JONATHAN LANSEY


Mechanical drawing of the leaning tower of Pisa

Description: (2002)

This is a scale point projection onto a plane, of the Leaning Tower of Pisa. It is on a checkerboard so you can tell that its actually leaning towards you.

Motivation:

I had this really boring English class, I took this project on as a challenge.

  Leaning Tower of Pisa, Areal View

General discussion

The drawing on left shows what perspective work went into the drawing on the right before I erased the extra lines.

One of the cooler things about this drawing, although some people aren’t able to notice it, the tower is in fact leaning towards you relative to a horizontal, flat, ground (the leaning is not to scale, I quadrupled it so it would be easier to notice.  Without the checkerboard, this effect would not have been possible.
Notice the shadows of the columns, see how they bend and figure out why,

A challenge to anyone who thinks they know perspective: what is the small circle in the middle of the tower for? what went into placing that little circle so scale would be correct, scale was the hardest part of the whole thing. hint: the little dot below the circle represents an eye, same thing with the one on the far right. another needed hint: I had an extension piece of paper above the tower to make a larger surface, this was needed.
extra credit: how did I place that circle

Shadow discussion

  • Find the vanishing point of the ground.
  • Take a look at the buildings shadow. Since the suns rays hit the earth parallel, the edges of the shadow of the building make two parallel lines on the ground
  • Find the vanishing point of those two lines, it is along a horizontal line to the left of the grounds vanishing point.
    this is because the shadow is on the same PLANE as the ground
  • Parallel lines have a vanishing POINT, a plane has a vanishing LINE! Since the shadow lies completely flat on the ground its vanishing point is on that line.

 

The Places I Estimated

  • At the tip of the shadow, the length of the thinner tip part is approximated.  The length of the whole shadow is arbitrary because the sun could be anywhere.
  • The curve at the top of the shadow is approximated.
  • I didn’t draw the very tip of the top of tower.
  • I drew the inner circles that are on the roof, in free-hand (the outer circle was mostly calculated)
  • The curve of the bottom of the bells, was guessed (actually made a mistake: I did not think about the fact that even when the tower leans, the bells hang straight down).
  • The actual lean of the tower is less then 5 degrees, I exaggerated its lean to about 20 degrees.

General Notes

Not including the neat lines on the bottom left, every single line in the right picture has a distinct purpose. I did not draw any just to make it look confusing or to look cool. There is only 1 vertical line in both these pictures.

I could not find a single picture of the leaning tower of pisa from above, they were all from below.
I had no idea whatsoever what to draw on the roof! so, I just made it up!

Materials:

  • Some pictures of the Leaning tower and a small to scale diagram of it. (all taken from the Internet)
  • Paper (lined, unlined)
  • A mechanical pencil
  • A pointy piece of metal
now your wondering, "don't you need a ruler! ... and at least a compass for that little circle ... and what's with the pointy metal?"

To make a ruler I folded a piece of paper,
to make a ruler longer then the 11 in. length of the paper I did this:
  1. Draw a line from the top right corner of a paper to the bottom left corner
  2. Fold along that line and you've got a nice sized ruler.

The lined paper helped with distances. I used the pointy metal and a lead pencil to make the compass, how I did it:
the concept is this:
two holes in a thin piece of paper,
make one hole sit still (by putting the pencil in it) while drawing around it through the other hole (with a free piece of lead)

To make the holes I used the pointy bit: I took a piece of lead out of the pencil, drew a circle with a radius of the distance between the two holes. The radius was very important for the scale to be correct.

To View Correctly:

Chances are, the way your looking at it right now, it will not have correct perspective. if you want it to look REALLY 3D (and really feel like your hovering above the leaning tower), then then do this: 

  1. (optional) print out the picture
  2. close one eye
  3. hold the page flat
  4. directly underneath your open eye (where a line from the eye is perpendicular to paper hits the paper at) the point where the thin part of the tower connects with the thick part.
  5. Hold the picture so close that
    • the angle from point(thin and thick part of tower touch) to your eye, then to (the base of the tower) is about 30 degrees
    • OR
    • The shortest distance from your eye to the paper is exactly the distance (On the picture at right) from (the little circle with dot) on the right, directly to the vertical line in center of tower.

      Look around, the perspective will be like you are actually there.
      If you get it right, it should be apparent that the tower is tilting towards you.

 

 

Bus reflection sketch

Description: (2002)

A warped reflection of a bus in a store window.

Motivation:

The same really boring English class coupled with a long bus ride to school

Analysis:

This is really the way busses look when they are reflected in large windows.  Windows are never perfect and larger ones tend to have larger imperfections. To draw it, I first drew a bus onto a grid (below).  Then I drew a warped grid onto the windows, then copy-warped the bus square by square onto the warped grid.

 

 

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