Perspective (graphical)

Magnification is the process of enlarging the apparent size, not physical size, of something. This enlargement is quantified by a size ratio called optical magnification. When this number is less than one, it refers to a reduction in size, sometimes called de-magnification.

Typically, magnification is related to scaling up visuals or images to be able to see more detail, increasing resolution, using microscope, printing techniques, or digital processing. In all cases, the magnification of the image does not change the perspective of the image.

The 15th century was the century which spans the Julian calendar dates from 1 January 1401 (represented by the Roman numerals MCDI) to 31 December 1500 (MD).

In Europe, the 15th century includes parts of the Late Middle Ages, the Early Renaissance, and the early modern period. Many technological, social and cultural developments of the 15th century can in retrospect be seen as heralding the "European miracle" of the following centuries. The architectural perspective, and the modern fields which are known today as banking and accounting were founded in Italy.

Proto-Cubism (also referred to as Protocubism, Early Cubism, and Pre-Cubism or Précubisme) is an intermediary transition phase in the history of art chronologically extending from 1906 to 1910. Evidence suggests that the production of proto-Cubist paintings resulted from a wide-ranging series of experiments, circumstances, influences and conditions, rather than from one isolated static event, trajectory, artist or discourse. With its roots stemming from at least the late 19th century, this period is characterized by a move towards the radical geometrization of form and a reduction or limitation of the color palette (in comparison with Fauvism). It is essentially the first experimental and exploratory phase of an art movement that would become altogether more extreme, known from the spring of 1911 as Cubism.

Proto-Cubist artworks typically depict objects in geometric schemas of cubic or conic shapes. The illusion of classical perspective is progressively stripped away from objective representation to reveal the constructive essence of the physical world (not just as seen). The term is applied not only to works of this period by Georges Braque and Pablo Picasso, but to a range of art produced in France during the early 1900s, by such artists as Juan Gris, Jean Metzinger, Albert Gleizes, Henri Le Fauconnier, Robert Delaunay, Fernand Léger, and to variants developed elsewhere in Europe. Proto-Cubist works embrace many disparate styles, and would affect diverse individuals, groups and movements, ultimately forming a fundamental stage in the history of modern art of the 20th-century.

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.

In mathematics, the concept of a projective space originated from the visual effect of perspective, where parallel lines seem to meet at infinity. A projective space may thus be viewed as the extension of a Euclidean space, or, more generally, an affine space with points at infinity, in such a way that there is one point at infinity of each direction of parallel lines.

This definition of a projective space has the disadvantage of not being isotropic, having two different sorts of points, which must be considered separately in proofs. Therefore, other definitions are generally preferred. There are two classes of definitions. In synthetic geometry, point and line are primitive entities that are related by the incidence relation "a point is on a line" or "a line passes through a point", which is subject to the axioms of projective geometry. For some such set of axioms, the projective spaces that are defined have been shown to be equivalent to those resulting from the following definition, which is more often encountered in modern textbooks.

Planar projections are the subset of 3D graphical projections constructed by linearly mapping points in three-dimensional space to points on a two-dimensional projection plane. The projected point on the plane is chosen such that it is collinear with the corresponding three-dimensional point and the centre of projection. The lines connecting these points are commonly referred to as projectors.

The centre of projection can be thought of as the location of the observer, while the plane of projection is the surface on which the two dimensional projected image of the scene is recorded or from which it is viewed (e.g., photographic negative, photographic print, computer monitor). When the centre of projection is at a finite distance from the projection plane, a perspective projection is obtained. When the centre of projection is at infinity, all the projectors are parallel, and the corresponding subset of planar projections are referred to as parallel projections.

Paul Cézanne (/seɪˈzæn/ say-ZAN, UK also /sɪˈzæn/ siz-AN, US also /seɪˈzɑːn/ say-ZAHN; French: [pɔl sezan]; Occitan: Pau Cesana; 19 January 1839 – 22 October 1906) was a French Post-Impressionist painter whose work introduced new modes of representation, influenced avant-garde artistic movements of the early 20th century and formed the bridge between late 19th-century Impressionism and early 20th-century Cubism.

While his early works were influenced by Romanticism—such as the murals in the Jas de Bouffan country house—and Realism, Cézanne arrived at a new pictorial language through intense examination of Impressionist forms of expression. He altered conventional approaches to perspective and broke established rules of academic art by emphasizing the underlying structure of objects in a composition and the formal qualities of art. Cézanne strived for a renewal of traditional design methods on the basis of the impressionistic colour space and colour modulation principles.

Jean Dominique Antony Metzinger (French: [mɛtsɛ̃ʒe]; 24 June 1883 – 3 November 1956) was a major 20th-century French painter, theorist, writer, critic and poet, who along with Albert Gleizes wrote the first theoretical work on Cubism. His earliest works, from 1900 to 1904, were influenced by the neo-Impressionism of Georges Seurat and Henri-Edmond Cross. Between 1904 and 1907, Metzinger worked in the Divisionist and Fauvist styles with a strong Cézannian component, leading to some of the first proto-Cubist works.

From 1908, Metzinger experimented with the faceting of form, a style that would soon become known as Cubism. His early involvement in Cubism saw him both as an influential artist and an important theorist of the movement. The idea of moving around an object in order to see it from different view-points is treated, for the first time, in Metzinger's Note sur la Peinture, published in 1910. Before the emergence of Cubism, painters worked from the limiting factor of a single view-point. Metzinger, for the first time, in Note sur la peinture, enunciated the interest in representing objects as remembered from successive and subjective experiences within the context of both space and time. Jean Metzinger and Albert Gleizes wrote the first major treatise on Cubism in 1912, entitled Du "Cubisme". Metzinger was a founding member of the Section d'Or group of artists.

Parallax is a displacement or difference in the apparent position of an object viewed along two different lines of sight and is measured by the angle or half-angle of inclination between those two lines. Due to foreshortening, nearby objects show a larger parallax than farther objects, so parallax can be used to determine distances.

To measure large distances, such as the distance of a planet or a star from Earth, astronomers use the principle of parallax. Here, the term parallax is the semi-angle of inclination between two sight-lines to the star, as observed when Earth is on opposite sides of the Sun in its orbit. These distances form the lowest rung of what is called "the cosmic distance ladder", the first in a succession of methods by which astronomers determine the distances to celestial objects, serving as a basis for other distance measurements in astronomy forming the higher rungs of the ladder.