San Carlo

In Rome, there is a small 17th-century church called San Carlo alle Quattro Fontane, designed by Francesco Borromini, a contemporary of Gian Lorenzo Bernini and one of the great masters of the Baroque period. Their rivalry produced some of the era’s most inventive designs.

Inside the church, the dome’s pattern consists of a repetition of Greek crosses, octagons, and hexagons. To make the dome appear higher, Borromini gradually reduced the size of these shapes toward the top, creating a striking optical illusion.

This illusion can be reconstructed and improved by projecting the 2D pattern from a cylindrical surface around the dome onto a viewpoint at the center of its base. The intersection of each projection line with the dome determines where the pattern should be drawn.

In the simulation below, you can experiment with this effect. Approaching the center of the dome, the structure appears to lift upward, with the illusion strongest at the origin.

Another fascinating example of optical illusion can be found in Sant’Ignazio di Loyola, where Andrea Pozzo painted a magnificent “false” dome on a flat ceiling — well worth a visit as well!

I completed this project after a high school trip to Rome in 2016, with the help of my excellent math and programming teacher, John Val.