Constructing shadows in perspective at the vanishing point of rays. Constructing shadows under artificial lighting

Projection drawings carried out during the design process, in addition to being conveniently measurable and metrically certain, should be visual and should give the most complete picture of the composition and appearance buildings, oh plastic solution in detail. This can be achieved by constructing shadows. Constructing a shadow on an orthogonal drawing, in axonometry and perspective consists of the following steps:

1) making the contours (borders) of shadows using precise techniques geometric constructions;

2) identification and transmission of illumination gradations in the drawing, taking into account physical laws.

Below are examples of constructing shadows in perspective, in relation to buildings and their fragments, as well as basic graphic techniques. These examples will help students complete the Building Perspective assignment.

Shadows enrich the image, make it even more expressive and convincing, and with the use of graphic techniques, they give maximum clarity to the perspective. Free drawing of shadows does not have a projection connection with the elements of the building and does not make it possible to identify and eliminate errors in the proportions of the future structure.

3.1 Constructing shadows in perspective

To make perspective images more expressive, they construct their own and falling shadows of the depicted objects. These constructions are based on the geometric premises of the theory of shadows, discussed earlier in the study of descriptive geometry. Without repeating them again, let's move on to specific examples constructions on which we will show some features inherent in these methods.

The construction of shadows in perspective has much in common with similar constructions in axonometry. Just as in axonometry, in perspective, to construct shadows, it is necessary to set the direction of the light ray and have its secondary projection in the drawing. But since perspective is based on central projection, and not parallel, then ray lines, their projections, parallel in space, have their own vanishing points in perspective.

Since the light source S is considered to be remote to infinity, then its secondary projection should be on the horizon line. Depending on the direction of the rays and the position of the light source relative to the viewer and the painting, the following three main shadow patterns are possible (Fig. 3.1).

On first of these, the sun is behind the viewer, to the left. In this case, the vanishing point of the projection of the rays is located on the horizon S 1, the vanishing point of the rays themselves (perspective of the sun S) - below the horizon on the same vertical with the point S 1.

On second diagram the sun is located in front of the viewer. Now the perspective of the sun ( S) is in front of the viewer above the horizon on the same vertical with the point S 1.

On third in the diagram, the rays of light are parallel to the picture plane, therefore they are depicted parallel in perspective, and their secondary projections are parallel to the base paintings, i.e. horizontal.

The obvious convenience of constructing according to the third scheme allows you to use it to complete the task. All further examples will be given according to this scheme.

3.2 Basic construction techniques

Rays of light, falling on the surface of a body, form an illuminated and unlit part on it (Fig. 3.2). The shadow formed on the unlit part of the object is called its own shadow.

The line separating the illuminated and shadowed parts on the surface of an object is called the contour of its own shadow (line AOB). In turn, this object casts a shadow on the bodies behind it. A shadow formed from one object on another is called falling shadow, and its outer boundary is outline of a falling shadow (line JSC T V).

Looking at Fig. 3.2, we see that there is a direct connection between the contour of its own and the falling shadow: both contours are formed by a ray surface, as if wrapping a given object and then intersecting the object plane.

In other words, the outline of the falling shadow is the shadow of the outline of its own shadow.

Thus, our task is to build the contours of the shadows. Identification of gradations of illumination within the zone of shadow and light will be discussed below.

When completing the task, we use three main methods of constructing shadows:

1) beam trace method- is based on the fact that the shadow falling from a point is the trace of a ray drawn through this point, i.e. beam S meets the object plane at that point O T, where it intersects with its secondary projection S 1(Fig. 3.2).

2) beam section method- consists in the fact that when constructing shadows of both their own and falling objects are cut by planes parallel to the ray of light, i.e. parallel to the picture plane. So in Fig. 3.3 radial plane a (cuts the object along the line 1 1 122 1 , on which there will be a falling shadow from the straight line AA 1 in segments 1 1 1 And 1A T. In this way, you can construct your own and falling shadows of any surfaces, although the constructions can be very rich and complex.

3) Back beam method- used, as a rule, to construct falling shadows from one object to another. The method consists in determining the intersection points of the contours of falling shadows from one and another model on the object plane. From these points they are then drawn return rays until it intersects with the contour of the object’s own shadow, on which the shadow of another object is built.

Rice. 3.3

Rice. 3.4

So, in Fig. 3.4 falling shadow from a straight line AB consists of three segments - A 1, 1-2 And 2 T W T. The contour of the falling shadow of an object and the shadow of a straight line are constructed on the object plane AB. Dot 2 T at the intersection of the contour NM T with a straight shadow AB T reverse transferred by the beam to the contour of the object’s own shadow, i.e. on the edge NM. Further construction can be seen from the drawing.

The method of backward rays is very simple and makes it possible to easily construct characteristic points of a falling shadow - its intersection with the contour of its own shadow.

3.3 Shadow from a point and a line segment on horizontal and vertical planes

To get a shadow from a point A(Fig. 3.5) in the drawing through a point A and its secondary projection is carried out accordingly by the beam S and its secondary projection S 1 until they intersect. Received point A T- trace of the beam on the object plane, i.e. point shadow A.

To find the shadow of a segment of various positions using the ray trace method, the following provisions of descriptive geometry are taken into account:

1) if the straight line is perpendicular to the horizontal plane, then its shadow on this plane coincides with the secondary projection of the light beam or is parallel to it (Fig. 3.6 and Fig. 3.7);

Rice. 3.7

2) if a line is parallel to any plane, then its shadow on this plane is parallel to the line. For vertical lines, their parallelism to their shadows on vertical planes is maintained in perspective (Fig. 3.6, b; rice. 3.7), and for horizontal lines this parallelism in space is taken into account in perspective by a common vanishing point F on the horizon line (Fig. 3.8, Fig. 3.9).

In Fig. 3.9 shadows from vertical lines AA 1 And BB 1 or coincide with the direction of the secondary projection of the light beam S 1(segments A 1 1 And B 1 5 on the object plane), or parallel to it on horizontal areas of the object (segments 6-7 , 8V T And 2A T). On vertical planes of an object, shadows from straight lines AA 1 And BB 1 parallel to them (segments 1-2 , 5-6 And 7-8 ).

Shadows from a horizontal line AB on horizontal areas of an object they have a common vanishing point F on the horizon line (segments A T 3 And 4V T). Shadow segment 3-4 obtained by construction:

first the shadow is built V T, then a segment is drawn B4 with direction to a point F, similarly found the shadow of the point A - A T, and a segment is drawn A T 3 with direction to a point F finally the dots are connected 3 And 4 .

In Fig. 3.10 shows the construction of a shadow from a rod AK(bracket) extending from the plane of the vertical wall at a right angle.

Shadow from a point A obtained on the object plane using the ray trace method. Shadow segment to the wall A T 1 has a direction to a point F because the bracket is horizontal. The shadow on the wall is obtained by connecting the break point of the shadow 1 with base TO bracket.

In Fig. 3.11 the shadow of the rod is constructed AK, emerging from the plane of the wall at an arbitrary angle.

Shadow from a point A constructed using the ray trace method. Then on the rod AK you need to take one arbitrary point, for example, M and build a shadow from it. Connecting the shadow A T with shadow M T, which are located in the object plane, continue the line A T M T until it intersects with the base of the wall, and then the inflection point of the shadow 1 connect the walls to the base of the rod on the plane TO.

If the shadow from the auxiliary point M hits the wall (Fig. 3.12), then the construction of the shadow must begin by connecting the base of the rod TO with the resulting shadow M T auxiliary point M to the point of inflection - the base of the wall and finish constructing a broken line of the shadow, connecting the point of inflection 1 with shadow A T points A.

Based on previous constructions, we will create the perspective of a falling shadow from a vertical wall onto a staircase and a shadow from the steps of a staircase onto an object plane - the surface of the earth and other surfaces (Fig. 3.13).

1. Shadow from a vertical edge BB 1 on the object plane and on the horizontal plane 1 stage is parallel to the secondary projection of the light beam, i.e. parallel to the base of the picture.

2. Shadow from the same edge BB 1 on the vertical plane of the riser 1 the steps are parallel to the rib itself.

3. Shadows from a horizontal edge BE the planes of steps parallel to it have a common vanishing point with the edge itself F on the horizon line.

4. Shadows from the edge BE on the vertical planes of the risers II And III directed to points WITH And D, in which the straight line BE intersects the riser planes extended upward (similar to the construction in Fig. 3.10).

5. Shadow from a point A constructed using the ray trace method; shadows from points are constructed similarly M And N.

6. The contours of the shadows of the risers on the object plane are parallel horizontal projection light beam, i.e. horizontal.

7. The contours of the shadows of the horizontal treads, as well as the perspective of their edges coming from the points A, M And N, have a common vanishing point F.

8. Rib Shadows BE And NK onto the vertical plane of the facade will pass through their bases, i.e. through points E And TO from inflection points 2 And 1 (similar to Fig. 3.10). The remaining constructions are clear from the drawing.

An example of constructing a shadow in perspective from the protruding elements of a building onto the plane of the wall and the plane of the window niches is given in Fig. 3.14.

1. The shadow of the cornice is created using an auxiliary point M, taken arbitrarily on the ledge of the cornice, because the cornice is parallel to the plane of the wall, then its shadow has a common vanishing point on the horizon line with the perspective of the cornice. Left extreme point cornice TO determines the further construction of its shadow, as can be seen from the drawing.

2. The shadow of the window slopes in the niche of the opening is constructed using the example of a point 1 or 2 . A vertical slope has its shadow also vertical, and a horizontal slope and its shadow have a common vanishing point on the horizon line.

3. The shadow falling from the balcony slab is determined by the contour of this slab’s own shadow. So, the contour of the balcony slab’s own shadow consists of segments: NА , AB, Sun And CD. An imaginary shadow has been constructed ( A T) from point A, on the same line in perspective there is a shadow from the point IN. Knowing the vanishing point parallel lines, you can draw a shadow outline ( A T)V T from the segment AB to the plane of the wall.

In window niches this shadow is shifted and its construction is shown in the drawing.

Segment Sun parallel to the wall of the building, i.e. his shadow V T S T located vertically.

Bases of segments AN And CD points N And D connect accordingly with the previously obtained shadows ( A T) And S T points A And WITH.

4. Falling shadows from the balcony railing are constructed on the basis of the previously given examples as shadows from segments parallel and perpendicular to the plane of the building wall.

Similar constructions must be performed in the presence of other architectural and structural elements protruding from the plane of the wall (belts, pilasters, columns, canopies above front door etc.). The task is simplified by the fact that almost all of the listed building elements have horizontal and vertical edges and planes parallel or perpendicular to the plane of the building wall

3.4 Shadow from a point and a line on inclined planes

The main technique for constructing falling shadows on an inclined plane is the ray plane method, noted earlier in Fig. 3.3. The shadow from the vertical rod on the inclined plane of the roof (Fig. 3.15) is constructed in the following order.

1. A vertical ray plane, parallel to the picture, is drawn through the vertical segment and, naturally, through its secondary projection. The base of this plane, i.e. horizontal trace, intersects with the bases of vertical walls at points 1 1 And 2 1 . Let's raise these points to the contour of the sloping roof (points 1 And 2 ) and select general outline sections - trapezoid 1 1 22 1 .

2. The resulting section, vertical segment AA K and beam S are in the same radial plane a. After holding the beam S through the point A before the intersection with the section contour, find the point at the intersection A T- shadow from a point A. By connecting it to the base of the mast (point A K), we get a falling shadow from the mast on the inclined plane of the roof of the building.

Using the described techniques, we will use an example to show the construction of a falling shadow from a pipe onto a roof (Fig. 3.16).

1. Determine the contour of the pipe prism’s own shadow. These are segments A K A, AB, Sun, SS K, from which you need to build the contour of the falling shadow.

2. Draw the first ray plane a through the segment AA K A 1 and find his falling shadow on the roof - period A T(as in Fig. 3.15).

3. A similar construction must be carried out by constructing a shadow from a point IN using the second ray plane a 2 (dot V T).

4. Connecting the dots A T And V T, we get the shadow of the segment AB pipes.

5. Segment Sun pipe is parallel to the roof, so the construction of its shadow is related to the point IN and overall accurate alignment F 1 on the horizon line. Straight line coming from a point V T to the vanishing point F 1 at the intersection with the ray drawn from point C of the pipe, it will give a shadow from this point - S T.

6. Connecting S T with the base of this pipe corner (point S K) taking into account the visibility of the straight line segment, we will complete the construction of the contour of the falling shadow from the pipe.

Similar constructions must be carried out to find the falling shadows on the inclined planes of the roof from other elements that take place on the roof of the building: ventilation duct boxes, dormer windows, antennas, etc.

3.5 Constructing shadows of individual building elements

In Fig. 3.17 the shadow of the ridge is built AB, falling on the roof of the extension and the shadow from the nearest overhang of a high roof on the wall of the extension.

1. Shadow A T points A construct using a secant ray plane drawn through a point A. The horizontal trace of the radial plane intersects the secondary projection of the extension at points 1 1 And 2 1 (overhang and ridge). Let's find these points on the perspective of the overhang and ridge of the extension - points 1 And 2 . At the intersection of the beam 3 from point A with this line 12 and the shadow of the point will be marked A - A T.

2. Let's continue the groove MN to the intersection with the ridge at the point 3 and connect 3 the desired line with A T.

3. Let's continue the groove MN to the intersection with the continuation of the overhang AD) at point 4 and connect the dots 4 with a dot A T, we get the desired shadow.

4. Construct a shadow from a point D on the extension wall - dot D'.

Dot D- this is the intersection of two segments - an overhang AD and cornice DM. Segment AD is parallel to the wall of the extension, which means that its shadow will be parallel to it, and in perspective these two straight lines will have a common vanishing point above the horizon.

5. Segment DM perpendicular to the wall of the extension, we will find its intersection with this wall (using the secondary projection) and finish constructing the shadow of the roof overhang by connecting the points. D T And 5 .

3.6 Building shadows of a building

Using the examples given, we build from large forms To small details(Fig. 3.18).

If a low horizon line is taken, then it is necessary to use a lowered plan, since the original plan is “crumpled” and its use can lead to significant errors. The choice of the angle of inclination of the light beam is related to the design of the building and the main task in this case is to give the most visual graphic image on the drawing plane of all architectural and structural elements.

Lecture 8

Constructing perspective and shadows in perspective

Plan

1. Perspective geometric bodies.

2. Choosing a point of view when constructing a perspective image.

3. Constructing a perspective image of the building.

4. Shadows in perspective..

1. PERSPECTIVE OF GEOMETRIC BODIES

Construction of a perspective image of a cube (Fig. 99). We draw the picture plane through the edge of the cube VM, in this case it will be projected on the picture plane in natural size. Let's set the position of the horizon line and make all the constructions similarly to the previous ones (Fig. 99). Vanishing points of lines AB,CD, AD And NE determined by the previously discussed method.

The transfer of points from the base of the picture plane to the picture is carried out as in the previous examples.

In a picture from a point V-M we restore the perpendicular on which we plot the natural length of the edge of the cube VM. We connect the extreme points of the edge with the vanishing points F 1 And F 2 , and from the points A To = E k and C k = G K we restore the perpendicular to the intersection with the lines representing the full perspectives of the lines coming from the edge VM to the vanishing points. Thus, we obtain a perspective image of the ribs AE And C.G.. To get an image of an edge DK, it is necessary from the extreme edges of the points AE And C.G. draw straight lines to vanishing points F 1 And F 2 . At the intersection of these lines we get edge points DK.

If the second vanishing point lies outside the drawing, for example the point F 2 , then you can build a perspective with one vanishing point F 1. To do this, we continue the horizontal projection D l A l until it intersects with the picture plane at the point N 1 , Full stop N 1 Let's transfer it to the picture and from it we will construct a perpendicular, on which we will plot the natural height of the cube. Connecting the resulting points with the right vanishing point F 2 , we get a perspective image of the edges of the cube AE And DK as a result of the intersection of lines N l F 2 with perpendiculars AE And DK, reconstructed from the picture plane.

You can also construct an image of a cube if you use straight lines perpendicular to the picture plane, drawn through the vertices of the cube. In Fig. 99, b shows the construction of the perspective of two edges AE And C.G.. In this case, the main line of sight is directed like this. so that it does not coincide with the edge KD.

A perspective image can be constructed with a magnification of several times. for example, 2 or 4, etc. To do this, all dimensions, both vertical and horizontal, are increased when all points are transferred to the picture. Figure 100 gives an example of constructing a perspective image of two geometric bodies, a cube and a parallelepiped, located on the same level. The picture plane is drawn like this. so that two edges (one at the cube, the other at the parallelepiped) are projected on the picture plane without distortion, i.e. the picture plane is drawn through the edge 4 parallelepiped and edge A Cuba. The horizon line is drawn so that the top base of a cube is visible, while the top base of a parallelepiped is invisible.

We position the viewer so that the main line of sight is perpendicular to the picture plane (picture) and the main point R was in the middle third of the picture.

Through all points of the figure we draw rays to the point of view and find the left and right vanishing points. Then we transfer the trace of the picture plane, together with all the points, to the place where the perspective image will be constructed.

In the picture, first we find the natural ribs 4 And A and from them we draw lines to the vanishing points. Drawing from the points 1 To , 2 TO , 3 To , D K , WITH To And IN To vertical straight lines, we find a perspective image of each point. By connecting them together, we obtain a perspective image of the given volumes.

2. CHOOSING A POINT OF VIEW WHEN CONSTRUCTING A PERSPECTIVE IMAGE

In order for an image to look good in perspective, it is necessary to take into account the person’s natural angle of view, so the relative position of the object, picture and point of view cannot be arbitrary.

When choosing a point of view, it is recommended to adhere to the following provisions:

The main line of sight should be directed perpendicular to the picture plane and divide the picture approximately in half or be in the middle third of the picture. That's what's called a painting. what will be contained between the extreme rays coming from the viewer to the object;

It is advisable to maintain the ratio AB/BC =A k B k / B k C k (Fig. 101);

U the gap between the base of the picture and the structure should be 20°...40°;

The viewer must be at such a distance from the object that the object is included in the cone of clear vision or is in the field of clear vision. To do this, the angle between the extreme rays of vision must be within 28°...37° (Fig. 102);

In the case when the vertical dimensions of a structure are larger than the horizontal ones, the viewer should move one and a half to two heights away from the structure so that the angle of view in the vertical plane is within the permissible limits (Fig. 103);

According to the location of the picture plane Regarding the object, perspectives can be of two types: central frontal perspective used for building interiors, i.e. perspectives internal view premises (Fig. 104); angular perspective(Fig. 105) is used when depicting individual objects, in this case the picture plane is located at an angle to the object.

According to the location of the horizon line perspective images can be (see Fig. 105, A): with normal horizon height, i.e. at a height of human height of 1.5... 1.7 m, it is used when constructing perspective on level ground (Fig. 105, b); when viewed from below used for individual parts observed from below, and for buildings standing on a hill (Fig. 105, V): with a high horizon, in this case, the horizon height is taken to 100 m and above (Fig. 105, G).

Based on the distance of the point of view from the subject, perspectives can be divided into perspectives with a sharp, sharp angle and perspectives with a blunt, flat angle. Foreshortening is the position of the depicted object relative to the picture plane, which results in a sharp shortening of parts distant from the foreground. The measure of perspective is the ratio of the perspective image of the ribs BB 0 in the foreground (see Fig. 106, A And b) to the edge A 1 A 0 the most distant edge of the same face BB 0 /A"A 0 .

When choosing a point of view, a necessary condition is the actual location of the point of view, i.e. the best. When choosing a point of view, you can use the following scheme (Fig. 107). When marking the standing points, mentally imagine what the building will look like. For example, dot 1 (see Fig. 106, 107) shows a side view of the building. The main part of the facade is hidden, point 2 reveals the main facade well, but the sides are not visible; dot 3 gives a view of both facades, then since the perspective angle for both facades is the same, the perspective of the building turned out to be inexpressive; point 4 can be considered the most successful, since from this point of view the composition of the building is revealed in the best possible way.

3. BUILDING A PROSPECTIVE

BUILDING IMAGES

The perspective of any building (structure) consists of the perspective of many points, each of which is constructed as a trace of a ray of vision on the picture plane. There are several ways to build perspectives. The main ways to build perspective include:

1. a method of architects based on the use of vanishing points of parallel lines;

2. method of rectangular coordinates and perspective grid;

3. radial method and combined height method.

Each of these methods of constructing perspective uses different elements of central projection. The choice of one or another construction method depends on the type of object and its volumetric-spatial structure.

The architects' method is based on the use of vanishing points of perspectives of horizontal parallel straight objects and is used in practice to construct architectural perspectives.

The essence of the radial method of constructing perspective is to determine the points of intersection of the projecting rays with the picture plane. This method is used mainly in the construction frontal perspectives streets, courtyards, building facades with protruding parts.

The essence of the coordinate method is to construct the perspective of an object related to a rectangular coordinate system. The coordinate method is used when depicting simple objects of irregular shape.

The perspective grid method, as a type of coordinate method, is used when constructing “planning” perspectives with a high horizon when designing urban and industrial facilities located over a large area.

We will look at one of them - the architect's method. This method comes down to determining the projections of the points of the structure onto the picture plane by rays coming from the points of view to each point of the structure.

When constructing a perspective using the architect's method, the picture plane is placed at an angle to the building and its trace is drawn through one of the corners (Fig. 109).

The viewer is positioned so that the main line of sight is perpendicular to the picture plane, and the viewer himself is at such a distance that the angle of view , determined by the extreme rays of view S { and S 5 was equal to 23°...37". Main line of sight SP should divide the picture approximately in half so that the point R was in the middle third of the picture.

T vanishing points for the main directions of the plan can be found if straight lines are drawn from the standing point S 1 parallel to the sides of the structure to re sections with the picture plane at points F 1 and F 2 .

Vanishing point F 1 (left) will be the vanishing point for all lines parallel to the sides 1-2, 3-4. 5-6, 8-9, and the vanishing point F 2 (right) – for parallel sides 1-7, 11-10, 2-3, 4-5 and parallel ones.

After installing the viewer, the picture plane and finding the vanishing points, rays of sight are drawn from all points of the structure and on the trace of the picture plane QC all intersection points are recorded 1 k... 6 K, etc.

To construct the perspective itself, we transfer the trace of the picture plane with all the points marked on it to the place where the perspective will be built (Fig. 110).

We draw the horizon line parallel to the base of the picture plane QC at a given height and transfer the vanishing points from the base of the picture plane to it.

Since the picture plane is drawn through the edge 4, then in the future it will be in natural length. From point 4 To we restore the nonpendicular to the trace of the picture plane and plot the height of the edge on it 4, taken from the frontal projection of the orthogonal drawing.

The lower and upper points of the rib 4 connect to vanishing points F 1 and F 2 . getting the direction of the sides of the building. Restoring perpendiculars from points 3k and 5 To before intersecting with the rays going to the vanishing points, we get the sides of the building. In the same way we find all the edges and sides of the structure in perspective.

To get points 8, 9, 10 to 11 in in the future we will continue the lines of the ridge 11-10 (see Fig. 109) until it intersects with the picture plane K K at the point N 1  , a line 8-9 to the intersection at the point N and move these points into perspective. From the obtained points we construct perpendiculars, on which we plot the heights from the ground to the ridge.

Connecting the dots N 1 And N 2 with vanishing points and intersecting the resulting lines with perpendicular straight lines constructed from the points 11 To , 10 To 8 To And 9 TO , we get a perspective image of straight lines 11-10 And 8-9, belonging to the roof ridges. We connect the found points, according to the orthogonal drawing, with the corresponding points, obtaining a perspective image of the roof.

So that the structure does not seem to be hanging in the air, it is necessary to draw a sidewalk, road, etc. near it, while ensuring that everything the drawn lines were directed to the vanishing points.

4. SHADOWS IN PERSPECTIVE

T Just like in axonometry, shadows in perspective can be constructed with various points location of the light source.

In Fig. 111 shows eight possible arrangements of light sources relative to the position of the point of view and two vertical rods from which a shadow falls on the horizontal plane. Here the shadows are from the tops of the rods, i.e. from the points A And IN, found as horizontal traces of light rays passing through these points. From the examples considered, it is clear that shadows from vertical lines fall in the direction of the vanishing point on the horizon, and the length of the shadow is determined by the intersection of the ray of light passing through the upper end of the straight line to the vanishing point of the rays with the surface on which the shadow falls.

The direction of the light rays can be chosen depending on the nature of the object being depicted and the desire to show it illuminated from one side or the other. In this case, one should be guided by aesthetic considerations, since the construction of shadows on a project is not an end in itself, but only a means for identifying forms and proportions.

In cases where the structure consists of arches and colonnades, it is good to use the so-called coming shadows. In this case, rays of light penetrating through the openings create a spectacular play of chiaroscuro.

Now let's determine the distance d, to which the vanishing point of light rays in space F 4 will be removed in the picture from the vanishing point of horizontal projections of rays F 3 . To do this, assume that the sun is located behind and to the left of the viewer, and the rays are directed down to the right, making an angle a = 35; 54". (At point S construct angle a and find the leg d right triangle SF 3 F 4, which is the desired value, and it should be plotted in the picture vertically down from the point F 3 of the horizon. All other constructions for finding shadows are clear from the drawing. To construct a shadow from a building that has a protrusion, we can recommend the following technique for choosing the direction of the light rays. Let's consider the construction (Fig. 112). To the corner 4 Apply a ruler to the ledge of the building KN so that the shadow falling from the ledge onto the facade 5-6 was either slightly smaller or slightly larger than the prospective projection size 4-5. and, drawing a projection of the light ray in plan along the edge of the ruler, we find point F 3 on the axis OH as a projection of the vanishing point of horizontal projections of light rays (S l F 3 \\ KN).

Let's consider the construction of falling shadows on the steps of the stairs from the side wall (Fig. 113). When constructing shadows in perspective from a building, they usually take the direction of the rays parallel to the picture plane, in this case the rays and shadows from the vertical lines will be parallel, the latter facilitates the construction of shadows in the drawing.

To construct a falling shadow from the side wall of the staircase on the steps, we used the technique of continuing the edge from which the shadow is constructed (in this case, the edge A B), until it intersects with the edge on which the falling shadow is constructed.

First we build a shadow from a vertical line A 0 A 1 . for this from the base A 0 We project the ray S 0 to the riser of the first step, at the base of which the shadow breaks and. as from the vertical, on a vertical plane it will go up to the tread. Having reached the second riser, the beam breaks again and rises vertically to the second step, then along the tread the beam will go in the direction of the projection of the beam S 0 until it meets the beam S at the point TO.

Now we build a shadow from an inclined one A B, for this we continue straight A 1 IN" to the intersection with the line IN 1 WITH 1 . belonging to the upper platform R. Shadow from the line A IN 1 at the point 1 will be equal to zero, and the straight line 1-B r will provide shade on the site R from IN to the point 4. To find the shadow on the tread N, let's continue A 1 IN 1 to the point 2, lying in the plane N. and look for the shadow of the point in the same plane IN 1 - this will be a point IN N . When connecting the dots 2 And B N the straight line will intersect the riser N at points 5 And 6. Point 7 on the tread M it turns out the same way. The shadow on risers II and III will be obtained by connecting the points 7 With 6 and 5 s 4.

Shadow from the line IN 1 WITH 1 , so from a horizontal straight line to a horizontal plane it will lie in the direction of the ray going to the same vanishing point as from the point IN r to the vertical wall, from where the shadow will go to point C 1. The remaining constructions are clear from the drawing.

Figure 114 gives an example of constructing falling shadows with rays parallel to the picture plane.

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 a small parallelepiped are constructed, obtained from the intersection of ray planes drawn through the contour of the own shadows of a 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 receiving 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 the one and the direction that best ensures the 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 great distance (sun, moon), and therefore the rays falling on 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 in 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 perspective of the ray, 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* onto 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 with 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 defined 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, in various ways located 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. Shadow from a point behind given plane is the point of intersection 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 to the object plane, through a point A project ca ray perspective and then through the point A hold perspective C.A. beam. The 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 a point artificial lighting The nature of the illuminated surface of an object and its shadows is not the same as in sunlight, since here the intensity of illumination of the surface 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 falls. light rays, and unlit, 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.