What if I tell you, that you can create drawings with convincing depth without having a special talent or spending $20,000 on art school?

Perceiving the depth in the real world is quite a complex thing. We see the surrounding space stereoscopically because we have two eyes. You get only the illusion of a real 3d on a flat surface. However, this illusion can be quite believable. Linear perspective is the only tool that helps you to create it.

The depth in perspective stands on three pillars:

- Scale change;
- Shrink;
- Overlap.

We have started to discuss the first and the second in this article. Now we will practice all three concepts to improve the sense of depth in your drawings and sketches. Believe or not, 90% of your draughtsmanship’s quality can be achieved by the use of simple approaches.

If you’re interested, you can read about fancy perspective grids and stuff on Wikipedia, or elsewhere. I suggest you learning all existing theories about linear perspective, if you have extra time. But for now, we will get away from the classical book explanations and focus only on practical things. I strongly recommend you to do exercises and practice techniques while you’re reading. This will make your progress way faster.

## How We Perceive the Distance

Let’s make a simple scene with a row of rectangles going away from the viewer.

All these rectangles have the same size and are close to each other. Basically, this is the same rectangle duplicated in space.

You can see that each following rectangle lessens on a perspective scale, although, in reality, it has the same physical size.

This phenomenon results in converging of parallel lines.

Change in size is a cue which helps your brain perceive depth. But the change in size is not linear. The Difference in scale between the first and the second rectangles is dramatic. However, as you move towards the horizon, the scale change between the adjacent rectangles diminishes. You can notice that the proportion of a rectangle changes as well. Those which are closer to the horizon are more compressed.

As you know from the previous part, each rectangle shrinks along its normal line when tilted away from the viewer. Here you see, that the plane shrinks even more when it is closer to the horizon line. So, the sequence of equal-sized rectangles going away from the viewer results in a non-linear change of the scale. Size difference between the adjacent pairs is more pronounced than of those near the horizon.

Let’s look at depth phenomenon from another angle. We put three horizontal lines in perspective. They are going away from the viewer just like the rectangles did.

Only one requirement for these lines: the intervals between them are equal on paper.

And here is the key part!

B is two times shorter than A, but C is six times shorter than B.

Why should you care about it?

Because every following inch on your paper includes more and more space, as you approach the horizon.

So, here is the reasonable question:

How do I create distances, that are equal in perspective?

This leads us to the next chapter.

Stay tuned!

## Measuring

You may ask: ”Why do I need to learn it?

Isn’t it only for a mechanical stuff?

Do I need to measure distance in space if I draw figures?”

I can tell for myself. Measuring always does a better job than eyeballing distance in perspective. No matter how hard I try.

And yes, it’s very useful for figure drawings too, because figures exist in space like any other object. You need to know exactly where the key points of the figure are situated three-dimensionally. That’s why you need to master measuring in perspective. And then you will be able to make educated guesses without constructions.

## Diagonals

As you may remember from geometry classes (I don’t), diagonals of a rectangle intersect in its center.

Guess what?

This happens in perspective as well.

This is how diagonals help you duplicate a rectangle.

Find the center using the diagonals.

- Draw the centerline in the direction of a desirable multiplication.

This centerline will pass through the border of the rectangle at the point A.

- Extend the borders of the rectangle in the same direction.

- Draw a line from a far corner through the point A. It will hit the extended border in the point B. Point B marks the width of a duplicated rectangle.
- Draw a vertical that makes a far border of a multiplied shape. This diagonal multiplication technique works in perspective as well.

- Find the midpoint at first, then duplicate the rectangle in any direction.

- Fill the entire page with these constructions.

You should mind that the center of a rectangle is shifted away from the viewer. This happens due to the converging of lines. When the perspective is flat (horizon is far away comparatively to the objects’ size) convergence is small, and shifting of the midpoint is insignificant.

On the other hand, shifting of the midpoint is very pronounced with the case of extreme perspective.

## Translating Orthogonal View in Perspective

Diagonals are useful for constructing irregular shapes in perspective.

The next exercise will show you how to do it.

- Draw a square.
- Sketch a random curve inside of it.
- Draw diagonals and center lines of the square. This rectangular construction will help you to translate the curve into perspective view.

- Determine the look of a square in perspective using an ellipse.
- Put the horizon line. Remember, the close it is to your ellipse, the more extreme is the perspective.

The easiest way to draw a rectangle is by using a so-called ‘1-point perspective’ where the lines are either parallel to a picture plane (and don‘t converge at all) or parallel to the line of sight. The ones which are parallel to the line of sight converge in the middle of the frame. This point is called the Central Vanishing Point, as you may know.

- So draw a square in 1-point perspective.
- Put the diagonals and center lines. They are your guides.
- Translate the points of intersection between the curve and guidelines from your original orthographic drawing. For example, if the curve touches square’s top border in the middle, it will do the same in perspective.

- Draw a curve through all points. You should also try 1.5 square proportion as a frame for your curve.
- Draw multiple curves in a frame.
- Fill a page with these constructions.

## Multiplying the Same Interval in Perspective by the Use of Ellipse

This technique stands on the fact that a circle has equal diameter all the way. The same happens when you put a circle in perspective. If two straight lines inside of an ellipse intersect at its midpoint, they will have an equal length.

- So you drop an ellipse of a desirable degree.
- Put a horizon line. The closer it is to the ellipse, the more extreme is the perspective.
- Draw a straight line through the center of an ellipse.
- Construct a square in one-point perspective outside an ellipse.
- Find the center by intersecting diagonals.
- Draw a straight line through the center.

- Transfer this ellipse to the desired distance in space. Do it multiplying the original square.

You can transfer it in a horizontal dimension without any scale change because this trajectory is parallel to the picture plane and doesn’t shrink.

- Draw a straight line through the center of a duplicated ellipse. It will be equal in length to the original line (just moved away in the distance). Here the lines are to be parallel so that they point at the same VP.

## The Wall of Cubes

- Construct a cube. Bottom plane is parallel to the ground, no fancy tilts.
- Start duplicating any plane of a cube with a diagonal technique. Use ghosting technique for directing your lines to the vanishing points.

Remember, a square is more compressed, as it goes away from the viewer. This effect is significant from the first square to the second. It becomes less obvious for each following pair. But it’s always there.

- Draw cubes one by one. You can go with this construction as far as you wish to fill the entire page with the wall of cubes.

I know, you may underrate drawing cubes.

But this is an extremely important thing to master before you pass on to sketching all that crazy stuff from your imagination.

It will help a ton, I promise you.

## Draw Through

Till now we drew only visible sides of our cubes.

It’s time to make your life difficult.

How?

By “drawing through.”

Why?

This is a powerful tool for drawing objects from your imagination.

”Draw through” means that you consider solid forms as if they are made of glass. Doing that you always know where the invisible margins of your form are situated.

Therefore, you can position one form to the other properly.

Now it’s time for the practical assignment.

- Draw a cube that stands on the ground plane – all the same stuff. But for now, draw invisible edges too.

- Duplicate a cube by shifting it to RVP. Put a distance of one cube between the cubes.

- Now draw a cube, shifted to the LVP. Leave the distance of one cube between the cubes.

- Fill the whole page with these constructions, varying viewing position and perspective extremeness.

I hope you’re following me.

I can’t control you doing these exercises.

I just stress that it’s essential to get better at drawing.

So, here is another phenomenon about that three cubes.

You may notice that some of the planes get more compressed (we already know why), but the other ones become more opened while moving away from the viewer.

This happens because the line of sight gets more perpendicular to the surface of such planes.

## Mass-Based Construction

Mass is a simple spherical or sausage-like form used as a basis to construct complex forms.

Think of it as a blob of clay which exists in 3d space.

I want to stress that It’s not a flat shape on paper, it has real physical volume.

Why do you need it?

Well, it’s easy to create the sense of scale in your scene using masses.

It solves the problem of overlapping and foreshortening as well.

So, mass approach deals with all three key components of depth in your drawings.

Now we will construct a cube from a spherical mass.

A cube (no matter how it’s turned) fits perfectly inside a sphere.

- Drop a circle.
- Construct a cube, using knowledge from the previous article. Tilt it as you wish, just try to match edges inside a mass.
- Draw a page of cubes in spheres right now. Vary the size and angles.

The main concept to keep in mind about arranging masses in space is that every mass has the center. The center of a spherical (or egg-like) mass always matches its geometrical center.

Let’s use this knowledge to construct equal-sized masses with equal distance between them.

- Draw a series of multiplied rectangles. Put a point in the middle of each horizontal edge. These points represent centers of the spherical masses.

- Now draw spheres around each point. Silhouette of each sphere should touch CVP line if you want them to be equal-sized.

- Draw cubes inside of the sphere masses. Rotate them as you wish, they will stay equal sized objects with equal distances between their centers.

Now, let’s draw cubes with a determined distance between their centers. Further, we will lift the cubes at a specific distance from the ground.

- Draw a square on the ground.
- Sketch a straight line inside of it. This line represents the distance between the two cubes.
- Mark the VP the line is pointing at.

- Construct a vertical plane from the original straight line. The plane’s top corners are the center points of your masses.

- Draw the first sphere. Sketch the line to the VP so that it touches the edges of your sphere. This line should also touch the edges of the second sphere.

- Draw the cubes inside of the masses. Tilt them as you wish.

## Cubes in Space Along Irregular Trajectory

Now we combine the exercises.

The goal is to construct equal sized cubes with the same distance between them, going along an irregular trajectory.

- Put a curve in perspective.

- Put the points with equal spacing along the curve. Each point corresponds to the center of the mass.

You can measure the distance between the points by eye or use an ellipse method.

- Draw a sphere around the closest point on the curve.

- Measure the scale of masses which are far away. Then it will be easier to eyeball the size of the ones in-between.

Do it this way: ghost straight through the 2 points, and further you will hit the horizon at some point (at VP). Alignment line which touches the edges of the both masses should also go to this one VP.

- Fill the entire pass with these spheres.

Now you can start drawing boxes inside of masses. Rotate them as you wish.

This cube series may seem boring, I know. The next chapter will be more exciting.

We will discover multipurpose principle of drawing any possible form.

See you!