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Questions have swirled around the Salvator Mundi for years, especially since it became the most expensive painting ever auctioned in 2017, selling for $450 million. Is it truly an authentic piece by Leonardo da Vinci? If so, why didn’t the artist, well versed in the physics of optics, distort the fabric of the robe behind the orb in the hand of Jesus? In the biography Leonardo Da Vinci (Simon & Schuster, 2017), Walter Issacson writes that “Leonardo failed to paint the distortion” and that he wanted to “impart a miraculous quality to Christ and his orb.”

When UCI Computer Science Professor Michael Goodrich read this biography, he questioned Issacson’s conclusion. “He had talked earlier about how Leonardo had been studying optics, but then he comments that, on this one painting, Leonardo da Vinci painted it wrong,” says Goodrich. “I thought to myself, ‘I’ve got these great computer graphics colleagues who have these great computer graphic students, so this is something we can test!’”

Goodrich recruited Assistant Professor of Computer Science Shuang Zhao and his Ph.D. student Marco Zhanhang Liang to help him determine whether da Vinci had in fact “painted it wrong.” Their paper, “On the Optical Accuracy of the Salvator Mundi,” forthcoming in the journal Leonardo, outlines how, using physically based rendering, they prove that the painting could portray an accurate depiction of someone holding a hollow glass object.

Although this kind of technique — specifically, inverse rendering — is common in physics-based graphics, this was a new application area for Zhao and Liang. “Most of the time, people apply this type of analysis to photos,” says Zhao. “This was the first time I had applied it to a painting.”

Liang explains that they started with a scanned-in version of the painting as a reference but “pulled out” the orb. “The hand,” he stresses, “was important.” He downloaded a free model of a hand and then manually rigged its position to match the one in the painting. He tried using some computer vision techniques to extract the depth of the image but instead ended up using Maya, 3D computer animation modeling software. “I thought, ‘why not sculpt one by myself?’” he recalls.

The 2.5D model of the Salvator Mundi used to simulate the fabric behind various compositions and locations of the orb.

Liang used the Maya software to sculpt and refine the 2.5D relief and 3D version of the hand holding the orb to complete their analysis. “We have the contents kind of pop out in a way that’s similar to an actual 3D model because we needed the proper shape to carry out the simulations,” explains Zhao.

The team then carried out simulations for a solid crystal ball, a solid crystal ball made with calcite, and a hollow ball. What they found was that both versions of the solid crystal ball distorted the fabric behind the orb. However, if positioned correctly, and made with very thin glass, the hollow orb kept the folds of the robe straight, just as shown in the painting.

The appearance of the fabric with a solid (left) and hollow (right) orb.

“I had to revisit my model to have a straight fold, exactly like the one in the painting,” admits Liang. Even a 1 centimeter shift in the position of the orb would bend the folds of the robe.

“What really matters here, which also speaks to the authenticity of this really being work by Leonardo,” says Goodrich, “is that in order for the folds to come straight through, they all have to be going straight to the center of the ball.”

The lines of the folds must go straight through the center of the orb to avoid any bends.

Their work not only proves that there is a physically plausible setting for the Salvator Mundi but that da Vinci would have been familiar with the physics of this setting. The paper includes reprints of notes written by artist, illustrating his in-depth knowledge of the topic and suggesting that he knew the folds wouldn’t bend given the composition and location of his painted orb.

“So maybe da Vinci painted it right,” says Goodrich, “and the hypothesis that the orb is solid is just wrong.”

The trio of researchers hope to apply the technique to other works of art and historical artifacts. “The method that we applied here,” notes Liang, “is by no means limited to this one painting.”

Shani Murray