Parallel Lines and Art

1. Parallel Linesand Art

2. 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

3. 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…

4. Task 1: Construct Parallel Lines Step 1: Put point A on line Draw a line through points P and A . P . A

5. 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.

6. 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

7. Task 1: Construct Parallel Lines Step 3: Do the same thing at point P . P . A

8. 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/Perspect.htm#Parallelx

9. 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.

10. 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.

11. How do draw an oblique letter • Start with a block letter that has ½ inch thickness • http://www.mmwindowtoart.com/wordart/lettering5.html • 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

12. How do draw an oblique letter • Erase the parts that go through the letter • Then connect the parallels to the front pieces E

13. Parallel Projection: Elevations • The elevations are just the front, top and side views of the object.

14. E Elevations of your letter • Look at your letter from the top

15. 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

16. 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… Oblique

17. 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

18. 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

19. 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/obstacleline.html

20. 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/obstacleline.html

21. Obstacle Line Drawings • Better example… http://www.mmwindowtoart.com/foundations/obstacleline.html

22. 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/obstacleline.html

23. Task 3: Create an obstacle drawing • Use at least the following in your drawing… • 2 numbers • 2 letters • 1 symbol/shape

24. E 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