In previous articles on perspective, we considered primarily the frontal perspective, that is, the perspective in which parallel lines converge in the main point of view of P or are parallel to the edge of the picture:

In the direct perspective, only 1 vanishing point is used. However, it is worth expanding the object relative to the vertical axis, for its image you will need 2 vanishing points:

The type of perspective construction, where 2 vanishing points of lines are used, is called **angular perspective**. The key point in the perspective drawing of objects located under **angle** to the viewer, there will be vanishing points. If you place these points incorrectly, the object you are building will appear distorted.

How to find them?

The simplest option is when objects are turned at an angle of 45` in relation to the artist’s gaze. Remember when we built the perspective of the room, the diagonals of the squares converged at the remote points? Since the angle of the diagonals is exactly 45`, it can be assumed that for **angular perspective** and the sides of objects located at this angle will also be directed to the remote points:

So, in this case, both vanishing points for parallel lines will be at an equal distance from the main point of view P and coincide with the distance.

If the object is turned at any other angle, the vanishing points will be at different distances from P, and the closer the 1st vanishing point to P, the farther from it the 2nd:

If you extend your arms parallel to the sides of the cube (building), you will show directly to the vanishing points:

The most common mistake made when building **angular perspective**, these are too close vanishing points for parallel lines:

*Testing yourself is very simple: the corner of a rectangular object closest to you in a perspective drawing should look dull. If this angle is 90` or less, then the vanishing points are too close to each other.*

Since the location of the vanishing points depends on how the object is turned to the artist, in the same figure there can be both a central and **angular perspective**:

*In a still life for each thing you have to look for your own vanishing points.*

To finally understand what is **angular perspective**, I suggest doing 2 tasks:

- Analyze a photo or picture in terms of perspective. Not on a computer, but on paper - that is, take a ruler and a pencil and find the horizon line and vanishing points of parallel lines. For example, like this:

Ge, “Peter I interrogates Tsarevich Alexei Petrovich in Peterhof”

- Make a still life of rectangular objects, such as books or boxes. Position them at different angles and try to outline their position in perspective.

And I want to remind once again that in painting, the observational perspective is used primarily. That is, you do not build objects, but draw what you see. And since the vanishing point of parallel lines is often far beyond the sheet, it is important to be able to see primarily the angle of rotation of objects. If visually it is difficult to evaluate this angle, you can use a simple trick: extend your hand with a pencil and combine it with the visible face of the object - it is easier to catch the direction of the lines.

For a video of typical mistakes of perspective based on training drawings, see HERE.

## Features of human visual perception

In the perception of a person, an object that is closer is always larger, and then less. Accordingly, a closer subject seems to be the largest. This principle is often used by photographers to take a picture with an optical illusion, for example, with the sun or with a small man in the palm of his hand. This effect of distortion of reality arises due to the structural features of the human eye and the processing of information by the brain. Visual perception is a complex mechanism in the process of which errors may occur. Once in the field of human perception, objects are processed and interpreted by the brain, taking into account already acquired knowledge. With a lack of information, he chooses the most optimal option, and as a result, reality may be distorted. But thanks to this feature of the process of processing visual images, the human brain can be forced to see in the picture not a flat image, but a voluminous object, visually very similar to the present. With the correct construction of the perspective, the objects in the picture will be perceived as an additional reality.

## The practical use of optical illusions

Perceiving an object, the human brain first concentrates on smaller and brighter spots. The more contrast the image, the faster its shape and size are determined. This is used by many animals disguised as the environment. Due to the particular arrangement of the eyes, the human brain more accurately perceives horizontal planes, and vertical distorts upward. This effect is well known to fashion designers and most women. Trying to adjust the volume of their figure, visually stretch it and make it more slender, ladies pick up clothes with vertical stripes and wide inserts on the sides that not only slim, but also help create a clear silhouette line.

## Examples of optical illusions

There are several types of optical illusions that are actively used in the visual arts:

- Illusion of color - if you arrange circles of the same color inside a dark and light square, then the circle inside the light square will appear lighter. This happens because in the perception of a person a dark shade takes over part of the light. But having received information that he was deceived, the brain is rebuilt and begins to see that the color is the same in both areas.
- The illusion of size distortion - objects of the same size deployed at an angle of 90 degrees seem different.
- Visual distortion, or Ponzo's illusion - the human brain tries to determine the size of the object, focusing on its background.
- The ratio of dark and light is a very well-known optical illusion, which is expressed in the perception of the light part of the picture as an object, and the dark - as its background. One of the most popular images demonstrating this illusion is a white bowl, obtained from two identical dark faces in profile.

“To deceive the brain” is quite simple: it is for this purpose that the construction of the frontal and angular perspectives, the combination of light and shadow, distributed on the surface of the subject in a special way, and other artistic techniques are used. They can be present in the figure simultaneously or separately from each other. When creating a picture, it is very important to choose the so-called point of view correctly - the position from which the viewer will look at the depicted object. There is also an additional parameter that is important to consider - the “angle of view". It usually ranges from 18 to 53 degrees. The angle of view is calculated based on the size of the canvas on the diagonal of the picture plane and the location of the observer.

## Types of linear perspective

In a linear perspective, all objects line up with straight lines. The frontal perspective, as well as the angular one, is a type of linear perspective. It is built in such a way that all objects are parallel to the viewer and the horizon, vertical lines always remain parallel to each other, and the lines of perspective reduction converge at one point. When constructing an angular perspective on the horizon, not one but two vanishing points are selected. This is its fundamental difference from the front. With a similar arrangement of the object, it will be perceived by the viewer from the corner, that is, its sides will be best seen.

## Preparation for building a perspective with two vanishing points

The construction of angular perspectives begins with the choice of the height of the horizon. This will determine which part of the subject, upper or lower, will be more open and visible to the viewer. The low position of the horizon is also called the “frog perspective”, and the high is “bird's-eye view”. When constructing the angular perspective of the house in the first case, the object itself will seem to rise above the viewer and its lower part — the walls and the base — and in the second — the roof will be best seen. Then you need to measure the diagonal of the picture plane - this will help to correctly postpone vanishing points.

## How to choose a horizon height

The next stage of construction is the definition of a point of view. A distance equal to the diagonal of the picture plane is plotted on the horizon — the extreme points of this segment will be vanishing points. The location depends on where the observer is located - the closer he is to the picture, the closer the vanishing points are to each other. They are not always located inside the workspace and may extend beyond the boundaries of the sheet if the viewer is far away. If the vanishing points are too close, the object is “threateningly” approaching and begins to cause tension in the viewer. Their distant location avoids distortion of the picture. The most optimal form can be achieved by locating at least one vanishing point outside the picture plane.

## The classic way to build a perspective with two vanishing points

In the angular version of the linear construction, the vertical lines are parallel, and all the others tend to vanishing points, forming peculiar bundles. There are several ways to build angular perspectives. The first of them is usually called classic. To build in the classical way on the picture plane, determine the horizon line, measure the diagonal and set aside two vanishing points. Then draw a vertical line - it should be perpendicular to the horizon line.

## Scale and construction of a meter grid

Before you draw an angular perspective of a room or any other interior, you need to postpone meters on the vertical. It is important to choose a convenient scale - this will help to accurately transfer the dimensions of the room, for example, take 1 cm for 1 meter of space. The scale for drawing in angular perspective depends on the size of the picture plane. After determining the height of the ceiling and measuring it vertically, draw lines connecting the vanishing points through the upper and lower points on the segment. Now the figure should make a room in an angular perspective - two walls, a floor and a ceiling. Then draw two more lines through the same vertical points — they should be parallel to the horizon line. Meters are also laid on them at a given scale. This will create a grid with a step of 1 m on the floor, walls and ceiling of the room. After all the marks are placed, it remains only to connect them with vanishing points.

## A simplified version of building a perspective with two vanishing points

For the second version of building an angular perspective, you only need to draw a horizon line and a vertical line. Select vanishing points arbitrarily, at any distance from each other, but it is desirable that they remain inside the picture plane. Then, on the vertical line, set aside the meters, as in the previous version, and connect the extreme points on the vertical line with vanishing points. In this version of building an angular perspective, it is not necessary to measure the diagonal of the canvas.

Moving from the vertical line to the right, on the bottom line put the meter to the scale, and then draw another straight line through this point, connecting it with the left vanishing point. The result should be a rhombus. Now you need to determine the location of the next point to draw a new line. To do this, draw two diagonals inside the rhombus. The point at their intersection must be connected to the left vanishing point. Then connect the left top of the rhombus with a point in the middle of its right lower edge and draw a straight line until it intersects with the line forming the upper right side of the rhombus. Connect it to the right vanishing point to get another square meter in angular perspective.

At the next step, all steps are repeated again: diagonals are drawn inside the rhombus, its center is connected to the left vanishing point, and the left vertex of the rhombus is connected to the point in the middle of the right side. Thus, the desired number of meters to the right of the vertical line is postponed. To create a grid on the left, a similar method is used: connect the center point in the first rhombus with the right vanishing point, draw a line through the top vertex and the middle of the lower left side of the rhombus, and then connect the resulting point with the left vanishing point. Repeat all the steps until you get the right number of meters in the future. Similarly, the grid is built on the ceiling and walls. There is nothing complicated in building an angular perspective. It is enough to understand the principle itself and actively use this technique to visualize interiors, buildings and solve other similar problems.

## Linear perspective (angular) and complex perspective cases. Part 2 Topic 16

Linear perspective (angular) and complex perspective cases. Part 2 Topic 16

**Good Thursday, friends, and the first day of summer!**

Today under #harmful_ advice **the second long-awaited part about the prospect)))**

I must say that you can discuss this topic endlessly and there will always be interesting moments and situations, but we will analyze the main and most important point: where and what assumptions we make when drawing, yet we are artists, not architects,)

Last time, we discussed the simplest version of a linear perspective, frontal. Refresh those who have forgotten, as this part is completely based on the previous one. And now we will get acquainted and **We will deal with the corner.** ,)

You remember that in the frontal perspective we had one vanishing point, **in the corner, there are two of them, since we look at the object “conditionally” from the corner and not one of its planes lies in the plane of our gaze or camera lens.** Therefore, all planes have perspective distortion **right to right, left to left.** What happens to the back sides of the cube, I think that you will figure it out yourself (they are subject to the same laws), but since we do not build projections or sections of buildings, I miss those planes that we don’t see. In order to simplify our life

An important point that I will not tire of repeating, h**then both vanishing points will always lie on the horizon (how to choose it, see topic 15**).

They are there, regardless of what angle we see the building, more it is deployed to us or less (mini drawing under the first cube)

Eventually **in a simple angular perspective**(next picture) we will always have

**three main types of lines: vertical, and those that converge at the right vanishing point and those that go to the left.**

At the same time, it is very important to understand that if everything is simpler in one building: that which goes (converges) to the right to the horizon to the right, that that goes to the left to the left, then if we look **for a group of buildings, it is important to consider this individually, and not relative to the very first building.**

Now you will understand what I mean.

Look carefully at the central building, everything is clear right-right, left-left, the next building also goes into perspective: the right side to the right, the left to the left point.

* In no case do we think that the right building is on the right in the figure relative to the central one and all its planes go to the right*.

**No matter how far your building is located, for example, on the right side, its left plane will always go to the left vanishing point.**

Therefore, in order not to get confused, in the case of such a construction, always divide your objects, imagine buildings as separate cubes, look for the edge (corner) closest to you, and then obey the laws of perspective.

This case can be complicated if you turn the street or narrow it, etc. (See topic 15). Then all the buildings in the figure will not converge at only 2 common points. Each building can have 2 points of its own and as a result, there can be infinitely many on the horizon.

**And here we turn on creative vision and think:** Is it necessary for our picture that each building was built difficult, had its own points, the street was bent, or does this not bear the main semantic load and this can be neglected? For the most part, you can really neglect this and simplify your task by constructing an angular perspective of two points, as in my picture. In this case, neither the prospect will suffer and you will make your life easier. Do not get confused in pencil construction, do not spoil the sheet with endless erasures Remember, you are the main one! You control the pattern

We go further into the wilds! Do not be afraid, give a hand, I will guide you,)

We will gradually complicate. We look at the figure below.

**This case is figuratively called the "well effect"**

Speaking frankly, and I think you and I are already at this stage in the development of relations ,,), then the prospect is not only towards the horizon, **but also up**

Yes, yes, somewhere there, far, far there is a point where infinitely long buildings and structures converge. But! Infinitely long does not happen, so everyone only wants to)

And there is no horizon on which it is, it's just a point. So how do you find her? -Say you. But don’t, I will say!

**You have already found it, it is you yourself!** You Remember that the horizon line is conditionally the line of your gaze. Here also. You just need to go outside and watch. **По сути точка прямехонько находится над Вашей головой ,)**

Поэтому, Чем ближе вы находитесь к зданию, тем круче оно уходит вверх, стремится в точку над вашей головой. Отсюда и тот самый эффект колодца в Питерских дворах. Точка над вами, вы смотрите вверх и все здания сходятся, будто мередианы к полюсу.

А вот, если Вы далеко от здания, то оно почти не искажается по вертикали, так как его стремление к этой точке бесконечно мало из-за расстояния между Вами. Also, with such a distortion, it is important to remember that the sizes of objects (windows, balconies) obey the law: the higher, the less, you need to be careful,)

**And here is another simplification point***if this does not carry an important semantic load, draw buildings without distortion upward, as if you are far away and brought them closer in the camera lens. So you avoid unnecessary difficulties and mistakes. I wrote about the right photos for work in Topic 10, where they just discussed how best to produce photo material without distortion. After all, often on a journey we go, looked up, how beautiful! We photographed from below, as a result, we looked at home: what a distortion of perspective, and did not draw. For the most part, such material is not suitable. And the vision is just plein air, where you understand how to make assumptions convenient for yourself.*

Go ahead. **In the upper figure in the center, I just showed the option of distortion in all three directions.** Of course, I exaggerated it for such low buildings, but it is.

And precisely because for small buildings in the distance it is infinitely small and tends to zero, we omit it.

**The upper figure shows the angular perspective + perspective up.**

And the picture below it shows f**horizontal + angular + vertical.**

Let us dwell on it a little. We often see this situation when approaching our own porch, of course, if you live in a high-rise building. At the same time, the windows in front of you are not distorted to the right or left, since they are in the same plane with you and this is a frontal perspective, in this part the building is distorted only upwards.

But the right and left buildings are already "tormented to the fullest"))) the right side of each building tends to the vanishing point on the right, the left to the vanishing point on the left. I didn’t deliberately put a point, because in fact they are on the horizon far from the right and far to the left, because if they were in the picture, there would be an unrealistic effect as if the “fish eye” distortion was too great.

**Here you should understand that there is a prospect, but you will not test yourself with a ruler, unless, of course, you start building on the floor and find a point somewhere in the corridor**

In this moment, practice is very important and the same “observation” You learn only at real objects to truly see and present a perspective, to predict vanishing points, confidently lead your windows, doors, houses and so on to them. ,)

**Well, finally, I’ll tell you about a difficult case**In my figure (below), this is still a case of frontal perspective.

**So what is the difficulty?** Remember, in Topic 15 we discussed that if the road turns, narrows, widens, then the buildings will have several vanishing points. But, if the road is a hill, goes up or down, then there will be several horizon lines)

**The first line is higher** it includes buildings, nearby cars to the hills and the marking of the upper part of the road. Why? Because we conditionally forget about the slide, and we only remember about where we are standing and that the horizon line is equal to the line of our eyes.

Therefore, everything that before the descent in our case (or ascent in others) will be connected with this line.

**And the second horizon**is the line of our eyes if we were below the descent. While we are not there, we choose it conditionally, to our taste, as to what we see. And all that belongs to the road: cars on the descent, people walking along the sidewalk, trees on the sidewalk, lights on the descent will already obey it. If this were not so, then the height, for example, of lanterns at the top of the hill would be 3 meters, and below 30 meters so that their peaks belong to the first horizon line of our eyes. But they "belong to the road", so their lines obey a different vanishing point on the horizon. Such a construction in fact is not very complicated, since in the city landscape most of the objects, trees overlap each other and we do not completely build every house or car, but we need to understand where we get it from.

**Here we come to an end.**

Now we know all the main points of the prospect, and let's talk about simplification for a moment. Imagine again if in the last complex drawing I add another corner, and the perspective is up, and it is there, small, but there is That I will probably spend a year on the construction)))

**Therefore, working in kind,**

- get up so that you get the front
- if you want a corner, then at least from two common points, do not dig into the intricacies of each house, if this is not your goal.
- look for your ways, you are an artist! But do not neglect all the laws,)
- and, of course, try to see and understand yourself, through your experience, how objects around behave.

**And only practice will help understanding, and I will not tire of repeating that you can figure it out, but you can learn to build only in real life, observing every day. The artist has only one kind of vision - the artist’s view, noting all the nuances around and analyzing how to draw it every time**

**I wish you creative success!**

**The next issue will be in a week,)**