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Perspective - Part 6

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OTHER ELEMENTS: THE CIRCLE

The circle in perspective is going to give us more material to learn, as some of its properties also apply to a rectangle with all four sides equal.  The reason for that is that all circles are contained within such squares.  So, let us begin with drawing a perfect square in perspective.  First with one vanishing point, then with two.

In order to determine whether a square has equal sides, we need to measure segment S, which should be equal to L. To do this we follow these steps
  1. Draw a line from a corner to the opposite corner until it touches the horizon line (orange line.)
  2. The distance between this intersection and the vanishing point: L2 should be the same as L1.
  3.  If this segments are not the same, mark the distance of L1 on the horizon line, and work your way back.  The green square contains the circle in perspective. 

Now that we have the square, let us draw the circle:

  1. Divide the square with two line from its opposite corners (red lines.)

  2. Divide segment L1 into two equal halves.

  3. Draw a line (red) from this center to the vanishing point.

  4. Now that you now all 8 segments of the circle you can complete the   circle.

  5. The pink line, which is parallel to the front of the square divides the circle into two equal parts (in perspective.)

  6. The area where all lines intersect is the center of the circle.

 

 

In this second example, we are showing another circle, but this time with two vanishing points.  The basic rules are the same for the above circle.  Just make sure that you have have a perfect square before you begin the circle.  To verify this, all you need to do is draw a base line parallel to the horizon line at the closest corner of the square.  Next, project the two converging lines farthest to you (black dotted lines) until they intersect the green base line.  If your square is perfect, L1 should be identical to L2.  If not, make the necessary adjustments.

Application:   In this example, the circle uses the principles explained.

Ancient Ruins Used as Public Baths by Robert Hubert 1798
State Hermitage Museum.
The principles we have just learned have been applied on the arches in the forefront and background.  As you can see, these rules also apply to semi-circles.

The Piazzetta- Looking South, by Canaletto
1727, Royal Collection
The circles on the side of the building are an examples of these techniques both from this lesson and from the diminishing size lesson.

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