear some phrases used interchangeably with "parallel" usch as "infinite" or "orthographic". Be careful however since some, like "orthographic", have specific meanings that go beyond a simple lack of vanishing points.

An image where none of the lines (from one object) converge.

In the next section we'll look at perspective utilizing three or more vanishing points.