Origen de la projective geometry: Renaissance [ School ]

One of the parts of the geometry that is more prevalent in the corresponding representation is descriptive geometry. Among the works that have made my students, some have focused on the origins of the different geometries, like the one I present today which relate historical aspects and characters that have contributed significantly to this field of science of great application to ingeniarías and Art.

By Geometry Hicks (originally published here)

Perspective

Projective geometry appeared as a solution to the problem of the artist to paint three-dimensional world in his paintings dimensional.
Projective geometry has its origins in the work of Renaissance artists(S.XV); although some concepts already appear in the Greeks. To paint pictures more realistic, Renaissance artists sought to discover the laws governing the construction of the projection of the object on a screen. Coming to develop the elements of a fundamental theory of geometric perspective, in the fifteenth century were the best physicists and mathematicians.

This interest in developing projective geometry is due to the change in the subject of the painting. In the medieval period the paintings were mostly religious in nature and painters represented the characters and objects in a highly stylized, generalmente sobre fondo dorado, to emphasize that the box had no connection to the real world. In the Renaissance with the advent of humanism and anthropocentrism painting focuses on the representation of the real world.

Filippo Brunelleschi (1377-1446) was the first artist to have a theory about the method to use. He says his interest in mathematics led him to study the prospect, and he began to paint to apply the geometry.

The first book was written by Leone Battista Alberti (1404-1472), considered the theoretical genius mathematical perspective, who presented his ideas on "Della Painting" (1435).

Alberti proposed rules to paint what he sees an eye (aware that normal vision in both eyes see the same scene from different positions and the brain perceives depth by superimposing these two images, try to get the illusion of depth to base of light and shadows and intensity decrease). The method is based on a tool called the "Veil of Alberti". Its basic principle is the following: Consider a pyramid of rays from the eye of the painter and terminate at each point of the scene you want to paint. This pyramid call it projection ray. If between the scene and the eye is placed a glass screen, each ray determines a point on the glass thus forming a section. And this section creates in the eye the same image as the scene itself. Depending on the position of the screen, have different sections of the same object.

Alberti

Although many artists wrote about perspective, stand:

• Da Vinci said the painting should be an exact reproduction of reality and mathematical perspective it would. His writings on perspective are in their "Tratatto Della painting" (1651).
• Piero della Francesca established the mathematical principles of perspective in a fairly complete. His work "De prospectively pingendi" some progress contributed to the ideas of Alberti. Its procedures are useful for artists, but lack the rigor least some demonstrations that are simple constructions.

Projective Geometry