A simple way to construct falling shadows in perspective. Constructing shadows under artificial lighting
It is known that a falling shadow follows the shape of the object that casts it. But everyone who has tried to draw has probably observed how the shape of the shadow is distorted and does not absolutely accurately follow the contours of the object. So what are the rules by which a falling shadow is constructed and what patterns can be identified here?
Constructing falling shadows
First, let's look at this using the example of a simple geometric body - a cube. The figures below show a diagram of the construction of a falling shadow:
- The light source is determined.
- A perpendicular is drawn from the light source to the plane on which the object stands.
- From the point on the plane where this perpendicular rests we draw rays towards the object.
- Imaginary rays are drawn from the light source and pass through the edges of the object.
- We mark with dots the intersection of the rays on the plane and the rays from the light source.
- We connect these points with a line and get the outline of the falling shadow.
To summarize the above and put it more simply, you need to: firstly, draw lines from the light source in space; secondly, draw lines on the plane from the perpendicular. The intersection of these rays will be the contour of the falling shadow.
In a cube drawing, this construction of shadows is relatively simple. But what if our subject is complex? For example, a vase, a tree, a car? Or even “worse” - a human figure? From my experience I will say that falling shadows from such complex shapes I always draw approximately. And, probably, most artists do the same. However, this approximate drawing is still based on the above principle. In the mind, in the artist’s imagination, the same approximate projection is made, and on its basis the outline of the shadow is drawn. But to do this, you need to know the key principle that I outlined above. In the next picture you can see how I approximately lined up the falling shadow from the vase. Everything is done very roughly, but the principle is respected.
(Approximate shadow projection)
How does the shape of a shadow depend on the position of the light source?
In the following pictures I want to show how the position of the light source affects the shape of the shadow and its direction:
If the lamp (or the sun) is located directly above the object from above, then the falling shadow will either be very short or disappear completely. The more the light source is shifted to the side relative to the subject, the longer the shadow will be. The lamp can be located directly in front of the object or, conversely, behind it. In this case, the falling shadow will either move backward from the viewer or approach it forward. All these “stretching” or “compressing” of the shadows will affect its shape. In the above figure, I drew the shadows of the ball. But if you project a falling shadow from human figure, then its contour will be distorted in a similar way - sometimes stretched, sometimes shortened. It doesn't matter what object we draw a shadow from. The principle will be the same.
How the saturation of the shadow and the clarity of its contour changes
There is a pattern that the artist must understand well - the further the shadow is cast from the object, the lighter it is. The closer the shadow comes to the object from which it falls, the darker it is. This change in saturation can be stronger or weaker depending on the brightness of the light, the size of the shadow, and the distance of the light source. But in any case, the shadow will not be “dull”. It should “breathe” or be “transparent”, which is achieved by changing the saturation. If we are talking about academic drawing, then solid shadows should be avoided dark spots. If we are talking about black and white graphics, then, of course, the shadows can be completely black, but this is a conventional image, not a realistic one.
In addition, novice artists should also pay attention to the clarity of the shadow outline. The more focused the light (electric lamp, sunlight on a cloudless day...), the clearer the outline of the falling shadows will be. And, conversely, the more diffused the light (light in cloudy weather when it is cloudy), the more blurred the shadow outline will become.
Conclusion
Correctly projecting the shadow, determining how its saturation and clarity of the contour changes - these are the main tasks that the artist needs to keep in mind when he draws shadows. Beginners, at first, will have to gradually implement all this in their drawing. But, each time these tasks will become easier and easier. And with the accumulation of experience, the drawing will be obtained on an intuitive level.
Lecture 24 Constructing shadows in the interior Position of the light source Constructing shadows geometric bodies Inverse beam method Ray section method
The construction of shadows in the interior is quite difficult task. This is explained, firstly, by the presence of various lighting sources - solar, diffused and artificial light and, secondly, under conditions of illumination with artificial light sources, a large number of them, a variety of shapes and locations in modern interior make the task of accurately constructing shadow contours 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 о 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 secondary projection 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 the overall contour. 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 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 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.
Constructing 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 the upper corner of the 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 ° С ° ° Ао Вo
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 “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 ° °
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 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 distant 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 an 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 to 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.
Segment bases 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.
When constructing shadows in perspective drawings, the sun is taken as the light source, which can occupy different positions in relation to the picture:
1. the sun is located behind the object and the shadow falls towards the observer (Fig. 104);
Rice. 104. The sun is behind the object
2. the sun is located behind the viewer, the shadow falls towards the horizon line from the base of the object (Fig. 105);
Rice. 105. The sun is behind the viewer
3. the sun is located on the side so that the rays run parallel to the picture (Fig. 106).
Rice. 106. The sun is on the side of the object
The last case is most often used by engineers when constructing perspective images of buildings and structures, so we will dwell on it in more detail.
Let's consider constructing a point in perspective. We will assume that the object is illuminated from the left (or right), the rays go parallel to the picture, making an angle of 45° with the object plane. Let us write these conditions symbolically:
1. S ∥k;
2. S^ T= 45°.
Let's draw through the point A(Fig. 107) the perspective of the ray, and through its secondary projection (point a) – secondary projection of the beam. Since the ray is parallel to the painting, its secondary projection is parallel to the base of the painting t – t. The point of intersection of the ray's perspective with its secondary projection will determine the actual shadow of the point A on the ground - a point A T .
Rice. 107. Shadow of a point in perspective
Let's construct the own and falling shadows of the parallelepiped standing on the ground (Fig. 108).
Note that the conclusions that were formulated earlier for constructing shadows in orthogonal projections are also valid for central ones.
Rice. 108. Constructing shadows of a parallelepiped
Let's analyze the illumination of the faces of the parallelepiped. For a given direction of the ray flow, the top, left visible and invisible edges of the object in the drawing will be illuminated. The remaining edges will appear in their own shadow. Let's determine the contour of the body's own shadow. It will include the ribs [ 12 ] – [23 ] – [34 ] – [45 ] – [56 ] – [61 ], forming a closed chain in the form of a spatial broken line. From the identified contour we construct a falling shadow. Since point 1 lies on the ground 1 = 1 T. Let's draw through the point 2 perspective of the ray, and through its secondary projection (point 1 ) – its secondary projection. At the intersection of these lines we find a point 2 T. Since the edge [ 23 ] parallel to the object plane, its cast shadow is equal and parallel to it. Edge vanishing point [ 23 ] is on the horizon line (point F 1 ). Connecting the dot 2 T with this point (i.e. draw a line through it parallel to this edge). On the same line is the shadow of the point 3 . Let's draw through the point 3 perspective of the ray until it intersects with the constructed line - determine the point 3 T . In this case, a secondary projection of the ray should not be constructed, since the desired point has already been established by the intersection of two lines. Rib [ 34 ] also parallel to the plane T, its shadow is parallel to the edge.
The vanishing point of these lines is the focus F 1 . Drawing the perspective of a ray through a point 4 to the intersection with the segment [ 3 T F 1 ], define the point 4 T. Points 5 and 6 are located on the object plane T, That's why 5 = 5 T And 6 = 6 T. The contour of the falling shadow of a parallelepiped consists of a set of segments [ 1 T 2 T ] – [2 T 3 T ] – [3 T 4 T ] – [4 T 5 T ] – [5 T 6 T ] – [3 T 4 T], representing a closed loop.
Let's consider the tasks associated with constructing perspective and shadows of building fragments
Task 1
Construct shadows from straight barriers on the stairs, ground and wall (Fig. 109).
Rice. 109. Staircase with straight barriers
First, let's construct the shadows of the right barrier (Fig. 110). Since for a given direction of the light flux the right side of the barrier is in its own shadow, it is easy to see that the edges located on the border of light and shadow will be part of the contour of its own shadow. Let's define the falling shadow of a vertical edge. Dot A belongs T, That's why it may be noted that A = A T. Let's draw through the point IN the perspective of the ray, and through its secondary projection - the point A secondary beam projection perspective. At the intersection of the constructed lines we define a shadow IN T . Another rib [ B.C.] parallel to the object plane, therefore, its shadow is parallel to the edge and has the same vanishing point F 2 . The real part of this shadow on the ground is the segment [ IN T 1 T]. Since the point 1 T located on the border between the land and the wall 1 T = 1 T " . Using the back ray, you can determine a point on the edge [ B.C.], which cast this shadow. Dot WITH horizontal edge is on the wall, so WITH = WITH T " . Shadow of the segment [ 1 C] falls on the wall. Its shadow is the segment [ 1 T " WITH T " ].
Rice. 110. Constructing the contour of the falling shadow of the right barrier
The contour of one's own shadow is always closed. Reasoning based on its definition was given in many problems. An outline element can coincide with its shadow (if, for example, it is on the ground, a wall, or adjacent to another object). This factor should be taken into account when constructing a falling shadow.
At the left barrier, the right side is in its own shadow, therefore, the edges [ LN] And [ L.M.] are part of the defined contour (Fig. 111). Let's construct the falling shadows of these edges.
Rice. 111. Constructing the contour of the falling shadow of the left barrier
Radial plane (frontal plane of the level) passing through the edge [ LN] crosses the ground and the bottom step in parallel straight lines, leaving shadow marks on them, and the riser in a vertical straight line. Top point L This edge casts a shadow on the first step and is determined by the intersection of the ray with its secondary projection. Rib [ L.M.] parallel to the plane of the bottom step, so its shadow is parallel to the edge. Connects the dot L T with a vanishing point F 2 and mark the real part of the shadow of this edge on the bottom step to the point 2 T = 2 T " . Note that this edge is with a nail in relation to all risers. Let's carry out auxiliary lines to find common points for the edge [ L.M.] and the edges of all risers. These constructions will allow you to determine the falling shadows on the risers. In Fig. 111 on edge [ L.M.] all its sections are marked, casting shadows on specific fragments of the stairs, the ground and the wall.
Rice. 112. Own and falling shadows from direct barriers
In Fig. 112. The final version of the solution to the problem is presented.
Shadows of the ribs [ L.M.] And [ B.C.] on the wall and risers are parallel and represent an example ascending straight lines. Their vanishing point is located above the horizon line, and the vanishing point of their secondary projections lies on the horizon line.
Task 2
Construct a perspective of the roof eaves and determine its own and falling shadows (Fig. 113).
Rice. 113. Condition of task 2
Let us indicate the position of the picture plane on the orthogonal drawing of the problem conditions and select the point of view in accordance with the recommendations given earlier.
To solve the problem, we will use the architects’ method and use some other techniques for constructing perspective. Let's determine the starting points of the direct dominant directions and mark them on a perspective drawing based on the picture. Let us determine the vanishing points of these lines.
By connecting the starting points with the corresponding vanishing points, we obtain the perspective of a flat figure (roof eaves plan). Let's walk through the point of view and points 2 And 4 rays, which, together with their secondary projections, define horizontally projecting planes that intersect the picture along vertical lines (Fig. 114).
Rice. 114. Application of two methods of constructing perspective
In accordance with these considerations, the perspective drawing
let's draw through the points 2 1 And 4 1 vertical lines along which the constructed planes will intersect with the picture. An edge that falls into the picture plane will be depicted on it in natural size, taken from the orthogonal drawing. Drawing straight lines through the top and bottom points of this edge to the vanishing points F 1 And F 2 , let's complete the construction of the two visible lateral edges of the cornice (Fig. 115).
Rice. 115. Construction of the side faces of the cornice
using the method of conic sections
Let's draw two straight lines through the lower points of the vertical side ribs of the cornice to the vanishing points F 1 And F 2 , and select the outline of the lower edge (Fig. 116).
Rice. 116. Drawing straight lines perpendicular to the picture
To construct the perspective of the walls, straight lines are used, perpendicular to the picture, passing through the points 5 , 6 And 8 .
Rice. 117. Formation visible walls in the future
After finding the secondary projections of these points on the perspective drawing, we draw through them vertical lines(Fig. 116).
Let's move one of the vertical edges into the picture plane in any direction. Let's put it on it from the base of the picture from the point 5 0 the actual size of the rib, taken from the orthogonal drawing (Fig. 117).
Let us draw a straight line through the top point of this edge to the vanishing point F 2 . Let's outline the right wall. Then we will construct parallel lines with a vanishing point F 1 and outline the left wall.
Rice. 118. The final stage of building perspective
In Fig. 118. the final result of constructing the perspective of the structure is shown.
Let's move on to building shadows. Let's determine the illumination of the object's edges for a given direction of the light flux and highlight its own shadows. Let's construct a falling shadow of the roof eaves on the walls. Let's find the shadow of a point A on the left visible wall. Let's draw through the point A the perspective of the beam, and through A secondary projection to the intersection with the left wall. Note that the ray and the edge are intersecting lines. The intersection of the drawn ray with the wall will occur at the point A T " . Since the lower front edge of the left edge of the cornice is parallel to the left wall, its shadow will go along the wall to the right of the point A T " parallel to this edge. Therefore, through A T " and vanishing point F 1 we carry out a direct line.
At the point A three ribs of the cornice converge. His lower left rib is with a nail in relation to the left wall. Let's define the shadow of this edge. In Fig. 119 shows two options for finding a shadow.
In the first case (Fig. 119, A) on this edge we construct a point using the inverse ray IN which will cast a shadow IN T " on the left vertical edge. The shadow of the nail is the segment [ A T " IN T " ].
In the second case (Fig. 119, b) found a common point for the left wall nail. To do this, the upper horizontal edge of the left wall is extended until it intersects with with a nail and the point is marked WITH T " . Since the segment [ WITH T " A T " ] lies in the plane of the wall and intersects its left vertical edge, a point can be marked on it IN T " and highlight the real part of the shadow of the nail.
Both methods give the same result.
Rice. 119. Options for finding the falling shadow of the cornice
on the wall of a building:
A– using a point B T " ;
b– using a point WITH T " (“base” of a nail on the wall)
In Fig. 120 shows the perspective of this structure when choosing a different point of view, in which the shadow of the point A falls onto a wall invisible in the picture. In relation to this wall the edge [ AB] is with a nail and partially casts a shadow on it in the form of a segment [ WITH T " A T " ]. On the left wall there is a shadow of the lower edge of the visible left edge of the cornice.
The construction of the shadows of the cornice on the fragments of the structure was carried out in various options, because it causes difficulties for students when performing work.
Rice. 120. Constructing the shadow of the cornice with a changed point of view
Let's construct the falling shadow of the cornice on the ground separately from the lower part of the structure (Fig. 121), having previously determined its own shadow contour.
Rice. 121. Falling shadow of the cornice
Then we will find the contour of our own shadow and determine the contour of the falling shadow of the building without taking into account the cornice (Fig. 122).
Let's outline the general contour of the falling shadow of the structure and highlight it with color (Fig. 123).
Rice. 122. Contours of falling shadows of two objects
Rice. 123. Own and falling shadows of an object
The color of the falling shadow depends on the object on which it appears (on grass, asphalt, etc.) and has a thicker shade compared to its own shadow, as shown in the figure above.
Task 3
Based on the given views of the building, create a view on the left and construct own and falling shadows (Fig. 124).
Rice. 124. Condition for problem 3
Let us show on the building plan the position of the picture plane, the point of view, the vanishing points of parallel straight lines of two directions and draw auxiliary straight lines to construct a perspective (Fig. 125).
Rice. 125. Choosing a picture and point of view on the building plan
Rice. 126. Perspective of the visible walls of the building
Let's plot the starting points of the lines based on the picture. Let's construct a perspective of the visible walls of the building (Fig. 126).
Let's create a niche in the facade wall. Fragments of a niche with construction lines are shown in Fig. 127.
Rice. 127. Prospects for niche fragments
On an edge lying in the picture plane, we will draw division points to construct windows and connect them to the vanishing point F 1 . To build vertical lines, we use straight lines perpendicular to the picture, with a vanishing point P(Fig. 128).
Rice. 128. Formation of windows in perspective
Parallel straight lines with the vanishing point are drawn through the division points on the lower edge of the niche F 2 . On the rear edge of the niche, vertical straight lines are built and window compartments are outlined (Fig. 129).
Rice. 129. Fragment of window depiction
Using the lines drawn on the plan, we begin building the steps (Fig. 130).
Rice. 130. Start building steps
Using the actual dimensions of the vertical segments on the picture plane, we outline the profile of the steps and the right part of the canopy (Fig. 131).
Rice. 131. Construction of the profile of the steps and part of the canopy
We build the left part of the stairs and the canopy (Fig. 132).
Rice. 132. Construction of the left fragment of the building
In Fig. 133. shows an enlarged fragment of part of the visor, on which the edge located in its own shadow is visible,
Rice. 133. Left side of the visor
In the above drawings, the images showed their own shadows for a full perception of the drawing. No explanations were given regarding their constructions, since a sufficient number of problems on this topic were previously considered.
Rice. 134. Constructing a falling shadow of a canopy on the wall of a building
The falling shadows of the visor (Fig. 134) should be built from those edges that are on the border of light and shadow. This boundary (the contour of its own shadow) is clearly visible in Fig. 135.
Rice. 135. Fragment of a visor with its own and falling shadows
The elements of this contour are the lower front edge of the visor, parallel to the wall, and the lower left edge, perpendicular to the wall. Dot A is common to these edges. To find the shadow, we draw a ray through it and build its secondary projection. The intersection of the beam with the wall will occur at the point A T " . Draw a straight line through this point to the vanishing point F 1 . Using the back ray we determine the point IN on an edge perpendicular to the wall, which will cast a shadow on the left edge of the wall. Segment [ A T " IN T " ] – falling shadow nail on the wall.
In Fig. 136 it is clear that the edges of the staircase profile, parallel to the ground, and their shadows have a common vanishing point F 2 , edge [ 45 ] casts a partial shadow on the wall, starting from a point 6 , found using the back beam.
Rice. 136. Falling shadows from steps on the ground and wall
To find the shadow of the visor in a niche, you can proceed as follows. First, construct a complete outline of the falling shadow on the wall without taking into account the niche (Fig. 137). Define the shadow of a point A on the plane of the wall (point A 1T " ). Connect the constructed point with IN T " and draw the real part of the shadow of the nail on the wall. By moving the point A 1T " deep into the niche until it coincides with its back edge, we will find the shadow of a point on it A(point A 1T " ).
It was possible to carry out the construction in reverse order. First determine the shadow of the point A in the niche of the window (point A T " ). Then find the shadows of the vertical and horizontal edges in it.
In Fig. 138 a shadow is visible on the window sill and on the window glass from the front vertical edge of the side edge of the niche.
Rice. 137. Falling shadow of the canopy on the wall and in the niche
Rice. 138. Fragment of constructing the falling shadow of the visor
On the right side of Fig. 138 it can be seen that the secondary projection of the ray passing through the point A, intersects the secondary projection of the rear edge of the niche. A vertical line is drawn through the intersection point, on which the point is marked A T " .
Rice. 139. Constructing a falling shadow of a building on the ground
When determining the falling shadow of a building (Fig. 139), the edges included in the contour of its own shadow are used. This is a vertical edge located in the picture plane, the top right visible edge with a vanishing point F 2 and the top invisible edge with the vanishing point F 1 . The shadows of these edges on the ground are parallel to the edges themselves and have the same vanishing points.
Rice. 140. Perspective of a building with its own and falling shadows
The completed image (Fig. 140) shows that the falling shadows acquire the color of the surface on which they are cast, but the tone of the color becomes thicker.
