Parallel Linesand Art

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

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

Task 1 Construct Parallel Lines

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

. P

. A

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.

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

Task 1 Construct Parallel Lines

Step 3 Do the same thing at point P

. P

. A

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

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.

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.

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?

E

How do draw an oblique letter

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

E

Parallel Projection Elevations

- The elevations are just the front, top and side

views of the object.

Elevations of your letter

- Look at your letter from the top

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

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

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

E

E

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

E

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

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

Obstacle Line Drawings

- Better example

http//www.mmwindowtoart.com/foundations/obstaclel

ine.html

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

Task 3 Create an obstacle drawing

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

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)

E