Historical Footnotes on the two Constructions

As late as the 1620s, it was still not recognized that Alberti’s and the distance point constructions were actually equivalent.  In fact, Pietro Accolti misunderstood part of a serious mathematical discussion of perspective by Giovanni Battista Benedetti and believed that out of the two constructions, only Alberti’s was correct.  Accolti accordingly gave the Albertian method the name costruzione legittima or “legitimate construction”, which unfortunately stuck till this day.  It is perhaps an irony that the treatise in which Accolti coined this misnomer is entitled Lo inganno de gl’occhi or “Deceiving the eyes”.

It is unclear whether Alberti was aware of the distance point construction, though he proposed using the straight diagonal line to check if his method was correct.  He also believed that the centric point should be at the eye level of the figures in the painting, though many painters do not follow this rule.  Nevertheless, the centric point is the focus of attention of the painting.  It is usually the job of a curator to position the paintings such that viewers can obtain the right eye height and viewing distance. 

Furthermore, there is a practical advantage of using the distance point construction.  By definition, the right vanishing point R is always outside the edge of the painting, whereas it is possible for the distance point D to be within the painting.  Hence in practice, it is easier to determine D.  In fact, renowned mathematician Egnazio Danti (1536 – 1586) once wrote: “And first we shall consider the (rule that is) more well-known and easier to comprehend, but longer and more tedious in application; and in the second (part) we shall consider the (rule that is) more difficult to comprehend, but easier to follow (in practice)”.  As expected, the “first rule” refers to the Albertian construction, while the “second rule” is that for the distance point construction.