Vanishing point in the context of "Projective space"

De pictura (English: "On Painting") is a treatise or commentarii written by the Italian humanist and artist Leon Battista Alberti. The first version, composed in Latin in 1435, was not published until 1450. It is one of his three treatises on art; the other two are De statua and De re aedificatoria, that would form the Renaissance concept for the fine arts: painting, sculpture, and architecture.

Linear or point-projection perspective (from Latin perspicere 'to see through') is one of two types of graphical projection perspective in the graphic arts; the other is parallel projection. Linear perspective is an approximate representation, generally on a flat surface, of an image as it is seen by the eye. Perspective drawing is useful for representing a three-dimensional scene in a two-dimensional medium, like paper. It is based on the optical fact that for a person an object looks N times (linearly) smaller if it has been moved N times further from the eye than the original distance was.

In mathematics, a projective plane is a geometric structure that extends the concept of a plane. In the ordinary Euclidean plane, two lines typically intersect at a single point, but there are some pairs of lines (namely, parallel lines) that do not intersect. A projective plane can be thought of as an ordinary plane equipped with additional "points at infinity" where parallel lines intersect. Thus any two distinct lines in a projective plane intersect at exactly one point.

Renaissance artists, in developing the techniques of drawing in perspective, laid the groundwork for this mathematical topic. The archetypical example is the real projective plane, also known as the extended Euclidean plane. This example, in slightly different guises, is important in algebraic geometry, topology and projective geometry where it may be denoted variously by PG(2, R), RP, or P₂(R), among other notations. There are many other projective planes, both infinite, such as the complex projective plane, and finite, such as the Fano plane.

The radiant or apparent radiant of a meteor shower is the celestial point in the sky from which (from the point of view of a terrestrial observer) the paths of meteors appear to originate. The Perseids, for example, are meteors which appear to come from a point within the constellation of Perseus.

Meteor paths appear at random locations in the sky, but the apparent paths of two or more meteors from the same shower will diverge from the radiant. The radiant is the vanishing point of the meteor paths, which are parallel lines in three-dimensional space, as seen from the perspective of the observer, who views a two-dimensional projection against the sky. The geometric effect is identical to crepuscular rays, where parallel sunbeams appear to diverge.

Paolo Uccello (/uːˈtʃɛloʊ/ oo-CHEL-oh, Italian: [ˈpaːolo utˈtʃɛllo]; 1397 – 10 December 1475), born Paolo di Dono, was an Italian Renaissance painter and mathematician from Florence who was notable for his pioneering work on visual perspective in art. In his book Lives of the Most Excellent Painters, Sculptors, and Architects, Giorgio Vasari wrote that Uccello was obsessed by his interest in perspective and would stay up all night in his study trying to grasp the exact vanishing point. Uccello used perspective to create a feeling of depth in his paintings. His best known works are the three paintings representing the battle of San Romano, which were wrongly entitled the Battle of Sant'Egidio of 1416 for a long period of time.

Paolo worked in the Late Gothic tradition, emphasizing colour and pageantry rather than the classical realism that other artists were pioneering. His style is best described as idiosyncratic, and he left no school of followers. He has had some influence on twentieth-century art and literary criticism (e.g., in the Vies imaginaires by Marcel Schwob, Uccello le poil by Antonin Artaud and O Mundo Como Ideia by Bruno Tolentino).

Dieric Bouts (born c. 1415 – 6 May 1475) was an Early Netherlandish painter. Bouts may have studied under Rogier van der Weyden, and his work was influenced by van der Weyden and Jan van Eyck. He worked in Leuven from 1457 (or possibly earlier) until his death in 1475. His name also appears at various museums and institutions as Dirk Bouts.

Bouts was among the first northern painters to demonstrate the use of a single vanishing point (as illustrated in his Last Supper).

A sunbeam, in meteorological optics, is a beam of sunlight that appears to radiate from the position of the Sun. Shining through openings in clouds or between other objects such as mountains and buildings, these beams of particle-scattered sunlight are essentially parallel shafts separated by darker shadowed volumes. Their apparent convergence in the sky is a visual illusion from linear perspective. The same illusion causes the apparent convergence of parallel lines on a long straight road or hallway at a distant vanishing point. The scattering particles that make sunlight visible may be air molecules or particulates.