Linear Perspective

What is perspective?

• A method of organizing forms in space

• Used primarily to create the illusion of depth or space on a 2D surface

• We tend to see perspective as a system of ordering pictorial space in terms of a single point

• Lines converge to mark the diminishing size of forms as they recede into the distance

Leonardo da Vinci "The Last Supper"

c.1495-1498

Discovery of Perspective

• Filippo Brunelleschi

• Developed the mathematical system of linear perspective

• Saw the picture plane as a transparent window through which the observer looks into the constructed, pictorial world

• All lines perpendicular to the picture plane meet in a single point on the horizon line (eye line)

• This discovery was enormously important to Renaissance artists for what was called the "rationalization of sight"

• It brought infinitely various visual sensations under a simple rule that can be expressed mathematically

• The combination of art, math and science is a hallmark of the Italian Renaissance

• The artists of the Renaissance were often mathematicians...and it has been said that the most creative work done in mathematics in the 15th century was done by artists

• Most early Renaissance artists were not primarily mathematicians but rather saw perspective as a way of organizing a composition

• The use of perspective made paintings exact and space understandable

• Plato said, "the excellence of beauty of every work of art is due to the observance of measure."

• The "measure" or the ability to mathematically observe artworks was considered the height of beauty

Raphael, "The School of Athens" 1509-1511

Pierro Della Francesca,"The Flagellation of Christ", 1455

Perugino, "Christ Delivering the Keys to the Kingdom", 1481-1483

Andrea Mantegna, "The Dead Christ", 1501

Andrea Mantegna, ceiling of the Camera degli Sposi, 1474

Rules of Linear Perspective

• A perspective drawing always has a horizon line, a vanishing point (point of convergence) and converging lines

• Convergence: Lines or edges of objects which in reality are parallel appear to come together as they recede from the observer

• In 1pt perspective, height is always vertical, width is always horizontal, depth always recedes to the vanishing point

-Diminution: Things appear to become smaller as they go into the distance.

-Foreshortening: Lines or surfaces parallel to the observers face show their maximum size. As they revolve away from the observer they appear increasingly shorter.

-Convergence = Diminution + Foreshortening

• Leonardo da Vinci added to the illusionistic effect of linear perspective by discovering "atmospheric perspective"

• He said that as things go into the distance they become smaller, lose detail and colors lose intensity

• da Vinci called it the "perspective of disappearance"

Filippo Brunelleschi

• 1377-1446

• Trained as a goldsmith but was well known as a sculptor

• Began working with architecture after being rejected for a competition to design baptistry doors

• He took several trips to Rome was very interested in the Roman ruins

• In trying to accurately draw the ruins he developed linear perspective

• His unique blend of architectural knowledge with an analytical and inventive mind permitted him to solve a problem no other 15-century architect could solve

• Brunelleschi won the commission to design and build the dome for the huge crossing of the unfinished cathedral of Florence

• Dedicated to Santa Maria del Fiore, the cathedral was built in 1367...10 years before Brunelleschi was born

• The opening for the dome was left open until Brunelleschi's design was accepted in 1420 and completed in 1436

Giorgio Vasari

"The Last Judgement"1572-1579

• Span of the dome was 140 feet, too wide for traditional wooden construction

• Brunelleschi devised new building methods and most of the tools necessary for construction

• Designed the dome around an ogival section, which reduces the outward thrust around the dome's base

• An ogival section is a pointed arch (based on Gothic architecture)

• To reduce weight he designed a double-walled shell

• The double shell is supported by 24 ribs, 8 of which are most prominent and visible from the exterior

• To hold the 8 segments of the dome in place, Brunelleschi designed a heavy lantern the sits atop the dome and stops the ribs from separating

• This was added after his death