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Diminution – Objects Appear Smaller As Their Distance From The Observer Increases]TTL
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 see this is to extend your arm forward with your 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.
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.
Convergence – Lines 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.
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 help to give a drawing form and a sense of the third dimension.
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.
This principle is worth noting despite the fact that only a few artists apply it in 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 foreground-clear background effect might be used to emphasize the center of interest as well as the 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.)
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'AmelioCHAPTER 2
REALITY AND APPEARANCE
In Perspective Drawing You Draw What You See From A Specific Viewpoint, 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 mental image of the subject.
The true appearance of dishes on a table would 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 unrealistic eye in side view (right). Again the idea was drawn instead of the true appearance.
Wave 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.
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 come 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 looking up we notice that for the first time the vertical lines 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 facade rectangles again converge and foreshorten. But here 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.
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.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 rays 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.
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, THEREFORE, IS THE PICTURE PLANE. ON IT IS DRAWN WHAT WOULD BE SEEN IF IT WERE TRANSPARENT AND HELD PERPENDICULAR TO YOUR CENTRAL VISUAL RAY.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 Plane" Applied To Diminution
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.
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.
"Lines Of Sight Through Picture Plane" Applied To Diminution And Convergence
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?
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.
"Lines Of Sight Through Picture Plane" Applied To Foreshortening And Overlapping
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.)
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.
Excerpted from PERSPECTIVE DRAWING HANDBOOK by JOSEPH D'AMELIO, Sanford Hohauser. Copyright © 2004 Dover Publications, Inc.. Excerpted by permission of Dover Publications, Inc..
All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher.
Excerpts are provided by Dial-A-Book Inc. solely for the personal use of visitors to this web site.
|Overlapping ... Shades and Shadows||12|
|Color and Value Perspective ... Detail and Pattern Perspective ... Focus Effect||13|
|Professional Applications of Fundamentals||14|
|Chapter 2||Reality and Appearance||15|
|In Perspective Drawing You Draw What You See, Not Your Idea or Mental Image of the Subject||15|
|Reality and Appearance--Example: United Nations Buildings from Different Viewpoints||16|
|Reality and Appearance--Example: Park Bench from Different Viewpoints||17|
|Chapter 3||How We See for Perspective Drawing||18|
|Cone of Vision ... Central Visual Ray ... Picture Plane||18|
|Basis of Perspective--Lines of Sight Through a Picture Plane||19|
|Chapter 4||Why Appearance Differs from Reality--Theory||20|
|"Lines of Sight Through Picture Plane" Applied to Diminution||20|
|"Lines of Sight Through Picture Plane" Applied to Diminution and Convergence||21|
|"Lines of Sight Through Picture Plane" Applied to Foreshortening and Overlapping||22|
|Chapter 5||Principal Aids: Vanishing Points and Eye Level (Horizon Line)||23|
|Aid No. 1||Vanishing Points--All Lines which in Reality are Parallel will Converge toward a Single Vanishing Point||23|
|Vanishing Points (cont.)--When There are Many Sets of Parallel Lines going in Different Directions, Each will Converge toward its own Vanishing Point||24|
|Aid No. 2||Eye Level (Horizon Line)--All Horizontal Lines Converge to a Single Horizontal Vanishing Line||26|
|What Locates the Vanishing Line for All Horizontal Lines?||27|
|Why the Observer's Eye Level Dictates the Horizontal Vanishing Line--Theory||28|
|What Locates the Vanishing Point of a Particular Set of Parallel Lines?||29|
|Why the "Parallel Pointing" Method of Locating Vanishing Points is Important||30|
|Nature's Horizon Always Appears at Observer's Eye Level. Therefore, it Can be Used as the Vanishing Line for Horizontal Lines||31|
|Why Nature's Horizon Appears at Observer's Eye Level--Theory||32|
|What Happens to Eye Level (Horizon Line) When You Look Straight Out, Down or Up?||33|
|What Happens to Eye Level (Horizon Line) When You Look Straight Out, Down or Up (cont.)?||35|
|Reasons for Choosing a Particular Eye Level (Horizon Line)||36|
|Chapter 6||Drawing the Cube--Prerequisite to Understanding Perspective||37|
|Looking Straight Out at the Cube||38|
|Looking Down at the Cube||40|
|Looking Up at the Cube||42|
|Cube Studies Applied to Drawings of United Nations Buildings||44|
|Cube Studies Applied to Drawings of United Nations Buildings (cont.)||45|
|Many Cubes Oriented in the Same Direction Results in Only Two Sets of Converging Lines||46|
|Cubes Oriented in Many Directions Results in Many Sets of Converging Lines||47|
|Why a Thorough Knowledge of Simple Shapes is Important||48|
|Applications of the Basic Cube and Brick Shapes||49|
|Chapter 7||"One-Point" and "Two-Point" Perspective--When and Why?||50|
|Distorted and Correct One-Point Perspective||52|
|Chapter 8||More on Looking Up, Down, and Straight Ahead||53|
|Things Seen by Looking Straight Out and Things Seen by Looking Up||54|
|Things Seen by Looking Down||55|
|Review: Looking Up, Straight Out, Down||56|
|Looking Straight Out||57|
|Chapter 9||Perspective Distortion||58|
|Related to Vanishing Points and to Cone of Vision||58|
|Observer-Cone of Vision-Vanishing Points Relationship (Horizontal Distortion)||59|
|Vanishing Points Too Far Apart||60|
|Chapter 10||Determining Heights and Widths||61|
|Heights Related to Eye Level|
|1||Heights When Observer is Standing||62|
|2||Heights When Observer is in Elevated Position||63|
|3||Heights When Observer is Sitting ...|
|4||Heights When Observer is Lying Down||64|
|Heights Outdoors ... and Indoors||65|
|Determining Widths in Perspective--Width Lines||67|
|Chapter 11||Determining Depths||68|
|Finding Center Points by Diagonals||68|
|Equal Spacing by Diagonals||69|
|Subdividing a Surface by Diagonals ... Dividing a Surface into Equal Spaces by Using a Measuring Line and a Special Vanishing Point||70|
|Dividing a Surface into Unequal Spaces with a Measuring Line and Special Vanishing Point||71|
|Determining Depths and Widths of Room Interiors by the Measuring Line Method||72|
|Another Way of Getting Depths: The Sliding Ruler and Diagonals Method||73|
|Drawing Equal-Sized but Unequally-Spaced Elements--Vanishing Point of Diagonals Method||74|
|Diagonals as an Aid in Drawing Concentric and Symmetrical Patterns on Rectangles and Squares||75|
|Any Design or Pattern can be Reproduced in Perspective by Means of a Grid that Locates its Important Points||76|
|Chapter 12||Inclined Planes||77|
|Vertical Vanishing Line and Horizon Line are Based on Same Theory and Serve Similar Purposes||78|
|Uphill and Downhill (Inclined Planes)||79|
|Some Applications of Inclined Plane Perspective||80|
|Chapter 13||Circles, Cylinders and Cones||81|
|Circles and Ellipses||81|
|Drawing the Ellipse||82|
|The Center of a Circle Drawn in Perspective Does Not Lie on the Corresponding Ellipse's Major Axis||83|
|Chapter 14||Shade and Shadow||87|
|Parallel Light Rays (Sunlight) Parallel to Observer's Face||88|
|Parallel Light Rays (Sunlight) Oblique to Observer's Face||90|
|Parallel Light Rays Oblique to Observer's Face (cont.)||91|
|Shade and Shadow Created by Local Point Sources of Light||94|
Posted May 14, 2010
This text by Joseph D'Amelio serves as a great introduction into perspective for artists wanting to get their feet wet in a land of vanishing points. I particularly appreciated the unusual level of rigor and information in this text; most introductory books in this price point do little more than give formulaic recipes for constructing images without justification or formality. This book gives lots of inspiring, if relatively simplistic, images, but it also provides an appreciable amount of justification for the theory.
Buy it for the introduction, keep it for the valuable reference.
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