Download Perspective and Art - Ambedkar University Delhi

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What is Perspective?
"Perspective is the rein and rudder of painting"
Leonardo da Vinci
What do the pictures below tell you?
We have observed certain things from these pictures.
Even though paintings and pictures are two-dimensional, some
of them convey a sense of depth like photographs whereas
others do not.
The key to conveying depth is perspective.
What would be a working definition of Perspective?
What are key features in paintings with perspective?
If we want to draw some simple figures in perspective what
rules should we follow?
Is proportion important? If so what are simples rules of
proportion in drawing?
Working definition of Perspective
Perspective in the graphic arts, such as drawing, is an
approximate representation, on a flat surface (such as
paper), of an image as it is perceived by the eye.
The two most characteristic features of perspective
are:
1) Objects are drawn smaller as their distance from the
observer increases.
2) The distortion of items when viewed at an angle.
In the figure above ABCD is a square. A’B’C’D’ is its image
in the plane. Note that not only is the image smaller in size
but it is also distorted because the picture plane is not
parallel to the plane of the square.
History of Perspective in
western Art
Excerpts from `Mathematics and Art’
by
J J Conor and E F Robertson
Before beginning the discussion of perspective in western art, we should mention the
contribution by al-Haytham. It was al-Haytham around 1000 A.D. who gave the first correct
explanation of vision, showing that light is reflected from an object into the eye. He studied the
complete science of vision, called perspectiva in medieval times, and although he did not
apply his ideas to painting, the Renaissance artists later made important use of al-Haytham's
optics.
First let us state the problem: how does one represent the three-dimensional world on a twodimensional canvass? There are two aspects to the problem, namely how does one use
mathematics to make realistic paintings and secondly what is the impact of the ideas for the
study of geometry.
By the 13th Century Giotto was painting scenes in which he was able to create the impression
of depth by using certain rules which he followed.
He inclined lines above eye-level downwards as they moved away from the observer, lines
below eye-level were inclined upwards as they moved away from the observer, and
similarly lines to the left or right would be inclined towards the centre.
Although not a precise mathematical formulation, Giotto clearly worked hard on how to
represent depth in space and examining his pictures chronologically shows how his ideas
developed.
Some of his last works suggest that he may have come close to the correct understanding of
linear perspective near the end of his life.
The person who is credited with the first correct formulation of linear perspective is
Brunelleschi. He appears to have made the discovery in about 1413.
He understood that there should be a single vanishing point to which all parallel lines in a
plane, other than the plane of the canvas, converge.
Also important was his understanding of scale, and he correctly computed the relation
between the actual length of an object and its length in the picture depending on its distance
behind the plane of the canvas.
Using these mathematical principles, he drew two demonstration pictures of Florence on
wooden panels with correct perspective. These perspective paintings by Brunelleschi have
since been lost but a "Trinity" fresco by Masaccio from this same period still exists which uses
Brunelleschi's mathematical principles.
Some rules for perspective drawing
Rule 1 The image of a line segment is a line segment (unless viewer sees the line
end on in which case the image is a point).
Rule 2 A line segment PQ that lies in a plane parallel to the picture plane (plane of
projection) has as image a line segment P’Q’ that is parallel to PQ (in the plane
EQP).
Plane of projection (picture plane)
Original Plane
Y
Eye
Q
Q’
E
P’
X
P
Z
Rule 3 If line segments PQ and RS are parallel and lie on a plane parallel
to the plane of projection then their images P’Q’ and R’S’ are parallel.
Plane of projection
Original Plane
Y
Eye
Q
S
Q’ S’
E
P’
R’
R
P
X
Z
Rule 4 and Rule 5
Image of a line L in space not parallel to the picture plane or plane of
projection will appear to vanish at a point V on the plane of projection. V is
called the vanishing point and EV is parallel to L.
Any line L’ parallel to L will also have the same vanishing point V.
Y
image of L’
image of L
E
V = V’
Z
L’
L
X
Rule 6 If a line L is perpendicular to the picture plane its vanishing point
is the origin. (Note that such an L is parallel to Z axis and so has same
vanishing point as Z axis namely origin by Rule 5.)
Rule 7 A shape (PQR) lying in a plane parallel to the picture plane has a
perspective picture (P’Q’R’) that is an undistorted miniature of the original.
Y
R
R’
Q’
E
P’
P
X
Q
Z
Rule 8 The perspective image (T’) of the centre (T) of a rectangle (PQRS)
is the intersection of the images of its diagonals.
Y
R
R’
S’
s
T’
T
Q
Q’
E
P’
P
X
Z
Images (L’ and M’) of parallel lines (L and M), not parallel
to picture plane, meet in the picture plane at the
vanishing point (V).
Y
V
E
Z
M’
M
L’
L
X
Images (L’ and M’) of parallel lines (L and M),
perpendicular to the picture plane, meet in the picture
plane at the vanishing point (V) which is the origin.
Y
E
V
M’
X
L’
Z
M
L
EXAMPLES OF PERSPECTIVE DRAWING
The simplest form of perspective is one point perspective. Imagine driving
along a straight road, the fences and power-poles all diminishing towards a
single spot far ahead of you. That's single-point perspective. Single- or onepoint perspective is a simplest method of making objects look threedimensional. Lines that we know are parallel in real life seem to converge to
a single point (vanishing point) on the picture plane. We can see this in the
picture of the Taj Mahal at Agra and AUD.
‘The School of Athens’ by Raphael (1518), is a fine
example of architectural perspective with a central
vanishing point.
Brunelleschi made a ground plan for the Church of Santo Spirito on the basis of
which he produced a perspective drawing to show his clients on how it would look
after it was built. We can compare this drawing on the left with a modern photo of
the actual church.
Last Supper with Central
Vanishing Point
Two-point perspective is slightly more complex, as both the front and back
edges, and side edges, of an object must be diminished towards vanishing
points. Two-point perspective is often used when drawing buildings in the
landscape. The effect can be carried even further, with three-point perspective
used to create impressive visual effects, such as a view from a skyscraper.
Duplicating rectangles.
A
B
E
C
F
o
D
Step 1 Draw a rectangle say ABCD and extend the lines AB and DC.
Step 2 Draw the diagonals AC and BD and let O denote the point of intersection.
Step 3 Draw a extended horizontal line through O.
Step 4 The point where this horizontal line meets line BC is the mid-point of BC.
Step 5 Draw a line from D through the mid-point of BC. The point where this
line meets the extended line AB will be the upper right corner of the duplicate
rectangle BCFE.
V
Duplicating rectangles in perspective.
B
A
o
E
C
V’
F
D
Step 1 Draw a rectangle say ABCD and extend the lines AD and BC. Their point of
intersection is the vanishing point V. Extend the lines AB and DC. Their point of
intersection is the vanishing point V’.
Step 2 Draw the diagonals AC and BD and let O denote the point of intersection.
Step 3 Draw a extended line through O and V’.
Step 4 The point where this extended line meets line BC is the mid-point of BC.
Step 5 Draw a line from D through the mid-point of BC. The point where this
line meets the extended line AB will be the upper right corner E of the duplicate
rectangle.
Step 6 Draw a line from V to E. The point where this line meets the extended
line DCV’ will be the lower right corner F of the duplicate rectangle BEFC.
Example of duplication of rectangles as seen in the pillars at The Qutab Complex.
While drawing human figures it is important to keep proportions in mind.
Artists have made measurements and come up with important rules:
•! The adult human body, including the head, is approximately 7 to 7 and 1/2
heads tall.
•! Your open hand is as big as your whole face.
•! Your foot is as long as your forearm (from elbow to wrist)
It would be a good idea to try these rules with yourself and some of your
friends!
Artists who understand human proportions also know how to bend the rules to
achieve the effects they want. Comic artists are a good example of this.
REFERENCES
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=258)#,&#:&2F@288#,8DG&&&
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http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Art.html&&
3. http://www.dartmouth.edu/~matc/math5.geometry/unit11/unit11.html
(for historical development of perspective during the early Renaissance)
4. http://mos.org/sln/Leonardo/LeonardosPerspective.html (for Leonardo da Vinci’s
paintings and perspective)
5. http://www.internal.schools.net.au/edu/lesson_ideas/renaissance/
renaissance_perspective.html (for lessons and worksheets in perspective)