Parallel Lines and Art

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Parallel Linesand Art
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Objectives

• To apply parallel lines to construction,
  technical drawing and art
• There are three tasks you are going to be asked
  to do today
• Task 1 Geometric Construction of Parallel Lines
• Task 2 Parallel Projection Elevation, Oblique,
  Isometric
• Task 3 Obstacle Drawing

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Geometric Construction

• In geometry, constructions utilize only two tools
  - the straightedge (an unmarked ruler) and the
  compass.
• Never draw freehand when doing a construction!
• The compass

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Task 1 Construct Parallel Lines

• Step 1
• Put point A on line
• Draw a line through points P and A

. P
. A
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Task 1 Construct Parallel Lines
Step 2 Find the center of the circle thing on
your compass and place it the center on point A.
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Task 1 Construct Parallel Lines
Step 3 Adjust the moving thing to about 3 on
the ruler. Then make an arc off of point A
. P
. A
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Task 1 Construct Parallel Lines
Step 3 Do the same thing at point P
. P
. A
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Parallel Projection

• Parallel transformation of points.
• The perspective transformations that describe how
  a point in three space is mapped to the drawing
  plane can be explained using elementary geometry.
  
• Begin by setting up coordinates. A projection
  involves two coordinate systems. A point in the
  coordinate system of an object to be drawn is
  given by X(x,y,z) and the corresponding in the
  imaging system (on the drawing plane) is P(u,v).
  
• If we use the standard right handed system, then
  x and y correspond to width and depth and z
  corresponds to height. On the drawing plane, we
  let u be the horizontal variable and v the
  vertical.

http//www.math.utah.edu/treiberg/Perspect/Perspe
ct.htmParallelx
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Parallel Projection

• The most frequent parallel projections are called
  elevations, oblique projections and isometric
  projections.
• To illustrate, let's begin with an object in
  three space, say a simplified house.

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Parallel Projection Oblique Projections

• In oblique projection (Cavalier projection), the
  front view is undistorted, but the sections of
  the object are drawn up and to the right
  depending on how far back you go
• Of course horizontal and vertical lines also
  preserve measurement.

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How do draw an oblique letter

• Start with a block letter that has ½ inch
  thickness
• http//www.mmwindowtoart.com/wordart/lettering5.ht
  ml
• Then choose a length on your ruler - I chose an
  inch
• Off of every corner draw a line either off to the
  left or right - what do you notice about all the
  lines that go off the corners?

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How do draw an oblique letter

• Erase the parts that go through the letter
• Then connect the parallels to the front pieces

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Parallel Projection Elevations

• The elevations are just the front, top and side
  views of the object.

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Elevations of your letter

• Look at your letter from the top

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Parallel Projection Isometric Projections

• The isometric projections are that class or
  parallel projections for which a round sphere
  projects to a round circle. The most common case
  is when measurements along the x-axis are plotted
  at 30, those along the y axis at 150 and the
  vertical axis.

x-axis
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Task 2 Create a Parallel Projection

• Use a straight edge for straight line and a
  compass for curves
• Using the first letter of your name

Oblique
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Task 2 Create a Parallel Projection

• Use a straight edge for straight line and a
  compass for curves
• Using the first letter of your name

Top view
Elevations
Front view
Side view
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Task 2 Create a Parallel Projection

• Use a straight edge for straight line and a
  compass for curves
• Using the first letter of your name

Isometric
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Obstacle Line Drawings

• Where "line as movement" is curvilinear and
  softly dances across the page, "Obstacle Line" is
  angular, sharp and intense as it circumscribes
  the "obstacles" in the composition. These
  "obstacles" can be words, numbers, images, icons,
  etc. and are first collaged or painted on to the
  background. Since lines in this design close upon
  themselves, shapes are created.

http//www.mmwindowtoart.com/foundations/obstaclel
ine.html
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Obstacle Line Drawings

• Where "line as movement" is curvilinear and
  softly dances across the page, "Obstacle Line" is
  angular, sharp and intense as it circumscribes
  the "obstacles" in the composition.

http//www.mmwindowtoart.com/foundations/obstaclel
ine.html
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Obstacle Line Drawings

• Better example

http//www.mmwindowtoart.com/foundations/obstaclel
ine.html
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Obstacle Line Drawings

• Rules The lines never "blend" or touch each
  other. They are always parallel. They are as
  intricate in detail as their curvilinear cousin,
  depending upon the movement and alignments the
  designer conceives. The linear effect is like a
  maze and often results in op-art illusionary
  motions.

http//www.mmwindowtoart.com/foundations/obstaclel
ine.html
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Task 3 Create an obstacle drawing

• Use at least the following in your drawing
• 2 numbers
• 2 letters
• 1 symbol/shape

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Summary

• Construct a parallel line
• Oblique letter
• Elevation of letter (top, side, front)
• Isometric (2 pt. perspective)
• Obstacle drawing (2 letters, 2 numbers, 1 symbol)

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