photo from reference 1
Santissima Sindone is a chapel located in Turin, Italy and designed by the architect Guarino Guarini. One of the most fascinating features of the chapel is the dome. This is because Guarini not only created a complex architectural structure, but he used the structure to create an optical illusion. The purpose of this study is not only to understand Santissima Sindone by recreating Guarino Guarini's dome using a computer model, but also to use this model in order to comprehend his optical illusion.

Various models are needed in order to understand the dome and its distortion. The computer reconstruction of Santissima Sindone is based on a side-elevation [reference 1] shown below. From this elevation, one is able to recreate pieces of the interior structure of the dome by using basic geometric shapes. The first basic shape exists at the top of the dome. Since the model is of the interior structure, this shape appears to be the top half of a sphere or a hemispherical dome, not the spire. This hemispherical dome sits on top of a section that in simplified geometric terms is a portion of a cone. Below the cone is a cylinder. The base of the cylinder ends at the clear horizontal lines located at the center of the side-elevation. These lines correspond to the large circle seen in the picture above. The remainder of the elevation no longer comprises the interior of the dome, but the interior of the chapel.

Although these three shapes provided a visual idea of Guarini's dome, two more shapes were used in order to create a more accurate representation. These two shapes lie between the cone and the cylinder. Above the cylinder is a section of the model that contains pentagons on the walls. This section is labeled the trapezoid layer. This is because the circular arches between the pentagons have been simplified by representing the top of the windows as triangles rather than semi-circles. So, the sections of the wall between the windows form trapezoids. Above the trapezoid layer is a cone made up of six rows of semi-circular windows. Based on the measurements taken from this elevation, it is evident that the first five layers lie on a common cone (main cone), while the bottom layer is a slightly different conical section, the base cone.

In this way, one is able to regenerate Guarini's dome. So, the final model that was created included five basic parts and shapes: a hemispherical dome, main cone, base cone, trapezoid layer, and cylinder. This forms the simplified model since it is made up of basic shapes taken from the side-elevation in reference 1.

photo from reference 1
Another model that helps one to understand Guarini's dome is a skeletal model. This model displays the breakdown of the main and base cone into their individual layers. Each layer is formed by six windows. The bases of these windows are straight lines that when connected form a hexagon. These six hexagons are seen in the view into the dome located above. Like in the trapezoid layer, the curves of the windows have been simplified into straight lines. Thus, the spaces between each window become triangles. This six-hexagon-layer configuration is one element of Guarini's fame.

Guarino Guarini used optical illusion in his creation of the dome at Santissima Sindone. When standing directly below the dome and looking up, the brain naturally assumes that the distances between the hexagon layers are equal, while the eye perceives an illusion that the differences between the layers are decreasing. Guarini decreased the height between each triangle layer creating the illusion that the dome recedes farther up into space than it really does. So, to study this optical illusion, one can arrange the heights between each layer to be equal to create a model of what the brain thinks it is naturally seeing. The shape that is produced is a representation of what the dome would have looked like without the distortion in the height between triangle layers.

Optical Illusion & Projection in Domes: A Study of Guarino Guarini's Santissima Sindone