Download Spatial Organization/Perspective Conveying the idea of depth on a

Spatial Organization/Perspective
Conveying the idea of depth on a two dimensional surface
Converging parallel lines
Perspective: Linear
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Linear perspective is a technique for representing three-dimensional space on a flat
surface.
Raphael, School of Athens
Piero Della Francesca, Ideal City, Galleria Nazionale at Urbino.
Linear perspective is a mathematical system for creating the illusion of space and
distance on a flat surface.
To use linear perspective an artist must first imagine the picture surface as an "open
window" through which to see the painted world. Straight lines are then drawn on the
canvas to represent the horizon and "visual rays" (convergence lines) connecting the
viewer's eye to a point in the distance.
Horizon line-is always at eye level. Picture yourself at the seashore and looking out at
the ocean you notice that the water meets the sky at your eye level. This never changes.
You may be in an airplane 1000 feet up and the level that the ocean meets the sky is still
at your eye level! Or you may be lying down on the beach and the ocean level drops
with you. Think of it as an invisible plane that cuts through everything, that always
exists at eye level.
Vanishing Point-is the point to which all lines which are parallel to the viewer recede.
You may want to think of the last time you were looking down a long stretch of straight
highway. The edges of that highway appear to move at an angle upward until they
meet the horizon. In one point perspective all verticals and horizontals stay the same
and only lines that are moving away from or toward the viewer seem to recede on the
horizon at the vanishing point.
Hint: All planes must be perpendicular or parallel to you in order for this system to
work correctly. If you are looking at the corner of an object that is not at a 90 degree
angle to you this will create distortions!
Convergence Lines (also called orthagonals)-are lines that converge at the vanishing
point. These are any lines that are moving away from the viewer at an angle parallel to
the direction that the viewer is looking. In the case of the highway that we mentioned
above these lines would be the edges of the highway as they move away from you
forward into the distance.
One - Point Perspective
Two - Point Perspective
Calculating Diminishing Size in Perspective
Here is a formula for showing diminishing sizes of planes in a convincing way. Always
establish a horizon line and vanishing point before starting.
1. Establish a square or rectangular plane in perspective near the foreground in
your drawing. Subdivide this plane by drawing a line from corner to corner, then
repeat the process with the opposite two corners. The point where the diagonal
lines intersect will be the center of the plane in perspective. From this center
point draw a line back to the vanishing point (marked with a "V" in the diagram)
to establish a receding horizontal center line.
2. Draw a line from the top left corner of your plane through a point where the
vertical line that creates the back of the plane meets the horizontal center line
(this point is marked with a yellow dot in the diagram) and continue this line
until it intersects the bottom convergence line.
3. At this point, where the convergence line meets the (yellow) construction line,
draw a vertical and this becomes the back edge of the next plane adjacent to the
previously established one.
4. Repeat steps 1, 2, and 3 as many times as needed to continue diminishing size.
One can also plot diminishing size on horizontal adjacent planes by using the top or
bottom edge of each vertical plane. The horizontal white line near the bottom of the
diagram is merely a horizontal line that intersects with one of the vertical divisions.
From these points one can plot the dimishing size of the horizontal planes.
Shadows
Give information on the three dimensional form of objects as well as on the position of a
source of light.
Even shadows have vanishing points, but these may not correspond directly to the
standard construction vanishing points or horizon line. Shadows have their own
vanishing points which are called light vanishing points or shadow vanishing points.
To create believable shadows one must first draw an object in a transparent way. This is
because you will need to know where the back corners are in order to finish a shadow
which may disappear behind the object. Then you find the light source in relation to the
object. You may want to check to make sure that you are placing it in the proper
position, otherwise there will be distortions. You then create a vertical line descending
directly from the light source or light vanishing point until it intersects with the surface
where the shadow is being cast. This point will be your shadow vanishing point and
shadows will radiate out from this point. Send light convergence lines through all top
corners of the object (some may end up inside your object). Then send shadow
convergence lines through all the corresponding bottom corners until they intersect
with the light lines. This will mark the extreme edges of your shadow.
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Hint: Light radiates out in all directions. If you have a light source directly above an
object, then your object will cast shadows in all directions.
Hint: Shadows can be cast on a number of surfaces. For instance, if you have an object
sitting on a table, then there will be a different shadow vanishing point for the object
(which will be on the tabletop) and for the table (which is on the floor).
Hint: When the light source is the SUN or MOON, the shadow vanishing point is on the
horizon directly below the light source.
Three - Point Perspective
A third point can come into play in perspective, but only when dealing with extreme
heights or lows. Tall buildings are one example. In the case of looking up at a tall
building (worm's eye view) the edges of the building will not only recede to the two
vanishing points (if looking at corner), but there will be an upward (or downward)
recession to a vanishing point. This vanishing point is always directly in front of the
viewer at a 90 degree angle to the horizon line. If looking down at an object in three
point perspective it is referred to as a bird's eye view.
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