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Basic Perspective
By  Scott E. 'Sven' Johnson
Overview
On this page, I try to explain how perspective drawings
are constructed and how different types can be used to emphasize different
aspects of a composition. The illustrations are my own, usually drawn
over a hard copy of an AutoCAD model to ensure accuracy, or scanned from
the output directly. I stick to line drawings, to keep the examples
clearer.
What perspective is
Perspective refers to where we are looking at a scene from,
what we are looking at, and how much of the scene we are seeing.
It controls how lines converge and objects become smaller as they recede
into the distance.
In the Renaissance, methods for drawing linear perspectives
were developed, allowing artists to accurately depict scenes viewed from
a particular viewpoint. Until then, pictures sometimes had
larger characters and objects in the foreground and smaller ones in the
background, but the rules for it weren't really understood, and the drawings
weren't really accurate. We now understand these rules, and have
the option of using them to make more realistic drawings and paintings.
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Projection of a scene on to a picture plane
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When we draw, we are taking a real-world, virtual,
or imaginary 3D scene (as viewed from a particular point) and mapping it
onto a 2D plane: a canvas or sheet of paper. Each line or shape in
the scene corresponds to a line or shape in the perspective drawing.
It is as if we have a powerful movie projector in front of the scene, and
a giant movie screen (called a "picture plane") behind the scene, penetrating
even into the ground. It is as if beams of light come out of the
movie projector, shine through the scene, and cast shadows on the picture
plane (movie screen). Objects close to the projector have large shadows,
and objects close to the picture plane have shadows the size of the objects
themselves.
The image projected onto the screen in this manner is a perspective
image. It shows the scene as viewed from the position of the projector.
This viewing position is called the "eye point," "station point," "camera
point," or "look from point" (different books and rendering packages use
different terms).
Vanishing points
Lines which are parallel to each other in the 3D scene
will all converge toward a single point when the scene is drawn in perspective.
This point is called a "vanishing point." A different set of parallel
lines in the 3D scene, (parallel to each other, but running in a different
direction than the previous set of lines) will converge, or vanish,
toward some other vanishing point in the drawing. Parallel lines
which lie in the ground plane, or which lie parallel to the ground plane,
will always vanish toward some point on the horizon.
The exception is lines which lie parallel to the
picture plane in the 3D scene. When drawn in perspective, these lines
will not vanish. An example is the set of vertical edges in the scene
above, which remain vertical in the perspective image and don't converge.
If you look at a 3D scene, lines which are horizontal will appear to
vanish toward some point on the horizon. (Exactly where on the horizon
will depend on the lines' orientation to the viewer.) Imagine a set
of parallel horizontal lines that lie in a single vertical plane, like
the mortar joints of a brick wall, vanishing toward some point on the horizon.
Any diagonal lines on that same plane will vanish toward some point directly
above or directly below the vanishing point on the horizon. This
relationship is helpful for sizing objects in perspective.
Vanishing points and converging lines aren't just some sort of symbolic
convention used by artists. They are real-world phenomena: parallel
lines in the real world really do appear to converge when you look at them
obliquely. Find a brick wall sometime, stand next to it, and take
a good look at it. If you stare directly at it, the mortar joints
will appear parallel. But if you turn your head left or right, you
will see them as converging toward a point on the horizon.
Other characteristics of perspective drawings
If you look at an actual real-world scene, you will note other characteristics
of perspective, besides the way that parallel lines converge. Objects
get smaller as they recede into the distance. Things which are evenly
spaced (like telephone poles or railroad ties) appear to get closer together
the farther away they are. Shapes on the ground get foreshortened
so much that they become difficult to see; as they get farther away, they
become mere slivers lying on the ground. There are techniques for
projecting lines and so forth to create these effects convincingly in a
drawing, but just having an awareness of these things should allow you
to "fake" them fairly convincingly.
The horizon can be considered to be at the viewer's eye level.
If the viewer is standing on the ground with a group of people who are
doing likewise, the horizon will hit the other people at approximately
the level of their eyes -- a little below the eyes of taller people, and
a little above the eyes of shorter people. Objects which are lower
than the viewer's eyes will appear below the level of the horizon, and
the viewer will be able to see at least a little bit of their tops.
Objects which are entirely above eye level will appear above the horizon,
and the viewer will be able to see at least a little bit of their undersides.
But the farther away these objects are, the closer they will appear to
the horizon, and the more they will be seen from the side.
Shapes in a 3d scene will become distorted when seen or drawn in perspective,
except for shapes that are parallel to the picture plane. Shapes
that are parallel to the picture plane retain their shape, but are enlarged
or reduced in size, depending on their distance.
Other shapes will become distorted. Circles are seen as ellipses.
If such a circle is at the end of a cone or cylinder, the short axis of
the ellipses will align approximately with the axis of the cylinder.
However, the farther the circle is from the center of the drawing, and
the larger the cone of vision of the drawing (described below), the less
well the axes will be aligned. Fortunately, any tangent relationships
in the 3D scene will be retained in a correctly drawn perspective drawing.
This fact can help in trying to freehand circles and arcs in a perspective
drawing.
Seen in perspective, a sphere will appear elliptical, with the long
axis of the ellipse radiating away from the center of vision. The
movie projector analogy helps a bit in understanding this.
One-point, two-point, and three-point perspectives
Any given drawing might have any number of vanishing
points, for example, one for the front of a building, one for the side,
one for the hero's sword, one for the pikes in the phalanx opposing him,
one for the side of wagon he's defending, etc. There might be so
many lines vanishing in so many directions that none are dominant.
Or there might not be enough objects to be able to get a feeling for any
vanishing points. The drawing might be abstract, or a scene of a
planet viewed from space. In most realistic drawings, however, one,
two, or three of these vanishing points are probably going to be much more
noticeable than the others.
One-point perspectives
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Objects projected toward viewer
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Objects projecting to sides of viewer
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Perspective looking up
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When an image shows a view that appears to be looking directly
at a single main vanishing point, the scene is a one-point perspective.
This is the case when looking down a tunnel, looking down a gun barrel,
looking straight up at a skyscaper, or looking directly down at rooftops
of a city. It can be used to focus attention at the place where the
lines converge. It can also be used to try to draw the viewer in.
With a one-point perspective drawing elements seem to be aimed at the viewer,
or passing by on all sides.
Some artists avoid the one-point perspective, however.
They feel it gives the viewer the sensation of being led by the nose --
forced to look at something in a way that is not of the viewer's choosing.
Used inappropriately, the one-point perspective can be boring. For
example, you probably wouldn't want a one-point perspective looking directly
at a wall. Generally speaking, a wall is a rather static thing to be looking
at.
Of course, you have to use your own discretion.
You might feel that a particular one-point perspective is exciting, or
is the logical way to look at something. Or you might choose a one-point
perspective for a particular work precisely because it make the
viewer feel trapped, or because it feels static.
Two point perspectives
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Providing a "stage"
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Axial view plus vertical emphasis
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The two-point perspective is a much more common
type of drawing. The view can be of a scene outside, where buildings
or other elements vanish towards the horizon. Or it can be an interior
scene, where walls or other elements seem to wrap around the viewer.
Usually in a two-point perspective, the viewer is looking in a direction
approximately parallel to the ground, so vertical lines do not converge
with each other. The image above on the left is such a drawing.
Nothing is being thrown directly at the viewer, and the viewer is not looking
directly at a single wall or down a passage; instead the scene opens in
a couple directions. The most noticeable objects are seen obliquely,
rather than axially. This type of drawing tends to provide a sort
of stage for the characters of the drawing, where the viewer's attention
is not directed a forcefully toward a single point.
Note that with an interior two-point perspective,
you should be careful how the center of vision lines up with the room.
In most cases, you don't want to have the viewer staring directly into
a corner, or staring directly out of a corner. It can give the viewer
the sensation that he or she is being punished.
Usually, a two-point perspective has a left vanishing
point, and a right vanishing point. On rarer occasions, a two-point
perspective is of a different sort, where there is an upper vanishing point
and a lower one. You might do this if you wanted to give the viewer
the impression of walking down some sort of axis, but of looking somewhat
up or down, instead of parallel with the ground. Lines parallel with
the axis converge toward a point on the horizon, but vertical lines also
converge. Height is emphasized. The drawing above on the right
is an example of such a two-point perspective.
Three-point perspectives
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To emphasize height
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To emphasize equality of directions
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Three point perspectives are more complicated
to draw, and are rarer, since they typically involve the viewer looking
up or down at a scene instead of horizontally at it. You might use
a three-point perspective in a situation where you want a broad stage and
an emphasis of the vertical dimension (As was the intention in the image
above on the left). You might also use a three-point perspective
in a situation where you are trying to make every direction seem equivalent,
such as in outer space drawing above, where the drawing was supposed to
give the impression that there was no "up" direction.
Perspective angle/Cone of vision
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20-degree Cone of Vision
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100-degree Cone of Vision
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Cone of vision (or perspective angle) describes how
much of a scene shows up in an image, for any given eye point, direction
of vision, and picture plane. The wider the cone of vision, the more
of the periphery is seen, and the larger the drawing gets (or the smaller
everything gets on a drawing sheet of the same size).
If you're working on a certain size of paper, and
you want a wider cone of vision, but don't want your main character to
get smaller, you can move the eye point closer to the character.
Increasing the cone of vision while simultaneously approaching the target
slides the vanishing points closer together, and makes everything smaller
in relation to the target. This is shown in the images above.
Both of the images above are views of the same simple 3D model, produced
using AutoCAD Release 13. The view on the left uses a small cone
of vision, like that which is seen through a telephoto camera lens.
The view on the right is a view of the same model, but seen from a vantage
point closer to the group of figures, using a wider cone of vision, like
that seen through a wide-angle lens. You can use this to emphasize
a character or object in a drawing, drawing attention to it and giving
it monumental status. Note that the character will change a little
- you'll see more of the tops of his feet, more of the underside of his
hat, and so forth. But he will occupy approximately the same area
of the drawing.
You shouldn't overuse this option. It might
be appropriate in a scene where you are trying to call attention to a leader
in a mass battle scene. It is probably unnecessary in a scene showing
something more serene, like a romantic couple. Overusing an extremely
wide cone of vision is like putting an exclamation point after every sentence.
Another problem with extreme cones of vision is that
with greater angles, you get greater distortion, particularly at the corners
of the drawing. Eventually, this becomes confusing and disorienting.
Consider the view below, for instance, which was drawn using a cone of
vision of around 150 degrees -- .way too much The room depicted
is square, but it hard to tell even that much. In fact many people
see this image, and refuse to believe the room is square. But if
you examine it carefully, you'll see that the edges of the near right wall
and far left wall converge toward the same vanishing point, which can only
be the case if the edges are parallel to each other. So the shape
of the room is rectangular; it is just extremely distorted due to the extreme
cone of vision.
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150-degree Cone of Vision
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Most of the images in this article use wide cones of vision,
over 90 to 120 degrees or more. This is done to better illustrate the effects
of perspective. You will usually use a smaller cone of vision for
art work, in order to reduce distortion. It is often suggested that
you keep cones of vision below 90 degrees, and below 60 if you can manage
it. For a two-point perspective, this will mean that at least one
vanishing point lies off the edge of your paper.
Using a cone of vision of more than 90 degrees is not recommended;
using a cone of vision of 180 degrees or more isn't even possible using
the techniques described in this article (correctly termed "linear perspective").
You can't project anything from behind the eye point onto a planar drawing
surface. There are techniques for using wider cones of vision, but
to my understanding, they involve projecting the image onto a spherical
surface, then projecting this onto a 2D drawing. The result is similar
to a picture taken with a "fish eye" lens. An entirely different
set of drawing rules is required. Lines which are straight in the
3D scene appear curved in the resulting picture. A set of lines might
all emerge from a vanishing point on the left side of the image, spread
apart in the center of the drawing, and converge to a second vanishing
point on the right. This sort of perspective drawing is more complicated,
and isn't covered in this article. In fact, most of the books on
perspective that I have seen don't cover this sort of drawing.
Sizing objects in perspective
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Projecting lines to compute height
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Extending a grid
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Extending a fence
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It's kind of hard to size things properly in a perspective
drawing. After all, even things which are the same physical size
appear different sizes when seen in perspective. Fortunately, if
you know how large something would be at one place in the drawing, you
can project lines to determine how large it would be in another part of
the drawing. This is shown above on the left. If we can manage
to accurately draw the thief in the foreground, we can use him to determine
how large to draw the victim coming up the street. First we project
lines from the top of the thief's head and bottom of his feet out into
the street. Then we project the lines down the street to the point
where we want to draw the victim.
We can also project lines to help repeat a pattern
of tiles, bricks, paving stones, fence posts, pikemen, or other elements
repeat in a grid-like pattern. Start by choosing a line which is
parallel to the picture plane in the 3D scene. Go to where this line
appears in the perspective drawing, and mark off evenly-spaced tick marks,
as has been done with the vertical line in the middle picture, above.
Project lines from the tick marks to the vanishing point. Then draw
one brick, judging the size by eye. The diagonal of this brick will
also be the diagonal of numerous other bricks, allowing you to size
them. This should give you enough information to be able to size
many or perhaps all of the other bricks in the pattern, but if you need
more information for the bricks farther down the wall, you can project
more diagonals. All of the projected diagonals should meet at a point
directly above or below the vanishing point used for projecting the tick
marks.
If elements are arranged in a line, like fenceposts
or pikemen, we can position a third element based on the spacing between
the previous two. First, project lines from the top, midpoint, and
bottom of the elements to the vanishing point. Then draw a line from
the top of one element, though the midpoint of the next, and keep going.
The place where this line crosses the line of bases will be the place to
draw the next fencepost or pikeman.
Atmospheric perspective
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Approaching a port on a clear day
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Same port in fog
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Also known by less dramatic names, like "haze"
or "fog." Objects which are farther away tend to be a little hazier
(closer to light gray in hue and value) than closer ones, due to water
vapor, smoke, or other atmospheric ingredients. Atmospheric perspective
should reinforce visual indicators of distance, like converging lines,
diminishing size, level above/below the horizon, etc. In the pictures
above, the port should feel a little farther away in the right picture.
Both pictures were drawn from copies of the same original, and the tower,
island, hills, and buildings are pretty much the same size in both.
But the haze partially obscures these objects in the picture on the right,
making them seem a little farther away, and hopefully, making arrival at
the port seem a little less certain.
Atmospheric perspective varies in accordance with weather
conditions, location, and artist's will, of course. If you are painting
a panoramic view of a fabulous city, you might not want to use any atmospheric
perspective, so that the city can be seen in all its glory. If you
are depicting a scene in a foggy swamp or underwater, you will probably
want to use a lot of atmospheric perspective.
Atmospheric perspective plays a role as an indicator of
distance. Perhaps more important, however, are the other roles it
plays in a drawing. It helps draw attention to the foreground, since
objects in the foreground are clearer than objects in the background, and
contrast more with their surroundings. It can also set up a sort
of dreamy feeling, where mood is emphasized over detail, as is done so
well in Impressionist paintings.
Review of basic principles
In perspective drawings, certain relationships hold, and care
should be taken to ensure that they are being portrayed correctly.
These relationships include the following:
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In general, lines which are parallel in space will appear to converge
(vanish) toward a common vanishing point in the perspective drawing.
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When drawing a 3D scene that includes evenly-spaced elements receding
into the distance, the spacing will appear to get smaller as the objects
approach the horizon in the drawing.
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Shapes viewed straight-on retain their proper shape, they just get
scaled. This means that lines in space which are parallel to each
other as well as to the picture plane do not appear to converge.
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Lines which are straight in space will still appear straight in perspective
(assuming a cone of vision of less than 180 degrees). Colinear
points stay colinear. Points of tangency continue to be points of
tangency. These facts can be used to help size bricks, tiles, etc.
and draw curves,
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Given a plane which is vertical in a 3D scene, horizontal lines on
that plane will appear to converge toward some point on the horizon.
Any other set of parallel lines on that plane will appear to converge toward
a point directly above or below that point.
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| |  | Drawing in Perspective.
Booknews, Inc. , June 1, 1995. Translation of a German work (1993, Ravensburger Buchverlag Otto Maier GmbH) intended for graphic artists. After coverage of vanishing points, points of view, and perspectives, presents a systematic survey of one-, two-, and three-point perspective; shadows; reflections; and computer-aided drawing. Abundantly illustrated. No bibliography. Annotation copyright Book News, Inc. Portland, Or. |  |
FARP Article Guestbook
| Date | Name | Comment | | | 19 Apr 2008 |  Marillo | thanks it is very helpfull | |
| 28 Apr 2008 | Charles | nice! it refreshed what i know about perspective drawing. keep it up!!! | |
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