1《Perspective Drawing Handbook》英文原文(1)

作者: 季子乌 2013-03-08 11:10 | 分类:彼今城堡

今天许了个愿望,希望有人能翻译这本书。

我自己英文水平太太差了,半年零星翻译到一半了,却是好辛苦,翻一次头痛一次…… 还是把原文放出来,看有木有好心人热心人大好人感兴趣的人能把这个翻译出来~~

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以下是英文原文+图书pdf下载地址:http://p.pnq.cc/cg/PerspectiveDrawingHandbooks.pdf

文件中前后有几页小一些,是从别的文件里合并过来的,这样才是全书。。。

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以下是英文原文(我自己照书打的,可能有错字。。):

Perspective Drawing Handbook

Introduction

Chapter 1: Fundamentals

Diminution

Foreshortening

Convergence

Overlapping… Shades and Shadows

Color and Value Perspective… Detail and Pattern perspective… Focus Effect

Professional Applications of Fundamentals

 

Chapter 2: Reality and Appearance

In Perspective Drawing You Draw What You See, Not Your Idea or Mental Image of the Subject

Reality and Appearance-Example: United Nations Buildings frome Diffferent Viewpoints

Reality and Appearance-Example: Park Bench from Different Viewpoints

 

Chapter 3: How We See for Perspective Drawing

Cone of Vision… Central Visual Ray… Picture Plane

Basis of Perspective-Lines of Sight Through a Picture Plane

 

Chapter 4: Why Appearance Differs from Reality – Theory

“Lines of sight Through Picture Plan” Applied to Diminution

“Lines of sight Through Picture Plan” Applied to Diminution and Convergence

“Lines of sight Through Picture Plan” Applied to Foreshortening and Overlapping

 

Chapter 5: Principal Aids: Vanishing Points and Eye Level (Horizon Line)

Aid No. 1: Vanishing Points – All lines which in reality are
Parallel will converge toward a single vanishing point

Vanishing points (cont.) – When there are may sets of parallel lines going in different directions
Each will converge toward its own vanishing point

Professional examples

Aid No. 2: Eye level (Horizon line) – All horizontal lines
Converge to a single horizontal vanishing line

What locates the vanishing line for all horizontal line?

Why the observer’s eye level dictates the horizontal vanishing line – theory

What locates the vanishing point of a particular set of parallel lines?

Why the “Parallel pointing” method of locating vanishing points is important

Nature’s horizon always appears at observer’s eye level. Therefore, it can be
used as the vanishing line of horizontal lines

Why nature’s horizon appears at observer’s eye level – theory

What happens to eye level (Horizon level) when you look straight out, down or up?

Reasons for choosing a particular eye level (Horizon line)

 

Chapter 6: Drawing the cube – prerequisite to understanding perspective

Introduction

Looking straight out at the cube

Professional Examples

Looking down at the cube

Professional Examples

Looing up at the cube

Professional Examples

Cube studies applied to drawing of united nations buildings

Cube studies applied to drawing of united nations buildings (cont.)

Many cubes oriented in the same direction results in only two sets of converging lines

Cubes oriented in may directions results in many sets of converging lines

Why a thorough knowledge of simple shapes is important

Applications of the basic cube and brick shapes

 

Chapter 7: “One-point” and “Two-point” Perspective – When and why?

Introduction

Professional Examples

Distorted and correct One-point Perspective

 

Chapter 8: More on looking up, down, and straight ahead

Introduction

Things seen by looking straight out and things seen by looking up

Things seen by looking down

Review: Looking up, straight out, down

Looking straight out

 

Chapter 9: Perspective distortion

Related to vanishing points and to cone of vision

Observer-cone of Vision-vanishing points relationship

Vanishing points too far apart

 

Chapter 10: Determining heights and widths

Height lines

Height related to eye level-1: Heights when observer is standing

2: Heights when observer is elevated position

3: Heights when observer is sitting… 4: Heights when observer is lying down

Heights outdoors…and Indoors

Professional Examples

Determining widths in perspective-width lines

 

Chapter 11: Determining depths

Finding center points by diagonals

Equal spacing by diagonals

Subdividing a surface by diagonals… Dividing a surface into equal spaces
by using a measuring line and a special vanishing points

Dividing a surface into unequal spaces with a measuring line and special vanishing point

Determining depths and widths of room interiors by the measuring line method

Another way of getting depths: Te sliding ruler and diagonals method

Drawing equal-sized but unequally-spaced elements-vanishing point of diagonals method

Diagonals as and aid in drawing concentric and symmetrical
patterns on rectangles and squares

And design or pattern can be reproduced in perspective by
means of a grid that locates its important points

 

Chapter 12: Inclined planes

Introduction

Vertical vanishing line and horizon line are based on same theory and serve similar purposes
Uphill and downhill (Inclined planes)

Some applications of inclined plane perspective

 

Chapter 13: Circles, Cylinders and Cones

Circles and ellipses

Drawing the ellipse

The center of a circle drawn in perspective dose not line on
the corresponding ellipse’s major axis

Cylinders

Cones

Professional Applications

 

Chapter 14: Shade and Shadow

Introduction

Parallel light rays (Sunlight) parallel to observer’s face

Application sketches

Parallel light rays (Sunlight) oblique to observer’s face

Parallel light rays oblique to observer’s face (cont.)

Application sketches

Professional Examples

Shade and Shadow created by local point sources of light

Application sketches

Professional Examples

 

【P09】

Chapter 1: Fundamentals

Diminution – objects appear smaller as their distance from the observer increases

For instance, someone across the street appears smaller than the person next to you, someone down the street appears still smaller, and so on.

A good way to this to extend your arm forward with you hand held upright. Notice how someone close by (say 20 ft. away) stands about equal to your hand height, while someone 50 ft. away approximately equals the length of your thumb, someone 200 ft. away equals your thumbnail, and finally, someone 1000 ft. away (several blocks) equals possibly a hangnail on that thumb.

The cross-ties of railroad tracks, autos in a parking lot, heads in a theatre, and the cars of a railroad train are just a few other examples of things that we know are approximately equal in size yet which appear to diminish with distance.

This “truth” of seeing, when applied to a drawing, is a fundamental means of producing a sense of space and depth.

 

【P10】

Foreshortening — Lines or surfaces parallel to the observer’s face show their maximum size. As they are revolved away from the observer they appear increasingly shorter

  1. For instance, a pencil held parallel to observer’s face will show its true and maximum length.
  2. As it is slowly pivoted its length appears smaller…
  3. …and still smaller…
  4. …till finally the pencil points directly at observer, and only the end is seen. This could be called 100% foreshortening.
  5. This tube or oatmeal box seen end-on will appear as a full circle. None of the sides are visible.
  6. When it is pivoted slightly the circle “foreshortens” and appears as an ellipse. The sides (which were totally foreshortened) now begin to appear.
  7. The ellipse foreshortens even more (it becomes flatter) while the sides appear longer.
  8. Finally, the circular top foreshortens to a simple straight line and the sides appear at maximum length.

【P11】

Convergence — Line or edges of objects which in reality are parallel appear to come together(i.e., converge) as they recede from observer

 

When a brick wall is seen head-on(i.e., parallel to observer’s face) the top and bottom lines and all horizontal joints appear truly parallel and horizontal (level with the ground).

 

But if the observer shifts position and looks “down” the wall, then these lines cease to appear parallel and level with the ground and instead appear to come together (converge) as they recede.

 

Convergence equals diminution plus foreshortening: The pickets of a fence, when viewed head-on, appear equal in height and spacing. Also, the top and bottom lines are parallel and level.

 

But if the observer turns his head and looks “down” the fence, then the top and bottom lines appear to converge. Notice that this convergence relates directly to the diminution of the pickets as they recede. Furthermore, the true length of the fence no longer appears, but instead is foreshortened. (Note how the spacing and width of the pickets appear narrower in the distance.)

 

Therefore, convergence can be thought of as the diminution of closely-spaced elements of equal size. And it implies foreshortening since the surface is not viewed head-on.

 

【P12】

Overlapping, Shades and Shadows

Overlapping: This obvious and very simple technique not only shows which objects are in front and which are in back — it’s also a very important way of achieving a sense of depth and space in drawings. Notice the depth confusion when overlapping does not exist (right).

 

Shades and Shadows: Naturally the shape and structure of three-dimensional objects can be understood only when viewed in some form of light. But it’s really the shades and shadows created by this light that render the shapes “readable” and discernable. So working with light, shade and shadow will dramatically hep to give a drawing form and a sense of the third dimension.

 

【P13】

Color and Value Perspective

 

Values (black to white range) and colors are bright and clear when seen close up but become grayer, weaker, and generally more neutral as their distance from the observer increases.

 

Detail and Pattern perspective

 

Details, textures and patterns, such as blades of grass, the bark of trees, leaves, the distinguishing features of people, etc., are also clear and discernable when close but become “fuzzier” and less sharp when further away.

These principles are rarely discussed in perspective books yet they suggest useful techniques for increasing the sense of depth and space in a drawing.

 

Focus Effect

 

This principle is worth nothing despite the fact that only a few artists apply it in the their work.

The eye looking at a distant object will focus at that object’s range; things in the foreground, consequently, will be “out of focus” and therefore blurred.

 

For example, a distant steeple seen through a window might appear something like this. Such a blurred fore-ground-clear background effect might be used to emphasize the center of interest as well as sense of depth.

 

Conversely, when the eye focuses on foreground objects the background will appear blurred and unclear.

(This principle is rarely used because artists drawing a view such as this will focus back and forth in order to see and draw all parts clearly. Yet if emphasis or a “spot light” effect were desired this “truth” of seeing could well be applied.)

 

【P14】

Two professional examples, a painting and a landscape drawing, employing the fundamentals of Diminution, Foreshortening, Convergence, Overlapping, Shade and Shadow, Value Perspective, Pattern Perspective, etc., to achieve a sense of space and depth.

 

No passing, by Kay Sage. Collection of Whitney Museum of American Art, New York.

 

Project for Franklin D. Roosevelt Memorial Park. Joseph D’Amelio, Architect. Don Leon, Associate. Rendering by Joseph D’Amelio.

 

【P15】

Chapter 2: Reality and Appearance

In Perspective Drawing You Draw What You See, Not Your Idea or Mental Image of the Subject

 

We think of a table, generally, as being rectangular with parallel sides, and of dishes as round.

Children, beginners, and some sophisticated artists will draw them this way regardless of viewpoint (left) — children because they lack visual perception, artists because they wish to express the true essence and primary nature of the subject. Both, though, are doing the same thing — they are drawing their idea or metal image of the subject.

The true appearance of dishes on a table world be elliptical shapes on a converging, foreshortened surface (right).

 

The beginner, drawing a front view of the face, would tend to draw the idea of a nose (left) instead of its foreshortened appearance.

The same tendency created this un realistic eye in side view (right). Again the idea was drawn instead of the true appearance.

 

Ware your fist at someone across the room, 15 or 20 ft. away. A beginner, thinking only of the true sizes of hands and people, would probably tend to draw the scene this way (left).

But the careful observer would notice that the hand was almost one-third the height of the figure, and so draw it. Overlapping and value perspective help to dramatize the respective nearness and farness of these elements.

 

To a seated observer, a child close by and an adult further away might appear this way, and should be drawn this way. Your intellectual idea of the relative heights of children and adults might suggest differently.

A rifle pointed directly at your eyes might not appear very frightening at first, for you hardly see the lethal, yard-long weapon.

 

【P16】

Reality and appearance — Example: United Nations Buildings From Different Viewpoints

  1. We all know that the U.N. tower is a simple rectangular prism whose facades are all pure rectangles. When it is viewed directly from a distance, say from across the river, this pure geometry is revealed.
  2. But when it is seen from up the river or the avenue, its facades appear foreshortened and the roof and window lines seem to converge. Only the vertical lines maintain their true directions.
  3. If we now com closer, and look straight ahead, we see the bottom of the building, the entrance, and the foreground. From this viewpoint the horizontal window lines still converge.
  4. Upon looing up we notice that for the first time the vertical line appear to converge (upwards). Also, the roof and window lines now converge downwards to the left and right.
  5. Viewed from a helicopter, the roof and façade rectangles again converge and foreshorten. But hear vertical lines converge downwards, while horizontal lines point upwards.
  6. From directly above, only the rectangle of the tower’s roof is seen. This barely expresses the building’s form. Adjacent buildings with converging facades are more comprehendible.

【P17】

Reality And Appearance — Example: Park Bench From Different Viewpoints

  1. In reality, this bench is composed of simple rectangular prisms. A boy climbing a tree would have this rare view of its true geometry.
  2. His parents at ground level might have this view. The horizontal and vertical lines appear to converge and all surfaces are foreshortened. (The vertical lines give a sense of verticality but they are not actually parallel to the edge of the page.) Note that this viewpoint is more revealing than the first.
  3. Junior, who is only 3 ft. tall, would see it still differently. The verticals now appear truly vertical, while the horizontal lines still converge.
  4. If Junior walked around the bench and looked at the end head-on, the true geometry of the end rectangle would appear. The bench top, though, would strongly converge and foreshorten. Notice that the horizontal as well as the vertical lines of the end maintain their real directions.
  5. This “worm’s eye” view, which one might get by falling on the ground and looking up, offers a unique picture of the bench. The subject is rarely drawn from this (or the first) viewpoint since it is rarely seen this way.

【P18】

Chapter 3: How We See for Perspective Drawing

Cone of Vision… Central Visual Ray… Picture Plane

 

A Perspective drawing will look correct only if the artist’s viewpoint and his direction of viewing the subject are relatively fixed. This means drawing with a limited “field of vision.” This field is usually called the Cone Of Vision because of the infinite number of sight lines which radiate in a cone-like pattern from the eye. (In reality these lines are light ray coming from the subject to the eye.) The angle of this cone is between 45 and 60 degrees. If a greater angle is used in a drawing, it implies a moving cone of vision – and the picture will be distorted. You can test your cone of vision by looking straight ahead and swinging your outstretched arms in and out of sight.

 

When we look about, essentially what we do is focus upon a succession of spots or “centers of interest,” each of which is fixed by a sight line at the exact center of the cone of vision. This line is sometimes called the “center line of sight” or the “central direction of seeing.” We shall call it the Central Visual Ray. When you look through a telescope or hold a pencil so that it appears as a point the telescope or the pencil is exactly on your central visual ray.

 

To understand perspective drawing a Picture Plane must be imagined between the observer and subject. This Plane Has A Constant Right Angle Relationship With The Central Visual Ray. So when drawing a subject, whether it is above, below or straight ahead, imagine viewing it through an omnipresent picture plane which is perpendicular to your central visual ray surrounded by a cone of vision.

 

【P19】

Basis of Perspective – Lines of Sight Through a Picture Plane

 

The concept of the picture plane may be better understood by looking through a window or other transparent plane from a fixed viewpoint. Your lines of sight, the multitude of straight lines leading from your eye to the subject, will all intersect this plane. Therefore, if you were to reach out with a grease pencil and draw the image of the subject on this plane you would be “tracing out” the infinite number of points of intersection of sight rays and plane. The result would be that you would have “transferred” a real three-dimensional object to a two-dimensional plane.

 

You can refine this experiment by looking through a window that has vertical and horizontal pane divisions, or through any transparent sheet that has been marked off in a similar grid pattern with crayon or by scoring.

Here the vertical and horizontal lines of each small rectangle clarify the direction of oblique or converging lines beyond. Working with such a “reference grid” one can easily transfer the scene to a sketch pad. This is surely not a recommended drawing technique but it does dramatically show the basic theory of perspective. In fact, the word perspective comes from the Latin word “perspecta” which means “to look through.”

Your Canvas, Sketch Pad, Or Drawing Board, There-fore, Is The Picture Plane. On It Is Drawn What Would Be Seen If It Were Transparent And Held Perpendicular To Your Central Visual Ray.

 

【P20】

Chapter 4: Why Appearance Differs from Reality – Theory

 

By applying the notion of “lines of sight through a picture plane” to simple views of pencils of equal length, we can more precisely define the visual basis of Diminution, Convergence, Foreshortening, And Overlapping, and explain diagrammatically why the appearance of an object so frequently differs from its reality.

 

“Lines of sight Through Picture Plan” Applied to Diminution

 

Picture Plane Viewed From Side

Side View Of Condition

 

DIMINUTION – Objects Of Equal Size Appear Smaller As Their Distance From The Observer Increases. These pencils are both standing perfectly upright (but not directly in line with one another – if they were, the rear pencil would be overlapped and concealed). Pencil B appears smaller than pencil A. This is so because of the manner in which the lines of sight leading from eye to objects intersect (or “project” onto) the picture plane.

 

PICTURE PLANE VIEWED FROM SIDE

SIDE VIEW OF CONDITION

PICTURE PLANE AS SEEN BY OBSERVER

 

DIMINUTION – In this case, the pencils are lying in tandem on a table top, pointing away from the observer. Again the pencil furthest away appears and is drawn shorter. Why this is so is again explained by the way in which the lines of sight leading to each pencil intersect the picture plane.

 

【P21】

“Lines of sight Through Picture Plan” Applied to Diminution and Convergence

 

TOP VIEW OF CONDITION

PICTURE PLANE AS SEEN BY OBSERVER

 

DIMINUTION: In this case, both pencils are again lying down, but parallel to the observer’s face (i.e., parallel to the picture plane). The foreground pencil would appear, and so is drawn, longer than the rear pencil. This is again explained by the lines of sight and their points of intersection with the picture plane. Study these lines. Suppose many more pencils were laid out in a similar manner. Would this not be identical with, and explain, the familiar phenomenon of the diminishing railroad cross-ties?

 

TOP VIEW OF CONDITION

PICTURE PLANE AS SEEN BY OBSERVER

 

Convergence: Parallel Lines Appear to Approach each other as they Recede. In this example, the pencils are lying parallel to one another, pointing away from the observer. They would appear to converge and are so drawn. Why this is so is again explained by the lines of sight. Those leading to the far ends of the pencils (the pointed ends) intersect the picture plane relatively close together. Those to the near ends (the eraser ends) intersect the plane further apart.

Another way of visualizing convergence is to think of it (as explained on page 3) as a result of diminution. So compare this drawing with the one above. Pencils in both diagrams are laid out to “define” perfect and equal squares. Therefore the dark dotted lines in the lower drawing could be the pencils of the diagram above and as such would be subjected to diminution as described above. In fact an infinite number of other parallel and equal lines (e.g., the lightly dotted lines) will all diminish progressively, and their ends will trace out (or follow) the converging lines of the pencils.

 

【P22】

“Lines of sight Through Picture Plan” Applied to Foreshortening and Overlapping

 

SIDE VIEW OF CONDITION

 

Foreshortening: Lines and Surfaces always Appear Longest when Parallel to the Observer’s Face (i.e., to the Picture Plane). As they Revolve away from this Position they Appear Increasingly Shorter. Why this is so can be understood by noting how the lines of sight intersect the picture plane for each position of the pencil. (Note: when the pencil appears as a small circle, i.e., when just the eraser or the pointed end is in view, then it is 100% foreshortened and aligned with the central visual ray.)

 

SIDE VIEW OF CONDITION

 

OVERLAPPING: This obvious technique must be emphasized because may beginners tend to avoid it.

It is based on the fact that lines of sight intercepted by an opaque object simply stop, so that objects beyond are partially or totally concealed (literally “blocked off”). The result is a strong sense of foreground and background planes, forwardness and beyondness, in other words, DEPTH.

 

【P23】

Chapter 5: Principal Aids: Vanishing Points and Eye Level (Horizon Line)

 

In views of real life, and therefore in realistic pictures, the eye level (horizon line) is rarely visible, and vanishing points virtually never are. Yet the full significance of these concepts must be clearly understood. Working with an awareness of them and actually sketching them in temporarily are perspective drawing prerequisites.

 

Aid No. 1: Vanishing Points

Any two or more lines that are in reality parallel will, if extended indefinitely, appear to come together or meet at a point. This point is called the Vanishing Point of these lines.

 

The classic and still best example of this phenomenon is the tracks of a railroad. The rails, in reality parallel, appear to converge and ultimately meet at a point in the distant horizon.

Many historical paintings of church interiors look something like this. If all the column capitals on each side, and then all the column bases were “connected,” and these lines “brought back” into the picture, they would meet at the same point as other similarly-oriented parallel lines such as the center aisle or the procession.

(The only exception to this occurs when the parallel lines are also parallel to the observer’s face and to the picture plane. In this case, they neither recede nor converge and there fore do not have a vanishing point. For example, the edges of this brick wall and all its vertical and horizontal joints are exactly parallel to the observer’s face and to the picture plane. Therefore, the verticals still appear vertical and the horizontals still appear horizontal and parallel to one another.)

 

The general truth of seeing and drawing (except for the special case above) is: All Lines which in Reality are Parallel will Converge Toward a Single Vanishing Point.

 

【P24】

Vanishing points (cont.) – When there are may sets of parallel lines going in different directions
Each will converge toward its own vanishing point

 

Take a photograph of a house (or of any other object with several sets of parallel lines) and with straight-edge and pencil extend the converging lines until they meet. Notice how the siding, window sills, etc., will converge in one direction, the door, louvers, etc., in another, and the sloped roof, shingles, etc., in still another. Each set of parallel lines, in other words, has its own vanishing point.

 

This slightly disorderly chest of draws has more sets of parallel lines than the house above and hence the drawing has more vanishing points. Notice that some exist far to the left or right of the picture and some (the tipped drawer) far above or below.

 

Therefore: Regardless of Direction, Each set of parallel Lines will Converge toward its own Vanishing Point. Check this for yourself in the professional examples across page.

 

Putnam County Playhouse. D’Amelio & Hohauser, Architects. Rendering by Sandford Hohauser

 

Beach House. D’Amelio & Hohauser, Architects. Rendering by Sandford Hohauser

 

【P26】

Aid No. 2: Eye level (Horizon line) – All horizontal lines at eye level

Take a suitable photo or drawing and extend all converging lines that are in reality horizontal (i.e., parallel to the ground). Then connect the resulting vanishing points and notice how they all line up on a single horizontal line. This is the vanishing line for all converging horizontals.

Because our man-made environment consists primarily of shapes whose edges and markings approximate vertical and horizontal lines, this horizontal vanishing line plays a key role in perspective drawing.

What determines this line? … How is it used? … How does it affect drawings?…

All sets of horizontal parallel lines converge to points along the horizontal vanishing line.

Illustration courtesy of the Westinghouse Air Brake Company.

 

【P27】

What locates the vanishing line for all horizontal lines?

 

We’ve seen that this important line is straight and horizontal, but what determines its location? Very simply: It is aways on the same level as the Observer’s eyes. In other words, the observer’s “eye level” – an imaginary plane at the level of the eyes and parallel to the ground – dictates the location (i.e., the height from the ground) of the vanishing line for all horizontals in a given drawing.

 

A side view of the drawing above will show the eye level and the ground plane from their edges and therefore depict them as parallel horizontal lines. Here, the picture plane is also seen from its edge.

 

If we now look at the picture plane “front face” (as the observer views it) we again see the eye level plane in edge-on view – as a line. Here, though, the line also represents its projection onto the picture plane.

Whether the observer jumped or kneeled, and so raised or lowered his eye level, this relationship would remain unchanged.

Therefore: The eye level not only dictates but is synonymous with the vanishing line for horizontal lines.

 

【P28】

Why the observer’s eye level dictates the horizontal vanishing line – theory

 

In the drawing above and below note carefully the lines of sight. Those pointing to the foreground (1, 2) make relatively steep angles with the ground, while those pointing further away (3, 4, etc.) make increasingly smaller angles and become more and more horizontal. If the tracks went on endlessly then the sight lines viewing them at infinity (~) must be virtually horizontal.

 

Looking at this situation from above, we note that the lines of sight embracing the width of the foreground ties depart from the observer at a wide angle, and that this angle gets progressively smaller for sight lines to ties progressively further away. We can therefore conclude that at infinity this angle is so infinitesimal that a single sight line can be used. In that case we would “see” a 7-ft. –wide cross-tie by means of a single sight line; total diminution would have occurred and only a point would appear on the picture plane. This point, of course, is the vanishing point of the tracks.

Now look at the side view again and note that this same single sight line pointing to infinity (~) is horizontal (i.e., parallel to the ground). Therefore the uanishing point of the tracks must be at the observer’s eye level.

In fact, all horizontal lines, if extended indefinitely like the railroad tracks, would appear to converge to a point at the observer’s eye level.

So it is Accurate as well as Useful to Think of the Eye Level as the Vanishing Line for all Horizontal Lines and Planes.

 

【P29】

What locates the vanishing point of a particular set of parallel lines?

 

This is what our observer sees. His eye level is the vanishing line for horizontal lines. (Actually, it is a plane seen edge-on.)

But what located the specific vanishing point? Across page we saw that the horizontal sight line aimed at infinity parallel to the tracks points to it. So, very simply: the uanishing point of the tracks is the point at which the sight line parallel to them intersects the picture plane. (The vanishing point essentially is this horizontal sight line seen from its end.) All lines parallel to the tracks will naturally also converge toward this same point.

In Other words the Observer Simply “Pointed” with his Eyes parallel to the given set of Lines in Order to Locate their Vanishing Point.

 

The following will show that this holds true regardless of the direction of the set of lines.

Here the tracks are at an angle to the picture plane.

The side view across page again applies, so we know that the infinite point of convergence (vanishing point) must be at eye level.

 

Now, looking at this new top view, we see that sight lines embracing the width of the foreground ties depart, as before, at a wide angle. For ties further away this angle gets progressively smaller and also aims more and more to the right. When the ties are finally viewed at infinity only a single sight line remains and it is virtually parallel to the tracks. Therefore, the sight line parallel to the tracks “points” to the tracks’ vanishing point.

This little experiment would word for Any set of parallel lines that appear to converge, regardless of whether they were horizontal, vertical or oblique, or whether the observer were looking up at them, straight out or down. Therefore the universal rule is: The uanishing point for any set of parallel lines is the point at which the sight line parallel to the set intersects the picture plane.

In Other words the Observer Simply Points in the Same Direction as the lines in Order to Find Their Vanishing Point.

 

【P30】

Why the “Parallel pointing” method of locating vanishing points is important

In T-square and triangle perspective, this method of locating vanishing points is an essential step.

Thus, to draw the object below, we first construct a top view or plan (left), showing the object, the picture plane (seen as a line) and the observer’s position. On this plan, “sight lines” pointing parallel to the object lines are drawn to locate the vanishing points on the picture plane. Other sight lines “project” the object itself onto the picture plane. The picture plane line, therefore, shows the relationship of the object’s apparent size to the vanishing points.

This “measurement line” is then transferred to the actual picture (right), where it is superimposed on the horizontal vanishing line (eye level). Whether the subject is now drawn above, below, or straddling this line, the relationships remain the same.

 

In freehand drawing, whether from life or from imagination, this procedure naturally is inapplicable. The convergence of lines, foreshortening, etc., must instead be determined by careful observation or visualization.

Yet in this book the figure of an observer pointing toward a picture plane parallel to object lines will be shown repeatedly, in order to emphasize the importance of the observer-to-subject relationship even for freehand drawing.

The observer’s viewpoint and cone of vision, his distance from a subject, and the apparent direction of the subject’s lines are the principal determinants of how things appear in real life and therefore in perspective drawing. As these factors change, so will the picture. This is the key to and “system” of perspective drawing. Becoming aware of it and understanding it will strengthen your powers of visualization and observation.

 

【P31】

Nature’s horizon always appears at observer’s eye level. Therefore, it can be
used as the vanishing line of horizontal lines

In other words, if the observer is on a mountain top or descending in a parachute the horizon line will appear on a level with his eyes.

 

And when the observer is on flat ground the horizon line will still appear at his eye level. (In this case, though, notice that the amount of ground before him seems less than the amount seen from the higher level.)

 

And if the observer lies on the ground the horizon line will still appear at eye level. (But notice that here that amount of ground area leading to the horizon line seems even less than in the above two views.)

 

In fact, nature’s horizon line, whether visible or concealed (by these mountains, for instance, or by a house, trees or people), will always be at the observer’s eye level. The eye level, we have seen, is the vanishing line for all horizontal lines. Therefore, this line, which is both eye level and nature’s horizon, is of great importance, for on it are located the vanishing points of all sets of horizontal lines.

 

【P32】

Why nature’s horizon appears at observer’s eye level – theory

Nature’s Horizon Line: (i.e., where the sky appears to meet the ocean, prairie, or desert) is technically slightly different from observer’s eye level. The eye level plane is truly horizontal (i.e., constantly perpendicular to the line of the observer’s body ) while the earth actually curves away from the observer in all directions. The diagram shows this, but with tremendous exaggeration.

 

If this “cut” through the earth were drawn correctly with the eye level close to the ground and the earth’s curvature drawn to scale, the diagram below would result. The earth’s curvature is so infinitesimal for most observable distances that it can be disregarded. The earth’s surface and observer’s eye level would therefore be virtually parallel.

 

Thus, the diagrams on pages 28 and 29, showing a flat ground plane parallel to observer’s eye level, are realistic and the conclusions drawn from them are valid. In fact, artists have for ages, and in every field of fine and applied art, used the concepts “eye level” and “nature’s horizon line” interchangeably. In practical terms, this means that as the observer’s eye level is raised or lowered, nature’s horizon line always accompanies it and appears at the same horizontal level. It also means that a painting or drawing which show any part of nature’s horizon immediately indicates the artist’s eye level and his relationship to the subject.

In the illustration below, therefore, the observer’s eyes were exactly level with the picture’s “center of interest.” Note that both the horizon line and the line of the dune point to it.

Painted by William A. Smith for Redbook Magazine

 

【P33】

What happens to eye level (Horizon level) when you look straight out, down or up?

Looking Straight Out. Here, the central visual ray points horizontally (parallel to the ground). It therefore lies exactly on the eye level plane. Because the come of vision is symmetrical around this central ray, the observer sees as much above eye level as below. In the picture, consequently, the eye level (horizon line) is midway between top and bottom.

 

Looking Down. Here, the central visual ray points not at the distant horizon but down at the tracks. The cone of vision, therefore, just barely includes the eye level plane. (Note the proximity of top sight lines and eye level.) In the picture, therefore, the eye level (horizon line) is close to the top.

 

Looking Up. Here, the central visual ray points at something in the sky or at the top of a telegraph pole. The cone of vision barely “sees” the eye level plane with its lowest sight lines. In the picture therefore, the eye level (horizon line) is close to the bottom.

 

【P34】

An example of “looking up.” The horizon line (eye level) is low in picture.

Drawing by Joseph Bertelli for the Long Island City Savings Bank

 

An example of “looking straight out.” The horizon line (eye level) is approximately midway between top and bottom of picture.

Classic Landscape, by Charles Sheeler. Courtesy of Mrs. Edsel B. Ford and Museum of Modern Art, N.Y.

 

【P35】

What Happens To Eye Level (Horizon Line) When You Look Straight Out, Down Or Up (Cont.)

In extreme cases the eye level (horizon line) is completely above or below the drawing. The sketches below indicate, respectively, that you are looking downwards and upwards at still steeper angles than before.

 

So while it may be obvious that when you look up you see more sky or ceiling, and when you look down you see more ground or floor, what is not quite so obvious is that the eye level-horizon line (always on a horizontal plane through the observer’s eyes) shifts up and down inversely.

Therefore, if, when you start a drawing, you place the eye level (horizon line) high on the canvas or sheet, you must be looking down on the subject; if you place it midway, you must be looking out horizontally (the central visual ray is approximately on the eye level plane); and if you place it along the bottom you must be looking up at the subject. This holds true whether drawing or painting from life or from imagination. Try it and see.

 

So bear in mind: any drawing which shows or suggests its eye level-horizon line invariably indicates the artist’s direction of sight and whether the subject was viewed from above or below, or head-on.

 

Below: An example of “looking down.” The horizon line (eye level) is above the picture. National Cowboy Hall of Fame and Memorial Museum, Oklahoma City. (Second award, National Competition for Architectural Commission.) Joseph D’Amelio, Architect and Renderer

 

【P36】

Reasons for choosing a particular eye level (Horizon line)

 

Some factors in making this choice are: Horizontal planes will show their undersides when above eye level, and their tops when below… At eye level they foreshorten altogether and appear as simple lines… Also, all converging horizontal lines or planes will tend downwards when above eye level and upwards when below… At eye level they appear perfectly horizontal (so when you look at a drawing that does not show nature’s horizon line, you can find eye level by noting the receding horizontal line or plane that still appears horizontal – e.g., the top of the bookcase).

 

Object depicted below eye level in order to see top.

Object depicted above eye level in order to see underside.

 

Another reason for choosing a particular eye level is the nature of the subject being depicted. Some things are typically seen from above (e.g., furniture) others are typically seen from below (e.g., airplanes). Drawing a subject from its most common viewpoint helps to express its function.

 

Because so much of what we see in life is seen by looking straight out you’ll find that in the vast majority of drawings the eye level (horizon line) is within the picture.

 

【P37】

Chapter 6: Drawing the cube – prerequisite to understanding perspective

 

Drawing the simple cube (or any rectangular prism such as a brick, a book or the U.N. Secretariat) from many viewpoints is an important exercise which reveals and explores basic perspective principles. The following pages dramatize many of these. But these studies can only point to the problems involved and help to stimulate your powers of observation. To draw properly you must supplement them with intensive sketching and observation of your own. Get into this habit.

 

The six sides of a cube (or any rectangular prism) are “edged” by three sets of parallel lines. When the cube rests on a horizontal surface, such as a table top, one set of lines is vertical (i.e., perpendicular to the ground), the other two sets are horizontal (i.e., level with the ground) and at right angles to each other.

 

On the Following Pages:

-Verticals will be indicated by pipes

-One set of horizontals will be indicated by chains

-The other set of horizontals will be indicated by wires

 

Now a Quick Review: We see things, as shown on pages 18 and 19, by means of a central visual ray surrounded by a cone of vision. The central visual ray focuses upon the center of interest, while the cone of vision defines the roughly circular area within which we can see things clearly. Perpendicular to the central visual ray is the picture plane, which may be thought of as a piece of glass or the drawing paper or canvas itself. The observer’s face will also be considered perpendicular to the central visual ray, hence always parallel to the picture plane. Keep this schema in mind.

Also recall the following points:

Lines and planes parallel to the observer’s face (and consequently to the picture plane) undergo no distortion, but maintain their true directions and shapes.

Lines and planes which are not parallel to the observer’s face (picture plane) appear to converge and foreshorten. (Such lines are sometimes described as “receding.”)

The vanishing point for any set of receding parallel lines is the point at which the observer’s sight line parallel to the set intersects the picture plane. To locate this point, the observer merely “points” in the same direction as the lines.

The Diagrams on the next Several Pages are Based on these Fundamental Principles.

(In the following examples you can either think of the observer as walking around the cube, or of the cube as revolving. The results are identical.)

 

【P38】

Looking straight out at the cube

The pipes are parallel to face (and picture plane), so in all views they appear as true verticals. The vanishing points for horizontals must be at eye level (which is also in this case the plane of the central visual ray). The top views below show the method of locating these points.

 

The chains and wires converge and foreshorten. Their vanishing points are equidistant from the cone of vision in top view. Therefore they are equidistant from cube in picture. Note equal angles.

 

Again both sets of horizontal lines converge and foreshorten. But since observer’s right arm points further away, the right vanishing point is more distant. (See example across page.)

 

In this case, only the wires are oblique to the picture plane (actually, they are perpendicular to it ) and therefore they alone converge. The central visual ray itself points to their vanishing point. (See example across page.)

 

Note: The vanishing points are closest to each other when the two front vertical surfaces of the cube make equal angles with observer, i.e., when observer looks exactly at a corner (top of page). They spread apart as one surface draws parallel to observer’s face and the other foreshortens (center of page). Finally (bottom diagram), they are an infinite distance apart.

 

【P39】

Apartment House, New York City. D’Amelio & Hohauser,  Architects. Rendering by Joseph D’Amelio

 

Medical Clinic Entrance. D’amelio & Hohauser, Architects. Rendering by Joseph D’Amelio.

 

【P40】

Looking down at the cube

The pipes are no longer parallel to observer’s face (and picture plane) so they also converge and foreshorten. Their vanishing point on picture plane is located by pointing downwards in their direction.

 

The vanishing points for horizontals must be on the eye level-horizon line (pointed to by other arm). The manner in which a pointing observer locates them on this line is again shown in the different top views.

 

Neither chains nor wires are parallel to picture plane, so both converge and foreshorten. Their vanishing points are equidistant from picture because both pointing arms are equidistant from cone of vision.

 

Again, chains and wires are oblique to picture plane, so both converge and foreshorten. The chains’ vanishing point is further away because the pointing right arm is further from the cone of vision.

 

Chains are now parallel to picture plane so they appear parallel and horizontal. (If observer pointed in their direction (dotted lines) he would never intersect the picture plane.) Wires are not parallel to the picture plane. A sight line parallel to the wires (located directly above the central visual ray) points to their vanishing point on eye level.

 

【P41】

Two examples of “looking down.” Note the downward convergence of vertical lines.

 

18th-century drawing by Johann Schubler. Courtesy of The Cooper Union Museum, New York City

 

Midnight Ride of Paul Revere, by Grant Wood. The Metropolitan Museum of Art. Courtesy of Associated American Artists

 

【P42】

Looing up at the cube

The pipes, not being parallel to face and picture plane, will converge and foreshorten. Their vanishing point on picture plane is located by pointing upwards in their direction. The vanishing points for horizontal lines must be on eye level-horizon line. The top views below again show how they are located along this line.

 

Chains are parallel to picture plane so they remain parallel and horizontal. (Try pointing toward their vanishing point.) Wires are not parallel to picture plane; a horizontal sight line parallel to the wires (located directly below the central visual ray) points to their vanishing point on eye level.

 

Neither chains nor wires are parallel to the picture so both converge and foreshorten. The chains’ vanishing point is further away because the pointing right arm is further from cone of vision.

 

Again neither chains nor wires are parallel to picture so both converge and foreshorten. Their vanishing points are equidistant from picture because observer’s arms are equidistant from cone of vision. Note equal angles which result when “looking at corner.”

 

【P43】

Two examples of “looking up.” Note the upward convergence of vertical lines.

 

Windows, by Charles Sheeler. Courtesy of the Downtown Gallery, N.Y.

 

(Below) Painted by Austin Briggs for McCalls magazine.

 

 

【P44】

Cube studies applied to drawing of united nations buildings

Now let’s look again at the U.N. buildings. Each view results in a different type of convergence and foreshortening. Each should be referred back to the cube drawing of similar viewpoint.

 

Observer is across the river at ground level, looking straight ahead. (See page 38, bottom.)

 

Observer is now in Manhattan, still looking straight ahead and still at a distance. (See page 38, center.)

 

Observer is much closer but still looking straight ahead. (See page 38, center.)

 

【P45】

Cube studies applied to drawing of united nations buildings (cont.)

 

Observer is at same position but is now looking up. (See page 42, center.)

 

Observer is now in helicopter looking down. (See page 40, center.)

 

Observer is still in helicopter but now looking straight down at Secretariat Building. (Compare with page 38, bottom.)

 

【P46】

Many cubes oriented in the same direction results in only two sets of converging lines

 

Here, many parallel cubes, above and below eye level, are viewed simultaneously (within one cone of vision). Therefore the chains (all horizontal and parallel) will converge toward one vanishing point, and the wires (horizontal and parallel, but going in a different direction) will converge toward a different vanishing point. The pipes, being parallel to the observer’s face, will remain parallel.

Note that wires and chains above eye level converge downwards, while those below eye level converge upwards. (If any were exactly on eye level they would naturally appear horizontal.)

These simple principles are evident in the perspective rendering shown below.

 

Project for Hill City Inc. D’amelio & Hohauser, Architects. Rendering by Joseph D’Amelio

 

【P47】

Cubes oriented in may directions results in many sets of converging lines

 

A group of cubes (or bricks, deminoes, etc.) facing various directions has many different sets of horizontal parallel lines. Each set, if extended, would appear to converge to its own vanishing point on the horizon line (eye level). Below are applications of this principle.

 

General Rule: When there are Many Sets of Parallel Horizontal Lines, Each Set will Converge Toward its own Vanishing Point on the Horizon Line (Eye Level).

 

【P48】

Why a thorough knowledge of simple shapes is important

Once a Basic Shape such as a Cube or a Rectangular Prism is Drawn Correctly it can become the Guide from for a Wide Variety of Objects.

The Size of the Object does not Matter. For Instance, a Prism of this Proportion (below) Drawn at this Angle could become a Book, an Office Building, or even a Billboard.

 

Or, The Exact Same Shape could be “Laid down” to become a “Package” for Horizontal Objects of Similar Proportions, e.g., A Bed, A Cigar Box , A Gun, A Book, A Swimming Pool, Etc. (Note: Lines #2 which previously converged to the left now converge downwards. Lines #1 which previously converged downwards now converge to right.)

 

【P49】

The Basic Cube Can Become The Basis For An Endless Variety Of Objects

 

And So Can The Basic Brick Shape – Look Around And See

 

【P50】

Chapter 7: “One-point” and “Two-point” Perspective – When and why?

 

The ties of the railroad and the black lines of the structure at the right are parallel to the picture plane; therefore they do note converge. The rails and the fancy lines of the structure are perpendicular to the picture plane; therefore they do converge, and since the observer’s central ray points exactly in their direction, their vanishing point must be in the center of the picture. This is one-point perspective. Now look at the suitcase. Both sets of its horizontal lines are oblique to the picture plane; therefore they converge to left and right. The observer (top view) points in their direction to locate their vanishing points. This is two-point perspective.

 

When the observer his attention to the structure, the railroad ties and black lines become oblique to the picture plane, as do the rails and the fancy lines of the structure, in another direction. In the top view, the observer’s right hand points to the vanishing point of the first set of lines, while his left hand points to the vanishing point of the second. Now consider the suitcase: one horizontal set of lines has become perpendicular to the picture plane. Therefore the central visual ray points to its vanishing point, which must be in the center of the picture. The other set of suitcase lines is parallel to the picture plane; so the lines remain parallel in the drawing. The one- and two-point perspectives have been transposed.

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