The dome is divided into six layers and as the dome extends upward, the height between layers decreases. The decrease in height between layers is how Guarini created an optical illusion of a receding dome. This is because when a person views the dome, he or she naturally perceives the heights to be decreasing while the brain expects each layer to be equal. Guarini accentuates this effect by decreasing the heights of these layers. This diagram is a study of what the shape of the dome would have been had Guarini not decreased the heights, but kept the view from below the same. Notice that the exterior changes while the view from inside looking up remains the same. This diagram is created to study Guarini's optical illusion and why he created the dome to have decreasing heights between its various levels.
The diagram is a simulation of a person standing on the floor of the chapel looking up into the dome and depicts the cone shape of the dome in its most primitive form. The actual cone is depicted in black, and the measured heights of the layers are 1.70, 3.00, 3.78, 4.49, 5.10 and 5.69 respectively. The new heights are shown in blue equally spaced at 1.70 cm apart. Lines of sight (red) from the eye at the bottom through the original heights on the cone (black points) are extended until they intersect the new heights. The points of intersection (blue) appear to the observer to be in the same position as the originals (since they are on the same line of sight). If the mind assumes the layers are all the same height, the shape of the dome that the observer thinks he or she sees is the one depicted in blue.
Carrying out this procedure produces new radii and heights for the triangle layers.
Because the points are not collinear, the new shape is not a cone. Determining the slope between points on a line is one way to establish that the points are not collinear. If the slopes between each two consecutive points are the same then the points lie on the same line; if they differ than they cannot lie on the same line. For example, the slope of the line connecting the first two point is 1.67 while the slope between the second two points is 2.43. The next consecutive slopes are 4.86, 5.67, 6.30 and 6.07. Based on these computations it is evident that these points do not lie on the same line.
The distortion can be viewed using the computer
|Optical Illusion & Projection in Domes: A Study of Guarino