1. Linear Perspective

2. 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

3. Leonardo da Vinci
"The Last Supper"

5. 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)

6. • 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

7. • 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

8. Raphael, "The School of Athens" 1509-1511

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

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

11. Andrea Mantegna, "The Dead Christ", 1501

12. Andrea Mantegna, ceiling of the Camera degli
Sposi, 1474

13. 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

17. -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

18. • 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"

19. 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

20. • 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

24. Giorgio Vasari
"The Last
Judgement"
1572-1579

25. • 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

29. • 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