The geometry of the picture is extraordinarily carefully worked out: so carefully that it has proved possible to construct computer-generated views of the room that show what it would look like from directly above, from the sides, and from the floor. It is clear that Piero cared a great deal more about getting the geometry right than making any religious message in his picture comprehensible to viewers.  The fascination that the picture exerts derives from its utterly logical, rational and comprehensible proportion and perspective. Its religious message is so obscure that it is irrelevant to appreciating it — and one senses that Piero was well aware of that fact.

It is of course impossible to get at what Piero's religious beliefs "really" were. But it is striking that when he painted a fresco in his house in Sansepolcro he did not choose to depict a saint or any Christian figure, but the pagan demigod Hercules. He worked for the Franciscans and for religious confraternities — but also for condottieri such as Sigismondo Malatesta, ruler of Rimini, and Federico da Montefeltro, the count of Urbino. Both made their fortunes out of inflicting misery on others. Federico has had a better press than Sigismondo, who earned an excoriating condemnation from Pope Pius II for publicly sodomising the 15-year-old bishop of Fano in Rimini's central piazza. But if Federico was more restrained in his personal conduct than Sigismondo, Federico's troops probably inflicted more damage, most notably in their bloody sacking of Volterra. Piero dutifully painted official portraits of both men, making them look stately and dignified, even pious.