Constructing shadows in the perspective of a building. The natural light source is located in front of the observer. Constructing shadows from the sun located to the left in the neutral plane

Constructing perspective and shadows in perspective

Plan

1. Perspective of 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 straight 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 where 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 constructing frontal perspectives of streets, courtyards, and building facades with parts protruding forward.

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 in 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 from different points 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, the 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 extending 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 beam 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 frontal position.

Lecture 24 Constructing shadows in the interior Position of the light source Constructing shadows of geometric bodies Inverse ray method Ray section method

Constructing shadows in the interior is a rather difficult task. This is explained, firstly, by the presence of various lighting sources - solar, diffused and artificial light and, secondly, in conditions of illumination by artificial light sources, their large number, variety of shapes and locations in a modern interior make the task of accurately constructing the contours of shadows quite difficult.

Three cases of constructing shadow contours Depending on the type of interior lighting sources, three cases of constructing shadow contours are possible: With sunlight penetrating through window openings; With point light sources; In diffuse daylight

Constructing shadows in sunlight Task 4. 2 p. 34: Construct a sunspot from the contour of a rectangular window opening (the thickness of the walls is specified and taken into account during construction) The sun is in front of the viewer

Sequence of construction: 1. Construct a falling shadow from the inner contour of the opening: from vertical edges 1 and 2, shadows fall along the projection of the beam, from horizontal edges 2 -1 - in parallel. 2°

2. We build a falling shadow from the external opening (from vertical edges 4 and 3 - along the projection of the beam; from horizontal edges 4 -3 in parallel. We get overlays of shadow points 5 o and 6 o The shadow from edge 4 -3 (4 o-3 o) is superimposed on the shadow from edge 1 -1 at point 6 o. 2° ° °

3. Using a reverse beam, return point 5 o to the horizontal edge 2 -1 of the window sill. Return (.)6 o to the vertical edge 1 -1 ° ° 2° ° °

4. Edge 4 -3 rests on the right side wall at point 3 - the shadow closes. The shadow on the window sill from edge 4 -4 falls in the direction of the secondary projection of the beam. ° ° 2° Sunny “bunny” ° °

Creating shadows in sunlight Sunlight, penetrating through a rectangular window opening, forms a clear and contrasting quadrangle on the floor.

Constructing shadows with a point light source With a point light source, the ray lines are not parallel to each other and do not have vanishing points, they intersect at the “luminous” point of the light source Falling shadows are constructed using the secondary projection of the light beam

Problem 4. 4 p. 36: A vertical plane is given in the picture. It is required to construct a shadow from a plate with a point light source

If we take another light source - S*, then an overlay of falling shadows will occur. S* ° Во ° ° S 1* ° Ао

The final drop shadow is determined by general outline. The shadow at the place of the overlay will be darker S* ° Во ° ° S 1* ° Ао

Problem 4. 5 p. 36: The picture shows a vertical plate and a rod resting on its upper edge. It is required to construct a shadow from a plate and a rod with a point light source

Solution: 1. Let's construct a shadow from an inclined line: Let's draw a light ray through (.)S' and (.)A', and the secondary projection of the ray S' 1 and A' 1 and find their intersection. Ao‘

Since the straight line AC rests on the plane of the floor, the shadow at the point of support in it itself is C'= C 1'= Co' By connecting the points Co' and Ao' we get a shadow from the straight line to the floor

2. At point B, the rod rests on the plate - the shadow closes 3. Construct the shadow of the plate

Problem 4. 6 p. 37: The picture shows the perspective of a prism and a rod resting on its upper edge. It is required to construct a shadow from a prism and a rod with a point light source

2. Determine your own shadows on the prism. Constructing a falling shadow from a prism 2 1 21 11 1 o 2 o

3. To determine the shadow from the inclined straight line AB onto the upper plane of the prism, you can use: a) the reverse ray method: we return the point of overlap of the shadows from the straight AB to the shadow from edge 2 -3 (Mo) to edge 2 -3 3 m mo 1 11 2 21 1 o 2 o

Problem 4. 7 p. 37: the picture shows a triangular prism and a right circular cone. It is required to construct a shadow from them with a point light source

Solution: 1) To construct the shadow of a cone, find the shadow of its vertex (.)T‘ -To‘

2) Determine the falling shadow: draw tangents from (.)To‘ to the base of the cone, then determine our own shadow. 3) Using the ray section method, we determine the shadow from the top of the cone on the inclined plane of the roof

The second option for constructing a shadow from a cone onto a prism: using the inverse ray method (we return points 1 o and 2 o of the shadow overlay from edge B and the cone to edge B’) °° ° °

When constructing shadows in the interior perspective, you should first construct projections of the light source onto those enclosing planes of the interior on which you will need to construct shadows: floor, ceiling, walls

Task 4. 8. p. 38: Construct projections of a point light source onto the vertical planes of the walls and floor in a given frontal perspective of the interior

Solution: 1) We determine the projections of the light bulb S onto the walls, floor and ceiling (through the light source we draw perpendiculars from (.)S to these planes. Since the frontal perspective of the interior is a plane perpendicular to the side walls, floor and ceiling, parallel to the picture) .

Example: Light source L. Vertical straight line ВВ is perpendicular to the floor, therefore the shadow falls along the projection of the beam on the floor to the wall and vertically along the wall. °

L 1“ – projection of the light bulb onto the left side wall. With its help, we construct a shadow from the straight line “A.” °

L‘ - projection onto the end wall - since the side walls are perpendicular to the end wall, the shadow from horizontal straight openings falls along the projection of the ray onto the end wall drawn through L‘ Point of contact in the end plane ° ° Point of contact in the end plane

Task 4. 9 p. 38 b): Construct shadows from furniture with a point light source on the frontal perspective of the interior

From the vertical straight line 1 -11 the shadow falls along the projection of the ray, from the horizontal edge of the step - parallel and closes to the stop point. Point of stop

We determine the projections of the luminous point S on the plane of the steps (S 2, S 3, S 4). To do this, draw a plane parallel to the picture through the light source and determine the height of the steps at a given depth

We determine the lighting of the steps and build our own shadows. The vertical plane of the third stage is located in the same plane with point S (sliding beam). The vertical plane of the fourth stage is illuminated. Using (.) S 2 we build a falling shadow from the vertical edge 2 -21

From straight N-M on the rear end wall the shadow is parallel, then closes at the stop point M≡Mo. We construct a falling shadow from the cabinet using its secondary projection on the floor. Find the shadow from edge 1 -2 (1 o-2 o)

Edge 1 -3 is parallel to the wall, therefore its shadow falls parallel to the wall, i.e. we build using (.)P 4

Horizontal edge 2 -4 is also parallel to the plane of the wall. We build a shadow 2 o-4 o using point P. Next, the shadow closes at the point of contact of the straight line 4 -5 into the wall. Stop point

To construct a shadow from a vertical line A, we determine the projection of the light source onto the podium (Sp) using an arbitrary vertical plane (point F is taken arbitrarily)

The shadow from the straight line on the podium falls in the direction of the beam projection, on the vertical wall - parallel to the straight line

Task 4. 9 p. 39 c): Construct shadows from furniture with a point light source on the frontal perspective of the interior

Determine the shadows from points A and B (Ao 1 on the floor, Bo 2 on the wall)

We determine the break by constructing the shadow from (.)L and the closure of the shadow on the right wall C=Co Point of emphasis

We determine the falling shadows from the columns on the wall and on the ceiling (closed at the point S≡Sp); to construct a shadow on the balcony, we find the projection of the light bulb to the floor level of the balcony Sb ≡Sп ° Sb

To construct the falling shadow from the balcony onto the columns, draw an imaginary tangent plane to the columns and determine the lines of tangency on the columns. Imaginary plane tangent to the columns

Draw a shadow from a horizontal edge passing through (.)A on the imaginary plane using (.)P

At the intersection of this shadow from edge “A” with the tangents on the columns, we fix the points of the actually existing shadow (peak points)

We find the overlay of shadows from the columns and the balcony - points 1 o and 2 o and using the inverse ray method we return them to the contour of the columns’ own shadow - points 1 and 2 ° 2 1 ° ° 1 ° ° 2 o

Task 4. 10 p. 40: Construct projections of the light source onto two vertical planes of the walls, floor and ceiling in the angular perspective of the interior

Angular perspective of the interior. Method of combining the object plane with a picture Solution: Let's consider the first option - the room has a 90° angle in plan. C is the light source on the floor plan. Let us draw straight lines parallel to the walls of the room through (.)C and determine (.)1 and 2 picture traces of these straight lines 1 2

Constructing projections of a light source in a corner interior We construct perspective projections of a light source C using straight lines parallel to the sides of the plan: We construct the perspectives of these straight lines The intersection of perspectives of straight lines gives (.)Sp - projection (.)C on the floor we determine the nearest points 1 and 2 in the picture on ceiling

Constructing projections of a light source in a corner interior Constructing straight line perspectives The intersection of straight line perspectives gives (.)Sp - projection (.)C on the ceiling At an arbitrary distance we “hang” the light source C Sp ° ° C

Constructing projections of a light source in a corner interior To construct a projection (.)C onto wall P 2, you need to draw a perpendicular to it. Since the angle between the walls in plan = 90°, the perspective of a straight line perpendicular to the wall is constructed using (.) F 1 we determine (.) C 2

Constructing projections of a light source in a corner interior We similarly determine the projection of a light bulb on the right side wall C 3 (using (.) F 2.) ° C 3

Var. 2: Constructing projections of a light source if the angle between the walls on the floor plan is α≠ 90°. Perspective projection (.) C can be constructed using straight lines parallel to the walls of the room, i.e. using vanishing points F 1 and F 2 To determine projections draw the light source through (.)C straight lines m and n, perpendicular to the walls of the room

Construction of projections of a light source at an angle between the walls α≠ 90° on the floor plan Let us determine the vanishing points of straight lines m and n, for which, through the combined point of view with the picture (.)S', we draw straight lines parallel to m and n and find their intersection with the horizon line ( Fm and Fn respectively)

Construction of projections of a light source at an angle between the walls α≠ 90° on the floor plan. Using the vanishing point Fm, we find the projection C 2 of point C onto the side plane

Construction of projections of a light source at an angle between the walls α≠ 90° on the floor plan. Similarly, we determine the projection C 3 of point C on the right side plane using point Fn

Construction of projections of a light source at an angle between the walls α≠ 90° on the floor plan. planes were constructed passing through the light source (.)C and perpendicular to the side walls to determine the projections of the lamp onto the side walls

Task 4. 11 p. 41: Construct shadows from a point light source in a given angular perspective of the interior

Solution: 1. The internal partition in the closet is in its own Shadow. We build a falling shadow from it using a projection on the floor

We determine the shadows from points 1, 2, 3. From (.)1 hit the wall, from (.)2 and 3 to the shelves
Constructing shadows with diffused lighting With diffuse, diffused light penetrating through a window opening, light is emitted over the entire area of ​​the opening. The contours of the shadows seem to overlap one another, their boundaries becoming more and more “blurred” as they move away from the light opening. The planes of the slopes are illuminated, therefore the vertical and horizontal edges of the slopes of the opening, facing the inside of the room, are shadow-forming.

Construction of shadows in diffused lighting From the many “luminous” points in the opening, points located in the corners of the opening (1, 2, 4, 5) are distinguished. Using points 1, 2 and 3, cast shadows on the floor, and using points 4 and 5 - on the ceiling. To construct shadows, it is necessary to project these points onto those planes of the room on which shadows should be constructed: on the floor (points 1, 2), on the ceiling (points 4 and 5) and on the side wall (5"). Then draw from the “luminous” perspective points of ray lines through the shadow-forming points of the object until they intersect with the secondary projections of these rays

Constructing shadows with diffused lighting For example, let’s take “luminous” point 1, located in top corner opening. To construct a shadow from (.)A, it is necessary to draw a light ray through it and find its intersection with the projection of the ray on the floor. 1°° 11

Then we build shadows from AB and from BC ° 1 ° ° 11 Co ° Ao Vo

Let's take “luminous” point 2, located in the upper left corner of the opening. Let's construct shadows from points C and D and determine the shadow from straight line CD on the right wall. Let's complete the construction of the shadow from BC 2 ° Point of emphasis ° Co ° ° Ao Vo

Edge G of the inner part of the opening partially blocks the flow of light. Let's find the “luminous” point 3, located on the upper edge of the opening. To do this, we connect the projection of the vertical edge Ж (Ж 1) with the projection (.)А and extend it until it intersects with the projection of the outer side of the opening - (.)3¯ Ж ° С ° Ж 1 ° Ао Вo

Let's construct shadows from the vertical edge of the table leg E using the “luminous” point 3. We complete the construction of the shadow from the horizontal edge of the table passing through point E ° Point of emphasis in the lateral plane ° ° ° Ao Vo Co

Let's construct shadows from the horizontal edge of the LG opening using the “luminous” point 5 on the ceiling. g g ° Point of emphasis in the lateral plane of the wall ° ° С ° Ао Вo

Let's construct a shadow from the vertical edge GG 4 of the opening using the “luminous” point 4. On the ceiling the shadow falls along the projection of the beam, on the wall parallel to edge G). 44 ° G 4 f g ° Point of emphasis in the lateral plane of the wall 4 ° Co ° Ao Vo

Let's construct a shadow from the horizontal edge of the opening using the “luminous” point 1. The shadow falls on the floor parallel to the edge). f g ° ° ° Co ° ° ° Ao Bo ° °

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
with natural and artificial lighting

Example 1. Construct a falling shadow from a 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 B K, 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 intersection points 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. 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.

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 various 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 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 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* 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 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 in the picture as parallel, and their projections - 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. 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 - line 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