Homework #2

Assigned: Thursday, January 20

Due: Thursday, January 27

1. Construct a Perspectively-Correct Picture

Using a ruler and a pencil, construct a single-point perspective space on a sheet of paper using Leon Battista Alberti’s “construzione legittima” described in Della Pittura.

a. The drawing space: "First of all, on the surface on which I am going to paint, I draw a rectangle of whatever size I want, which I regard as an open window through which the subject to be painted is seen; and I decide how large I wish the human figures in the painting to be. I divide the height of this man into three parts, which will be proportional to the measure commonly called a braccio; for as may be seen from the relationship of his limbs, three braccia is just about the average height of a man's body. With this measure I divide the bottom line of my rectangle into as many parts as it will hold."

• Turn a sheet of paper sideways and draw a rectangle approximately 4" high by 5" wide on the right half of the page, leaving the left half blank. Sketch a human figure standing on the bottom line (the baseline), about half the height of the rectangle. One third of this figure's height is a braccio (about 23 inches). Mark off the base line in equal units of one braccio.

b. The vanishing point and orthogonals: "Then I establish a point in the rectangle wherever I wish; and [as] it occupies the place where the centric ray strikes, I shall call this the centric point. The suitable position for this centric point is no higher from the base line than the height of the man to be represented in the painting, for in this way both the viewers and the objects in the painting will seem to be on the same plane. Having placed the centric point, I draw lines from it to each of the divisions on the base line. These lines show me how successive transverse quantities visually change to an almost infinite distance."

• Draw a dot near the middle of the rectangle at the human figure's eye level, directly above one of the marks you made on the baseline. This will be the centric point, which is the same as the vanishing point, VP, but only in this 1-point perspective construction. Next, draw lines from the vanishing point to each of the marks on the baseline. These are called the orthogonals. Note that Alberti says they can be used to scale any "transverse quantities" -- the horizontal width of floor tiles, objects, gaps, etc. -- out to a nearly infinite distance.

c. The horizon line: "This line is for me a limit or boundary, which no quantity exceeds that is not higher than the eye of the spectator. As it passes through the centric point, this line may be called the centric line. This is why men depicted standing in the parallel furthest away are a great deal smaller than those in the nearer ones, a phenomenon which is clearly demonstrated by nature herself, for in churches we see the heads of men walking about, moving at more or less the same height, while the feet of those farther away may correspond to the knee-level of those in front."

• Draw a horizontal line through the vanishing point and all the way to the left edge of the page. This is called the horizon line or vanishing line.

d. The transversals: "I have a little space in which I describe a straight line. This I divide into parts like those into which the base line of the quadrangle is divided. Here I place a single point above and perpendicular to one end of this line and as high as the centric point is above the base line of the quadrangle. From this point I draw single lines to the individual divisions of this same line. Then I establish how much distance there is to be between the eye of the spectator and the picture, and here at the established place of the intersection, I establish an intersection of all lines it meets, by means of a perpendicular... This perpendicular line gives me by means of its coordinates the limits of each distance which should be between the transverse and equidistant lines of the pavement. In this way, I have drawn all the parallels. It can be proven that they were correctly described if a single and continuous straight line [can be drawn] as the diagonal of the conjoined squares in the depicted pavement."

• Extend the baseline out horizontally to the left and right edges of the page. On the right side, mark off more 1-braccio units. On the left side, draw the eye point, E, about 5" from the left edge of the rectangle at the same height as the vanishing point. The distance between E and the left side of the rectangle is the proper viewing distance for the picture, which determines the amount of foreshortening.

• Now draw lines between E and each mark on the baseline. These are the diagonals. Where they intersect the left side of the rectangle, draw horizontal lines across the rectangle. These are the transversals, which get more compressed toward the horizon. Each floor tile is one braccio square.

e. The true distance point. To test this perspective construction, draw several “check line” diagonals that connect the lower left and upper right corners of the floor tiles. If they all converge to a common point on the horizon line (called the true distance point, DP), the construction is correct. The distance between DP and VP is the proper viewing distance for the picture, which in this case should be about 5".

f. Is perspective "robust?” Carefully view this perspective drawing through your reduction screen from (a) the proper distance, (b) a closer point, and (c) a farther point. Does your viewing distance affect whether the floor tiles look square or rectangular? (d) Now view it from the proper distance directly in front of the VP, and (e) off to one side of the rectangle. Does your viewing angle affect whether the floor tiles appear to have square corners? Do the tiles look square from all viewing positions, or are they distorted? Is perspective "robust?”

g. Draw objects. Draw two cubes sitting on your perspective grid at different distances, aligned with the floor tiles. Draw a circle on the floor with radius equal to the width of one tile.

2. Perspective Analysis of Paintings

Given pavimenti (floor tiles) or architecture containing parallel lines in a perspective painting, you can work backwards to find the vanishing point(s), the horizon line, the distance point, and thus the proper viewing distance and direction of gaze (the centric point).

a. Find on the web (e.g., at the Web Gallery of Art, http://www.wga.hu ) images of the following paintings:

i. The Flagellation (c. 1460) by Piero della Francesca

ii. The Annunciation, with Saint Emidius (1486) by Carlo Crivelli

iii. A painting of your choice from the Italian Renaissance

b. Save each image on a separate slide in a Powerpoint file named lastname_hw2.ppt if you are working alone, or lastname1_and_lastname2_hw2.ppt if you are working with someone else.

c. Perform a perspective analysis by drawing and labeling brightly-colored lines and points on the image of each painting that indicate (a) a number of the orthogonals, (b) the vanishing point(s) (VP), (c) the true distance point (DP), and (d) the horizon line (HL). Also draw and label a “check line” to verify the correctness of the location of DP. Finally, indicate the correct viewing distance.

d. Copy your file to the folder \Student\Dyer – Science of Art\Homework 2\