August 19, 2018 Sunday
Bedtime Story
Vanishing Point
Horizon line forms a crucial part of a
perspective drawing into which points on any horizontal plane converges.
This line to the artist represents all the
objects that are infinitely away and hence are made to shrink to the
infinitesimal thickness of the line.
With the concept of horizon line, there by
default must coexist the concept of vanishing point.
Vanishing point concept is best understood
by considering two parallel lines for instance a railway track that is facing
the viewer of the image.
Two such parallel lines that are receding
away from the viewer will converge at this vanishing point and so to speak
“disappear” somewhere on the image plane or the picture plane.
This is what is commonly known as the
standard “receding railroad tracks” phenomenon.
When these parallel lines are perpendicular
to the picture plane the diagram is known as one-point perspective.
The vanishing point in instances of
one-point perspective paining is known as oculus or the eye point as it is from
this point that one would be able to get the correct perspective as intended by
the artist or the photographer.
The other element of a linear perspective
is the concept of picture plane.
Picture plane is the plane of the image
that lies between the oculus and the object being viewed and is actually
defined by the material on which the painting is being carried out.
The picture plane is always perpendicular
to the axis that comes out of the viewer’s eyes.
While looking straight at some bird flying
straight ahead of you and assuming that your eyes are horizontal to the ground
then the picture plane is perpendicular to the ground and to your visual axis.
Most artists use more than one vanishing point
maybe as many as even three in their depiction of scenes.
When you are armed with this knowledge of
perspective and then you go to some gallery of paintings, you will not find it
very difficult to differentiate paintings on the basis of the number of
vanishing points they contain.
The idea of perspective has been studied extensively
both by the Renaissance artists and mathematicians who have even gone on to develop
a vanishing point theorem.
The vanishing point theorem states that the
image in the picture plane pi of a line L in space, not parallel to the
picture, is determined by its intersection with pi and its vanishing point.
In non-mathematical language this can be
translated as – the image of a line includes its vanishing point.
Paintings that have the aspect of linear
perspective in them are drawn and painted in such a manner as if the rays of
light coming from the object are passing through a rectangular at a certain
distance from the object.
We shall continue our journey into both the
art and mathematics of perspective in the nights to come.
Stay tuned to the voice of an average story storytelling
chimpanzee or login at http://panarrans.blogspot.com
Good night Mon Ami and my fellow cousin ape.
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Another great educator and a teacher that I am aware of is
Professor Subhashish Chattopadhyay in Bangalore, India.
While I narrate stories, Professor Subhashish an electronic
engineer and a former professor at BARC, does and teaches real mathematics and
physics.
He started the participation of Indian students at the
International Physics Olympiad.
Do visit him here:
All his books can be downloaded for free through this link:
For edutainment and English education of your children, I
recommend this large collection of Halloween Songs for Kids:
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