Constructing shadows in perspective of geometric shapes. Constructing shadows under artificial lighting

The image of shadows gives the perspective additional expressiveness and volume. The direction of light rays, unlike a complex drawing, can be arbitrary. In this case, three cases of arrangement of parallel light rays coming from the sun are possible: rays are directed from the observer to the object, rays are directed from the object to the observer, rays are parallel to the picture plane (frontal position of the rays). In this case, the angle of inclination of the rays can be arbitrary in each of these cases. To construct shadows in perspective, it is necessary to know the perspective projection of the ray, as well as its secondary perspective projection. Figures 8.1 – 8.3 show the construction of shadows on the object plane from a horizontal segment in each of the above cases. Parallel rays will have a common vanishing point. Vanishing point of secondary ray projections F 1 t is on the horizon line. Vanishing point of perspective projection of rays F t in the first case it is below the horizon line (Fig. 8.1), in the second case (Fig. 8.2) – above the horizon line, in the third case (Fig. 8.3) there is no vanishing point. Perspective shadow projection A t from point A is at the intersection of the secondary projection of the light ray directed from the secondary projection of the point A 1/ to the vanishing point F 1 t, with a perspective projection of a light beam directed from a point A/ to the vanishing point F t. The shadow of a point is constructed in a similar way B, which allows you to construct a shadow from a segment using two points.

Shadow from a horizontal line AB to a horizontal plane is also a horizontal line A t B t, which is parallel to the original segment AB, and therefore has the same vanishing point F. The shadow from a vertical line onto a horizontal plane coincides with the direction of the secondary projection of the light beam (Fig. 8.4).

In practice, the first case of directing light rays is most often used, because most In this case, the object is illuminated and the perspective looks most expressive.

Of all the methods for constructing shadows, known from the shadows in a complex drawing, only two are used in perspective: the method of ray sections and the method of reverse rays. Other methods are not used, because lead to complex constructions.

The sequence of constructing shadows is the same as in a complex drawing: the contour of one’s own shadow is revealed, then the falling shadow is constructed from the contour of the own shadow of each geometric image onto the object plane (in the complex drawing onto the wall), then the falling shadows from one geometric image to another.

Figure 8.5 shows the construction of shadows using the example of two parallelepipeds. From the contour of your own shadow 1 / - 2 / - 3 / - 1 1 / - 2 1 / - 3 1 / small parallelepiped, a shadow is constructed on the object plane from both vertical and horizontal lines. Then a shadow is constructed from the contour of its own shadow 4 / - 5 / - 6 / - 4 1 / - 5 1 / - 6 1 / large parallelepiped onto the object plane. The contour of the falling shadow of both parallelepipeds is the envelope contour of both shadows. In addition, the shadow from the large parallelepiped falls on the upper horizontal and front vertical faces of the small parallelepiped. To do this, ray sections of the small parallelepiped are constructed, obtained from the intersection of ray planes drawn through the contour of the own shadows of the large parallelepiped. Such a ray plane is drawn through the edge 4 / - 4 1 / large parallelepiped, and it intersected the small parallelepiped along a section that is the contour of the incident one. Other sections of the large parallelepiped's own shadow provide shadows only on the object plane. In Fig. 8.6, shadows from the same parallelepipeds are constructed with the rays in the frontal position.

In a perspective drawing or composition, the correct identification of chiaroscuro enhances the transfer of the volume of objects, the depth of the depicted space, and therefore is the most important means obtaining a realistic image. It must be remembered that shadows are not meaningless spots, but a pattern, and therefore their construction is also subject to the rules of perspective.

Knowledge of the rules and techniques for constructing perspectives of shadows under different light sources allows the artist to choose which one and which direction in the best possible way provide identification of the main thing both in a drawing from life and when working on a composition.

Types of lighting.

Perspectives of shadows can be constructed with two types of lighting, differing from each other by different distances of the light source from the illuminated object:

1. The light source is located at a very large distance (sun, moon), and therefore the rays falling on the earth’s surface are considered parallel. This kind of lighting is called parallel silt and sunny.

2. The light source in the form of a luminous point (lamp, torch, fire) is located at a short distance from the object. The rays come from one point. This kind of lighting is called point or flare.

Since the type of lighting affects the shape and size of shadows, and also has some features in their construction, we will consider the construction of shadow perspectives under solar and spot lighting separately.

Perspective of shadows at natural light. The illumination of the depicted object, its own shadow, the direction and size of the falling shadow depend on the selected position of the sun. The latter can be set by the direction of the ray and its projection onto the object plane or by the falling shadow from any drawn object.

There are three possible positions of the sun - in front of the viewer, behind the viewer and in neutral space.

The sun is in front of the viewer. In this case, the sun's rays are ascending straight lines (Fig. 16). Their position in the picture is determined by the direction of the ray's perspective, for example AA*, and its horizontal projection aA*. The vanishing point of the perspectives of the rays is the point C- the perspective of the center of the sun, and the vanishing point of the horizontal projections of the rays - c. The vanishing point for horizontal projections of rays is always located on the horizon line and is a projection of the perspective of the sun onto the object plane. Therefore, the points lie on the same perpendicular to the horizon line; in this case, the point is above the horizon and usually outside the picture, since it is not possible to depict the brightness of the sun.

The shadow falling from an object is directed towards the viewer. The object itself faces the viewer with its shadow side if the sun is directly in front of it. If the sun is in front, but to the right or left, the object is facing the viewer by the dividing line of light and shadow. In this case, the shadow part is usually larger than the illuminated part. Its dimensions depend on the shape of the object and its position relative to the picture.

Rice. 16 Fig. 17 Fig. 18

The sun is behind the viewer. The sun's rays are descending parallel lines. Their position in the picture is determined by the direction of the ray's perspective AA* and its projections aA* to a horizontal plane (Fig. 17). Continuing the perspective of the horizontal projection of the ray to the horizon line, we obtain a vanishing point c for the projection of rays, which belongs to the vanishing line of the ray plane. Therefore, a perpendicular to the horizon line, lowered from a point before meeting the continuation of the ray AA*, will give the position of the vanishing point C for ray perspectives. Vanishing point C is the perspective of the center of the sun located in imaginary space.

So, if the sun is behind the viewer, the vanishing point for the perspectives of the sun's rays is below the horizon line, and the vanishing point for their projections is on the horizon line. The object faces the viewer with the illuminated side if the sun is behind the viewer.

If the sun is behind, but also to the right and left, then the object is facing the viewer by the dividing line of light and shadow. The falling shadow moves away from the viewer.

Thus, when the sun is positioned in front of or behind the viewer, the source of illumination can be set by vanishing points for the perspectives of the rays and their projections.

The sun is in neutral space (to the side). In this case, the perspectives of parallel rays, inclined at a certain angle to the subject plane, are depicted parallel in the picture, and their projections are shown parallel to the base of the picture (horizon line), since the sun is in neutral space (Fig. 18).

The object faces the viewer with a line dividing light and shadow. The ratio of the illuminated and shadow parts also depends on the shape of the object and its position relative to the picture. The falling shadow when the sun is on the right is directed to the left, and when the sun is on the left - to the right.

Rules for constructing falling shadows from points and lines. So, it has been established that the contour of the falling shadow is the shadow of the contour of its own shadow. But the contour of one's own shadow is a combination of lines located in different ways relative to the plane on which the shadow falls. Therefore, we will consider the basic rules for constructing falling shadows from lines perpendicular to the plane, parallel to it and inclined to it.

1. The shadow of a line perpendicular to the plane coincides with the projection of the perspective of the ray onto this plane. The length of the shadow is determined by the point of intersection of the ray's perspective with its projection. Therefore, to find the shadow of a segment AB falling on the object plane (Fig. 19), it is necessary to draw a projection through the base of the segment cB perspective of the ray, and draw a perspective through the vertex of the segment C.A. beam. Segment A*B and there is the desired falling shadow from the vertical segment AB on the object plane.

Fig.19 Rice. 20

2. The shadow of a point on a given plane is the intersection point of the perspective of a ray drawn through this point with its projection drawn through the projection of the point on a given plane. To find the shadow of a point A on the object plane (Fig. 20), you need to set the projection A points A onto the object plane, through a point A project ca ray perspective and then through the point A hold perspective C.A. beam. Intersection of the perspective of a ray with its projection at a point A* and there is a falling shadow from the point A on the object plane.

3. The shadow of a straight line parallel to a plane is parallel to the straight line itself, that is, it has one common vanishing point with it. Therefore, to determine the shadow of a horizontal segment AB, falling on the object plane (Fig. 21), you need to find the shadow from one of the points of the segment, for example from the point A, and then from the found point A* draw the direction of the shadow to the vanishing point F. The length of the shadow is determined by the point of intersection of the lines A*F And VS at the point IN*. Straight A*B* ~ the required shadow from the segment AB.

Rice. 21 Fig.22 Fig.23

4. The shadow of an inclined line passes to the point where this line meets the plane. To determine the cast shadow of an inclined line segment AB onto the object plane (Fig. 22), you need to find the shadow of the point A and from point A* direct the shadow to a point B— the point where the inclined line meets the object plane. Straight A*B - segment shadow AB on the object plane.

5. If the inclined line AB does not have a meeting point with the plane (Fig. 23), to construct a falling shadow, you must first determine this point. It is enough to continue the perspective of the line until it intersects with the continuation of its projection at the point WITH - the point where a straight line meets a plane. Then you need to find the shadow of the point A(or B) — point A*, from point A* direct the shadow to point C - the point where the straight line meets the plane - and find the shadow B* from point B. Straight A 0 B 0 and there is a shadow of a segment AB, inclined to the plane.

General provisions for constructing perspectives of shadows under artificial (spot) lighting.

With point artificial lighting, the nature of the illuminated surface of an object and its shadows is not the same as with solar lighting, since here the intensity of surface illumination depends not only on the strength of the light source, but also on its distance from the object. The closer an object is to the light source, the stronger the illumination of its surface, and vice versa. The degree of illumination is inversely proportional to the square of the distance between the light source and the object. So, if a group of people is depicted in a room illuminated by a candle, then the figures that are twice as far away from the nearest one will be illuminated not twice, but four times weaker.

With spot artificial lighting, not only the size of the shadows changes, but also their character. The darkest shadows are visible on objects closest to the light source. As a result of the weaker influence of reflexes, the contrast between one's own and falling shadows is less noticeable. As it moves away, the falling shadow weakens and turns into the tone of the unlit surface. Knowledge of these patterns helps the artist make the best use of lighting to figuratively reveal the main idea of ​​the work of art.

To construct his own and falling shadows, the artist must establish the position of the light source in space, that is, determine the position of the luminous point itself and its projection onto the plane on which the shadow falls.

The rules for constructing shadows with spot lighting are the same as with sunlight (Fig. 24):

1). shadow , incident on a plane from a line perpendicular to it , coincides with the projection of the ray onto this plane;

2). shadow , falling on a plane from a straight line parallel to it is parallel to the straight line itself, i.e., directed to the same vanishing point R

3). shadow , falling onto a plane from a straight line inclined to it , directed to the point where this line meets the plane.

The surface of any object has an illuminated part, on which light rays fall, and an unlit part, where direct light rays do not fall. The unlit part is in the shadow, which is called own shadow. The boundary between the illuminated and unlit parts is called the contour of its own shadow. An opaque body does not transmit light rays, so objects located behind it are unlit, i.e. is in falling shadow. The boundary of the falling shadow is usually clearly defined and is called outline of a falling shadow. Note that, with scattering light and with several sources, the contour of the falling shadow is blurry.

Thus, the contour of the falling shadow is the shadow of the contour of its own shadow. Therefore, it is advisable to begin constructing the shadows of objects by constructing the contour of your own shadow. However, in some cases it can be difficult to determine the outline of your own shadow. Then they first find the contour of the falling shadow, and from it - the contour of their own shadow.

Fig.25. An example of constructing shadows in a perspective image of a building

Questions for self-control:

1. What shadow waters do you know?

2. What is the gradation of light and shade?

3. How are shadows constructed on orthogonal drawings?

4. What features does the construction of shadows in axonometry have?

5. What types of lighting are there in the future?

6. What positions of the sun are used when constructing shadows in perspective?

Literature:

1. Anisimov N.N., Kuznetsov Ya.S., Kirillov A.F. Drawing and drawing. - M.: Stroyizdat, 1983.

2. Briling N.S. Drawing. - M.: Stroyizdat, 1989.

3. Briling N. S. Handbook of construction drawing. -
M.: Stroyizdat, I987.

4. Klimukhin A.G. Descriptive geometry. - M.: Stroyizdat - 1978

5. Koroev Yu.I. Descriptive geometry. - M.: Stroyizdat - 1987

It is known that a falling shadow follows the shape of the object that casts it. But everyone who has tried to draw has probably observed how the shape of the shadow is distorted and does not absolutely accurately follow the contours of the object. So what are the rules by which a falling shadow is constructed and what patterns can be identified here?

Constructing falling shadows

First, let's look at this using the example of a simple geometric body - a cube. The figures below show a diagram of the construction of a falling shadow:

1. The light source is determined.
2. A perpendicular is drawn from the light source to the plane on which the object stands.
3. From the point on the plane where this perpendicular rests we draw rays towards the object.
4. Imaginary rays are drawn from the light source and pass through the edges of the object.
5. We mark with dots the intersection of the rays on the plane and the rays from the light source.
6. We connect these points with a line and get the outline of the falling shadow.

To summarize the above and put it more simply, you need to: firstly, draw lines from the light source in space; secondly, draw lines on the plane from the perpendicular. The intersection of these rays will be the contour of the falling shadow.

In a cube drawing, this construction of shadows is relatively simple. But what if our subject is complex? For example, a vase, a tree, a car? Or even “worse” - a human figure? From my experience I will say that I always draw falling shadows from such complex shapes approximately. And, probably, most artists do the same. However, this approximate drawing is still based on the above principle. In the mind, in the artist’s imagination, the same approximate projection is made, and on its basis the outline of the shadow is drawn. But to do this, you need to know the key principle that I outlined above. In the next picture you can see how I approximately lined up the falling shadow from the vase. Everything is done very roughly, but the principle is respected.

(Approximate shadow projection)

How does the shape of a shadow depend on the position of the light source?

In the following pictures I want to show how the position of the light source affects the shape of the shadow and its direction:

If the lamp (or the sun) is located directly above the object from above, then the falling shadow will either be very short or disappear completely. The more the light source is shifted to the side relative to the subject, the longer the shadow will be. The lamp can be located directly in front of the object or, conversely, behind it. In this case, the falling shadow will either move backward from the viewer or approach it forward. All these “stretching” or “compressing” of the shadows will affect its shape. In the above figure, I drew the shadows of the ball. But if you project a falling shadow from a human figure, then its outline will be distorted in a similar way - sometimes stretched, sometimes shortened. It doesn't matter what object we draw a shadow from. The principle will be the same.

How the saturation of the shadow and the clarity of its contour changes

There is a pattern that the artist must understand well - the further the shadow is cast from the object, the lighter it is. How closer shadow approaches the object from which it falls, the darker it is. This change in saturation can be stronger or weaker depending on the brightness of the light, the size of the shadow, and the distance of the light source. But in any case, the shadow will not be “dull”. It should “breathe” or be “transparent”, which is achieved by changing the saturation. If we are talking about academic drawing, then shadows in the form of solid dark spots should be avoided. If we are talking about black and white graphics, then, of course, the shadows can be completely black, but this is a conventional image, not a realistic one.

In addition, novice artists should also pay attention to the clarity of the shadow outline. The more focused the light (electric lamp, sunlight in cloudless weather...), the clearer the contour of the falling shadows will be. And, conversely, the more diffused the light (light in cloudy weather when it is cloudy), the more blurred the shadow outline will become.

Conclusion

Correctly projecting the shadow, determining how its saturation and clarity of the contour changes - these are the main tasks that the artist needs to keep in mind when he draws shadows. Beginners, at first, will have to gradually implement all this in their drawing. But, each time these tasks will become easier and easier. And with the accumulation of experience, the drawing will be obtained on an intuitive level.

An artificial light source, like any point in perspective, is defined in the picture as the perspective of the luminous point itself and the perspective of the base ( see fig. 9.22).

The light source can be located anywhere relative to the illuminated object. It depends on how the artist wishes to use light in the composition of the painting.

The length of the shadow depends on the height of the luminous point and its distance to the illuminated object. The shadow should not extend beyond the horizon line or ABOUT-ABOUT. If it is above the horizon, it is an imaginary shadow. Therefore, you need to choose the right light source.

If an object is illuminated by several light sources, then the falling shadows overlap one another. The place where two falling shadows overlap is called full shadow . The mismatched parts of the falling shadows are called penumbra . First they build their own shadow, then the penumbra, then the full shadow, but not the black one, since it is illuminated by reflected light.

Example 1. Construct a falling shadow from the vertical for two given light sources ( rice. 9.27).

Solution

1. Determine the boundary of your own shadow. For a given position of the light sources, the edges of the shadow will be the boundary V" K V K And E" K E K, i.e. in its own shadow there will be edges A" K A K B" K B K And A" K A K E" K E K.

2. Construct falling shadows from edges A" K A K B" K B K And A" K A K E" K E K first from the first light source, and then from the second.

3. Determine the boundary of the full shadow and penumbra.

Example 3. Construct your own shadow and a falling shadow from a vertical cylinder. The position of the light source is determined by the perspective and the perspective of the base ( rice. 9.29).

Solution

1. Determine the zone of your own shadow. From point C" K(perspective of the base of the source) draw tangents to the lower base of the cylinder. Generators of the cylinder drawn from the points of tangency 1 K And 6 K, will limit the area of ​​their own shadow.

2. Let's build a falling shadow. To do this, we divide the arc of the base of the cylinder in the unlit part into an arbitrary number of sections of arbitrary length with dots 2" K, 3" K etc.

3. Let's draw generators through these points and construct shadows from these generators. Line 1 T-2 T-3 T-4 T-5 T-6 T will limit the area of ​​the falling shadow.

Constructing shadows in the interior

When depicting interiors, artificial lighting is most often used. Solar lighting in the interior is used only if there are large light openings (terraces). If the windows are of normal sizes, then the light “bunny” can be neglected.

Rule for constructing shadows

To find a shadow from a point, you need to draw a ray through the light source and the point and find the point of intersection of this ray with the plane on which the shadow falls. To do this, solve the problem of the intersection of a line and a plane. We draw an auxiliary projection plane through the light beam: if the shadow is on the floor, then the plane is horizontally projecting; if on vertical walls, it is frontally projecting.

Example 1. Construct a shadow from vertical lines on the floor and side wall room at a given position of the luminous point ( rice. 9.30).

Solution. In this example, it is convenient to draw horizontally projecting ray planes. The horizontal trace of these planes will pass through the perspective of the base of the light source and the perspective of the base of the points A And IN. The point of intersection of the trace of the plane with the light ray gives the shadow of the point A on the floor This construction is called the sail method.

9.3.4. Constructing shadows from objects on various surfaces
in natural and artificial light

Example 1. Construct a falling shadow from the balcony on a vertical wall in natural light ( rice. 9.32).

Solution

1. Determine the zone of your own shadow. With a given light source, the right side wall of the balcony and the lower part of the floor will be in their own shadow.

2. Construct falling shadows from the contour of our own shadows. To do this from the points BK, G K And L K Let's draw light rays at an angle of 45° and determine the points of intersection of these rays with the vertical wall of the house.

To determine the points of intersection of light rays with a vertical wall, we determine the perspectives of the base of all points of the balcony on the object plane (points A" K, M" K, L" K, E" K, J" K, B" K, G" K).

Through the perspectives of the base of the points B" K, G" K, L" K Let's draw the perspective of the base of the light rays until they intersect with the vertical wall (point 1 And 2 ). From points 1 And 2 Let's restore the perpendiculars until they intersect with the light rays drawn from the points B" K, G" K, L" K. Let's connect the obtained points B" K, G" K, L" K. These will be the shadows from the ribs B K G K, G K L K. By connecting V T With E K, we get the shadow from the edge L K M K.

Example 2. Construct a vertical drop shadow AB to the object plane N and onto the surface of a truncated prism ( rice. 9.33).

Solution. Since the point IN vertical belongs to the object plane, the shadow of the point IN coincides with the point itself IN. Thus, solving the problem comes down to constructing a shadow from a point A.

1. Through the perspective of a point A (A K) and source perspective ( S K) hold the perspective of the light beam. Point ( A T) – hypothetical location of the shadow from the point A on the object plane, if there were no obstacle in the path of the light rays.

2. Through the perspective of the base of the point A (A" K) and the perspective of the base of the source ( C" K) draw a perspective of the base of the light beam.

3. Construct a line of intersection of the horizontally projecting plane of light rays (plane CAB passing through the vertical AB and light source WITH) with the surface of a truncated prism – line 1 K 1" K 2" K 2 K.

4. Vertical shadow AB will go from the shadow of the point IN onto the object plane (coinciding with the point itself IN), along the perspective of the base of the light beam until it intersects with the surface of the prism (point 1" K). Next - along the line of intersection of the plane of light rays with the surface of the prism. The boundary point of the shadow ( A T) will be the point of intersection of the line 1 K 1" K 2" K 2 K with light beam perspective.

Bibliography

1. Makarova, M. N. Perspective / M. N. Makarova. – M.: Academic project, 2006.

2. Ivashina, G. G. Perspective / G. G. Ivashina. – St. Petersburg: SPbGHPA, 2005.

3. Solovyov, S. A. Drawing and perspective / S. A. Solovyov. – M.: graduate School, 1967.

4. Kotrubenko, M. E. Collection of problems for the course “Descriptive geometry and technical drawing” / M. E. Kotrubenko, O. K. Leskova, L. N. Karagezyan. – St. Petersburg: IPC SPGUTD, 2006.

Related information.

When studying the rules and methods of perspective depiction of lighting phenomena, they are usually distinguished based on the relative position of the rays of light: the rays of light from the sun and the moon are taken to be mutually parallel lines, therefore, in perspective, subject to the rules about the vanishing points of the perspectives of parallel lines; The rays of light from a lamp (luminous point), as is known, converge at one point (the use of fluorescent lamps spreading the rays of luminous cylinders can be considered as a case of illumination by several lamps).

The process of depicting lighting phenomena is greatly simplified if the artist understands the shape of both his own shadow on an object and that falling from it onto adjacent objects. Let's consider two separate questions: about the construction and forms of shadows in axonometric projections using examples of shadows from a straight line, a flat figure and geometric bodies, which will help us explain the general rules for constructing shadows and about the rules for perspective depiction of lighting phenomena. These rules are based on the following considerations: when observing shadows falling on the floor from vertical lines in a room where one lamp hangs from the ceiling (Fig. 16), we will notice, firstly, that all such shadows are directed to one point located on the floor exactly under the lamp; secondly, it is easy to verify that the length of the shadow from the vertical line to the floor is determined by the point of intersection with the floor of the ray of light passing through the upper end of the vertical line; repeating our observation, but already over the direction of the shadows from straight lines perpendicular to the wall of the room, that is, horizontal, we will notice that they are also directed to one point (like the shadows on the floor) and that this point is placed exactly in that place on the wall against which the lamp hangs; the exact position of this point can be determined by mentally drawing a perpendicular from the luminous point to the wall; on the other walls of the room we will notice exactly the same phenomenon. Let us agree to call the points of vanishing of shadows from straight lines on the floor or on the wall that we have marked as rectangular projections of the light source onto the plane on which the shadow falls. Consequently, to indicate lighting conditions in a drawing, it is necessary to indicate two points: the most luminous point and its projection onto the plane on which the shadow falls. In our example, there will be five such projections of the light source: on the floor, ceiling and three walls.

Constructing reflections in the mirror plane

The painting (Fig. 17) depicts a shore, along the edge of which there are lanterns, a low fence and a tent. First, let's construct a reflection of the vertical edge of the shore at the point A – a. To do this, from the projection of the point A put aside equal-sized segments Aa = aA * . Then we will construct a reflection of the vertical plane of the embankment, drawing its upper edge to the vanishing point F 2 .

If the object is located in depth on the horizontal plane of the earth, then additional constructions are used. In this example, lighting lanterns are located along the embankment, which are located some distance from its edge. Let's build their reflection in the water using the nearby headlamp B–b. First, draw a perpendicular to the plane of the mirror (water), continuing the height of each lantern down below the surface of the water. Then we determine the point of intersection of the perpendicular with the surface of the water. To do this, we will draw an additional vertical plane through it (frontal or arbitrarily directed) and construct a line of intersection of the frontal plane with the surface of the earth and will pass through the base of the lantern b along a straight line of latitude, the edge of the shore - along a vertical line and the surface of the water - along a straight line of latitude. The intersection of the perpendicular with this line will determine the point b 1 “touch” of the pillar as it continues with the surface of the water. Then we postpone from the point b 1 equal segments Bb 1 =b 1 B * .

Note that the bases and tops of all lanterns are on imaginary lines parallel to the edge of the shore, so they have a common vanishing point with it F 2 .

In the same way we will build a fence along a vertical post. E–e, but draw the auxiliary vertical plane in the direction of the point F 1. The line of its intersection with the surface of the earth will pass through the base of the rack e and vanishing point F 1, the edge of the shore in a vertical straight line and the surface of the water in a horizontal straight line with a vanishing point F 1. This line at the intersection with the perpendicular will determine the desired point e 1, reflection of the rack Her 1 = e 1 – E* and the entire hedge.

Let's build a reflection of the tent in the water. First, we will continue all the vertical edges beyond the plane of the mirror and determine the point of intersection with the water I 1 front rib only L – 1. Then, putting an equal distance behind the surface of the water LI 1 = IL*, construct a reflection of the desired point L * F 1 and F 2, which will be a reflection of the horizontal edges of this object.

To build a canopy, it is enough to determine the reflection of one point I by drawing a horizontal line through the point L. Then the horizontal line parallel to it L * L ∞ when intersecting a vertical line, it will determine the reflection of the point I * . Draw horizontal lines through it to the vanishing points F 1 and F 2, which will be a reflection of the edges of the tent canopy in the water.

Note that in this example the silhouettes of buildings located far from the shore at a considerable distance from it are depicted.