Math 139 Exercises 15

Exercise Set Linear Perspective Works of Art

1. The paintings shown are in one point perspective. Find the viewing target T and the correct

viewing distance, d. (a) Assume that the floor tiles are squares.

Raphael, School of Athens (b) Assume that the ceiling tiles are squares. Leonardo Da Vinci, The Last Supper

Math 139 Exercises 15

2. The following are pre-Renaissance paintings (before the rules of 3D perspective were discovered). According to Paul Calter in Squaring the Circle, errors commonly found in such paintings include

• Parallel lines that should converge but do not converge at all • A vanishing point in front of the object • A set of parallel lines that converge to more than one vanishing point • Failing to place vanishing points for horizontal parallel lines on the same horizontal line (the

picture horizon) Find examples of perspective errors in the following paintings.

(a)

Ambrogio Lorenzetti, Allegory and Effects of Good and Bad Government on City Life (b)

Simone Martini, The Miracle of the Child Falling from the Balcony