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### Course: Start here>Unit 2

Lesson 2: The language of art history

# How one-point linear perspective works

Linear perspective, a method of creating a three-dimensional world on a two-dimensional surface, was discovered by Filippo Brunelleschi in the early Renaissance. This technique, which uses a vanishing point, horizon line, and orthogonals, was used by artists like Leonardo da Vinci to create realistic and expressive art. Created by Beth Harris and Steven Zucker.

## Want to join the conversation?

• At Dr. Harris mentions that some may argue the ancient Greeks and Romans utilized some elements of linear perspective. My questions are:

1) Can someone please provide links to these ancient Greek or Roman instances of linear perspective?

2) More importantly, are there reasons why these techniques were "lost" or "under-utilized" after the ancient Greek and Roman cultures until the Renaissance?
• 1) I'd like to point out Elucid's Elements book as a source to ancient Greek/Roman instances of linear-perspective. Linear-perspective is a mathematical process that's fairly akin to orthogonal or orthonormal projections of a 3D object onto a 2D axis. The basic mathematical principles of Linear Perspective as later described in the book 'On Painting' were all developed by Greek and Roman society. Particularly, Elucid's element's Book 5: Ratios and Magnitudes as well as Books 2-4 and 6.

http://aleph0.clarku.edu/~djoyce/java/elements/bookV/bookV.html#defs
• We often talk about linear perspective (as is the case in the video) as a "discovery", but is this really correct? Can we call it a discovery in traditional terms, or is it more of an innovation, as other artistic techniques, such as shading, are used to make paintings more realistic?
• I think you have to examine the debate between mathematics being a discovery or an invention. The traditional view of 'copyright' as it pertains to mathematics. The general notion is that facts cannot be copyrighted.

For example, the location of the white house or it's address cannot be copyrighted; nor can my phone number. Math is considered to be a 'fact' and that new mathematical discoveries are just 'uncovering' pre-existing facts. Like for example, a right-angle triangle having at least one degree with 45 degrees is considered a fact that was discovered and could have been found in 'nature' with careful enough observation.

If you look at the book of 'steps' or 'rules' by which to create a linear perspective 'on painting' which is probably akin to a 3D to 2D translation section in a linear algebra textbook, I would describe that book as a publishing of a mathematic discovery of a fact. Infact, linear-perspective in mathematical terms would be an orthogonal projection.

I don't believe there is a significant degree of interpretation or creativity of the linear-perspective process is applied, but rather, a degree of accuracy. The end-result of the linear-perspective painting if the rules/steps are followed I think is more dependent upon the skill of the artist in terms of artistic techniques.
• Is it possible to create an illusion of a four-dimensional reality using our 3-d space (the fourth dimension not being time, but another spatial dimension)?
• Picasso's abstract works is often said to be based of this idea. It shows as example a portrait of a woman face, but like not ordinary single viewpoint but many viewpoints as once that can be looked like a object like in a many sides.
• Does mathematics have something to do with this Linear Perspective?
• When selecting a Horizon Point (HP) outside of the picture, how do you know where to place this on your horizon? Surely, where you place the HP will affect the angle of the rays (~) and thus the height of the intersections therafter.
• From what I understand from the video the Horizon Point (HP) is actually what will determine the Horizon Line (HL). Now again, the way I understand it, the HL is meant to be eye level with the viewer. Take a world for example, using the Equator as the HL. Now if you put the HP Northwest instead of due West, you haven't changed it you have merely rotated it. . . If I really wanted to screw with the intersections, I'd move the vanishing point.
(1 vote)
• I am very sorry to bother, But what are Orthogonals? (not Orthographic)
• In this context an orthogonal is a line that seems to recede into the depicted space of a painting but is in fact a diagonal line on the surface of the canvas.
• Does the figures eyes always have to be on the same level as the horizon line? What if in the composition, for example, there is one standing, one sitting, and one laying down? How do I know where to put them acording to the horizon line?
• You would make sure that the eyes of each figure would line up with rays drawn through the external point drawn on the horizon line, so that their perspective would be maintained no matter how big or how close they were.

The reason they put the eyes on the horizon line is for aesthetic reasons.
• Did Alberti base his knowledge of art off the Greeks and the Romans, other painters in his time, or his own works when he wrote "On Painting"?
• Alberti credits the concept of Linear Perspective to Filippo Brunelleschi. He even dedicated the 1436 edition of "On Painting" to Brunelleschi. Although, as an interesting side note... the first real depiction of linear perspective can be found in Ambrogio Lorenzetti's "Annunciation" from 1344 which precedes Alberti's work by nearly a century.
http://en.wikipedia.org/wiki/File:Lorenzetti_Ambrogio_annunciation-_1344..jpg