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Perspective (graphical)

Perspective Linear or Point projection perspective is one of two types of Graphical projection perspective in the graphic arts. Linear perspective is an approximate representation on a flat surface, of an image as it is seen by the eye; the most characteristic features of Linear perspective are that objects appear smaller as their distance from the observer increases. All objects will recede to points in the distance along the horizon line, but above and below the horizon line depending on view used. Italian Renaissance painters and architects including Filippo Brunelleschi, Paolo Uccello, Piero della Francesca and Luca Pacioli studied linear perspective, wrote treatises on it, incorporated it into their artworks, thus contributing to the mathematics of art. Perspective works by representing the light that passes from a scene through an imaginary rectangle, to the viewer's eye, as if a viewer were looking through a window and painting what is seen directly onto the windowpane. If viewed from the same spot as the windowpane was painted, the painted image would be identical to what was seen through the unpainted window.

Each painted object in the scene is thus a flat, scaled down version of the object on the other side of the window. Because each portion of the painted object lies on the straight line from the viewer's eye to the equivalent portion of the real object it represents, the viewer sees no difference between the painted scene on the windowpane and the view of the real scene. All perspective drawings assume. Objects are scaled relative to that viewer. An object is not scaled evenly: a circle appears as an ellipse and a square can appear as a trapezoid; this distortion is referred to as foreshortening. Perspective drawings have a horizon line, implied; this line, directly opposite the viewer's eye, represents objects infinitely far away. They have shrunk, to the infinitesimal thickness of a line, it is analogous to the Earth's horizon. Any perspective representation of a scene that includes parallel lines has one or more vanishing points in a perspective drawing. A one-point perspective drawing means that the drawing has a single vanishing point directly opposite the viewer's eye and on the horizon line.

All lines parallel with the viewer's line of sight recede to the horizon towards this vanishing point. This is the standard "receding railroad tracks" phenomenon. A two-point drawing would have lines parallel to two different angles. Any number of vanishing points are possible in a drawing, one for each set of parallel lines that are at an angle relative to the plane of the drawing. Perspectives consisting of many parallel lines are observed most when drawing architecture; because it is rare to have a scene consisting of lines parallel to the three Cartesian axes, it is rare to see perspectives in practice with only one, two, or three vanishing points. Of the many types of perspective drawings, the most common categorizations of artificial perspective are one-, two- and three-point; the names of these categories refer to the number of vanishing points in the perspective drawing. Aerial perspective depends on distant objects being more obscured by atmospheric elements, so more distant objects are less visible to the viewer.

In general, distant objects become lighter in darker at night as they recede. Aerial perspective can be combined with, but does not depend on, one or more vanishing points. A drawing has one-point perspective; this type of perspective is used for images of roads, railway tracks, hallways, or buildings viewed so that the front is directly facing the viewer. Any objects that are made up of lines either directly parallel with the viewer's line of sight or directly perpendicular can be represented with one-point perspective; these parallel lines converge at the vanishing point. One-point perspective exists when the picture plane is parallel to two axes of a rectilinear scene—a scene, composed of linear elements that intersect only at right angles. If one axis is parallel with the picture plane all elements are either parallel to the picture plane or perpendicular to it. All elements that are parallel to the picture plane are drawn as parallel lines. All elements that are perpendicular to the picture plane converge at a single point on the horizon.

Examples of one-point perspective A drawing has two-point perspective when it contains two vanishing points on the horizon line. In an illustration, these vanishing points can be placed arbitrarily along the horizon. Two-point perspective can be used to draw the same objects as one-point perspective, rotated: looking at the corner of a house, or at two forked roads shrinking into the distance, for example. One point represents one set of parallel lines, the other point represents the other. Seen from the corner, one wall of a house would recede towards one vanishing point while the other wall recedes towards the

2020 Copa Libertadores qualifying stages

The 2020 Copa Libertadores qualifying stages were played from 21 January to 27 February 2020. A total of 19 teams competed in the qualifying stages to decide four of the 32 places in the group stage of the 2020 Copa Libertadores; the draw for the qualifying stages was held on 17 December 2019, 20:30 PYST, at the CONMEBOL Convention Centre in Luque, Paraguay. Teams were seeded by their CONMEBOL ranking of the Copa Libertadores as of 15 December 2019, taking into account the following three factors: Performance in the last 10 years, taking into account Copa Libertadores results in the period 2010–2019 Historical coefficient, taking into account Copa Libertadores results in the period 1960–2009 Local tournament champion, with bonus points awarded to domestic league champions of the last 10 yearsFor the first stage, the six teams were drawn into three ties, with the teams from Pot 1 hosting the second leg. Notes For the second stage, the 16 teams were drawn into eight ties, with the teams from Pot 1 hosting the second leg.

Teams from the same association could not be drawn into the same tie, excluding the three winners of the first stage, which were allocated to Pot 2 and whose identity was not known at the time of the draw, could be drawn into the same tie with another team from the same association. Notes For the third stage, the eight winners of the second stage were allocated without any draw into the following four ties, with the team in each tie with the higher CONMEBOL ranking hosting the second leg; as their identity was not known at the time of the draw, they could be drawn into the same tie with another team from the same association. Second stage winner C1 vs. Second stage winner C8 Second stage winner C2 vs. Second stage winner C7 Second stage winner C3 vs. Second stage winner C6 Second stage winner C4 vs. Second stage winner C5 In the qualifying stages, each tie is played on a home-and-away two-legged basis. If tied on aggregate, the away goals rule will be used. If still tied, extra time will not be played, the penalty shoot-out will be used to determine the winner..

The qualifying stages are structured as follows: First stage: The three winners of the first stage advance to the second stage to join the 13 teams which are given byes to the second stage. Second stage: The eight winners of the second stage advance to the third stage. Third stage: The four winners of the third stage advance to the group stage to join the 28 direct entrants; the two best teams eliminated in the third stage enter the Copa Sudamericana second stage. The bracket was decided based on the first stage draw and second stage draw, held on 17 December 2019; the first legs were played on 21–22 January, the second legs were played on 28–29 January 2020. Guaraní advanced to the second stage. Universitario advanced to the second stage. Barcelona advanced to the second stage; the first legs were played on 4–6 February, the second legs were played on 11–13 February 2020. Cerro Porteño advanced to the third stage. Palestino advanced to the third stage. Independiente Medellín advanced to the third stage.

Deportes Tolima advanced to the third stage. Internacional advanced to the third stage. Tied 2 -- 2 on aggregate, Atlético Tucumán advanced to the third stage. Tied 2 -- 2 on aggregate, Guaraní advanced to the third stage. Barcelona advanced to the third stage; the first legs were played on 18–20 February, the second legs were played on 25–27 February 2020. Barcelona advanced to the group stage. Guaraní advanced to the group stage. Tied 1 -- 1 on aggregate, Independiente Medellín advanced to the group stage. Internacional advanced to the group stage; the two best teams eliminated in the third stage entered the Copa Sudamericana second stage. Only matches in the third stage were considered for the ranking of teams. CONMEBOL Libertadores 2020, CONMEBOL.com

Defender M

TenCate Defender M is a flame-resistant fabric used by both the United States Army and Marine Corps as the uniform material for ground troops in Iraq and Afghanistan because of new war threats like improvised explosive devices. The fabric has a proprietary blend of fibers which provides intrinsic flame-resistant qualities which protect soldiers from flame and high-temperature heat. Mike Sloane of PEO Soldier, the U. S. Army’s acquisition organization, “The burn rate has gone down significantly. We find that the soldiers who were wearing flame-resistant uniforms have sustained nearly no burns.” TenCate Defender M was invented in 2006 in response to increased burn threats in combat. After extensive evaluation, Defender M was selected for the Fire Resistant Army Combat Uniform and the Marine Corp’s Flame Resistant Organizational Gear programs in 2007. TenCate Defender M is worn by United States deployed ground troops and provides flame protection with fabric that self-extinguishes itself when exposed to fire or flame.

The fabric is composed of stable polymers that do not react with other substances, therefore, self-extinguishes when exposed to fire. The fabric does not melt or drip — which ensures that the fabric will not stick to skin and or intensify injury. In addition to being flame resistant, Defender M is lightweight and breathable; the fabric wicks away perspiration. The flame-resistant qualities of Defender M do not wash or wear out. Buy-American vs. Safety makes for battle over military uniforms, CNN, August 6, 2009 Interview with Georgia National Guard, Sgt. Nick Pence about ACU, Fox News Channel 2, July 6, 2010 IHS Jane's Defense & Security Intelligence & Analysis, Tencate Company Profile, 2011 Tencate Defender M