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# perspective

Visual artsIn**perspective**(Perspective,British: perspective) Is a general term for methods that visually express perspective.^{[1]}..In a narrow sense, the convergence of parallel lines was used in the perspective expression method.**Perspective projection**(British: perspective drawing)^{[2]}.

Especially in this paper, perspective projection (British: perspective drawing) Is explained.

## Overview

Humans can feel the depth of space from two-dimensional planes such as pictures and images.In visual arts, perspective is a method that makes a two-dimensional plane that originally does not have space feel space, that is, gives a sense of perspective.**Perspective projection**(British: perspective drawing),alias**Linear perspective**(British: Linear Perspective) Is a typical example, and is often called perspective.The figure drawn by perspective projection**Perspective**That.EnglishThen, "perspective", "perspective", "perspective", etc. are collectively called perspective.JapanNow, let ’s talk about perspective and perspective views.**Perth**Often referred to as. (Example: "Architectural perspective", "Perspective is tight", etc.)

In perspective, "to the human eye, parallel lines extending to the back converge to one point and appear (**Perspective projection**”)” Is used to create a sense of perspective by drawing converging parallel lines.As the parallel lines go deeper, the width becomes shorter, so in visual arts using perspective, "even objects of the same size"point of viewThe farther it is from, the smaller it is. "" Even if the length is the same, the length differs depending on the angle with the viewpoint (Abbreviation method) ”Appears.

There are various ways to achieve perspective.A painting,ComicIn, a point perspective method is often used in which a vanishing point is set and parallel lines in a specific direction are converged.Three-dimensional computer graphicsThen, not only parallel lines but the entire space is dropped into a two-dimensional plane by matrix operation.Perspective projectionI often get figures.写真To take a projection drawing with one viewpoint like the human eyePerspective projectionIt is a figure, and if there are parallel lines as a composition, the perspective projection is established.

As a perspective method other than perspective projection, draw the near clearly and draw the distance with indistinct and subdued saturation.**Aerial perspective**(Aerial perspective).

## Basic concept

Human capitalYou can feel the depth and three-dimensionality of the space even from the picture written on the plane ((English: depth perception）[1],Stereoscopic vision).Heuristics and visual studies have shown that various types of visual features produce depth perception, or perspective.By embedding these visual features in visual arts, you can give your work a strong perspective.Perspective is a general term for techniques and techniques that use visual features to give a sense of perspective.There are various perspectives depending on the visual features used and the drawing method at the time of expression.

The perspective projection (line perspective) is a human "two squeezing straight lines.**parallel**Feeling that, there**depth**Is based on the "feel" characteristic.When there are two lines that are not parallel as shown in the figure, humans tend to recognize them as parallel lines.Then, the depth is perceived in the direction in which these non-parallel parallel lines approach.Perspective projection is a technique that sublimates the characteristics of line segments that produce depth into detail and systematizes them.

It is the reason why you can feel the depth of parallel lines that are not parallel.**Incident light from parallel lines existing in space is not reflected in parallel by the eyes**Due to that.The human eye detects light incident from space like a camera.Here, it is assumed that there is a parallel line extending to the other side at the same height as the eyes (left in the figure).If you cut out the light from the parallel lines on a plane before it enters your eyes (obtain a projection drawing), you can see that the point in the back (blue) is reflected inside the point in the foreground (red).It is also assumed that this parallel line is below the line of sight (right side of the figure).From the side view, it can be seen that the point in the back (blue) is reflected on the line of sight side from the point in the foreground (red).In this way, the light from the parallel lines does not enter the eyes in parallel in the first place, but incidents closer to the center toward the back.therefore**The human brain perceives that the two lines are rather parallel when viewed at such an angle, and that an image closer to the center exists in the back.**..The processing performed in the brain is still unknown, but it is possible that two angled lines are detected and recognized as parallel, and parallel detection is performed after processing to correct this distortion in the brain. May have been done.In any case, the human who sees the space by the eyes recognizes the two angled lines as parallel and perceives the depth from there.

In perspective drawing, a perspective is given to the work by drawing a drawing with distortion similar to the projection drawing of space.That is, the basis of perspective is to capture the light passing through it on a projection plane placed in front of the viewpoint, which is similar to drawing the view seen through the windowpane directly on the surface of the windowpane.The figure copied on the glass reduces the three-dimensional scene and puts it on a two-dimensional plane.conversionIt will be the one that was done.If you prepare a picture written in perspective projection and place one eye exactly on the point set as the "eye" when drawing, you will see the same light as you see in the actual space. The brain recognizes parallel lines that are not parallel, which gives a sense of perspective from the picture.

Straight lines that are not parallel converge at the point at infinity, but this convergence point**Vanishing point**That is.It's easy to understand if you imagine two railroad tracks that disappear straight beyond the horizon (figure).Parallel lines at different angles converge to different vanishing points.

## History

### Early development

Prior to perspective, paintings and line drawings used to draw objects according to their spiritual subject.Especially in medieval art, painting emphasizes symbolism rather than realism, and does not draw people in different sizes according to distance, but the only way to express distance is to "hide a distant person behind the person in front." It was just that.

The earliest perspective was5th century BCAroundAncient greeceでStage artIt was used for.In order to give depth to the stage, he placed a flat panel and drew a deep picture on it.philosopher OfAnaxagorasとDemocritusIn that perspectiveGeometryI applied the theory.AlcibiadesIs said to have displayed such a perspective view in his house.EuclidEstablished a mathematical theory of perspective, which is modernDescriptive geometryThere is controversy and no established theory as to whether it is exactly the same as.

11st century OfPersian OfMathematicianWas also a philosopherIbn al-HaysumIs the light projected on the viewpoint in that workconeIt touches on forming, which was the most basic theory of realistically drawing an object.But Al-Hisam's interest is not paintingOpticsBecause of this, this theory was never used in painting.

The first time I used perspective expression since the Middle Ages13st century - 14st centuryItalian painterCimabue("Ognissanti Madonna^{[3]}"), Pietro Cavallini ("Birth of Our Lady^{[4]}”),Duccio di Buoninsegna("Ognissanti Madonna") And others.RenaissancePioneer ofGiotto di Bondone TheAlgebraI am trying a perspective projection using.But the problem with linear ratios is the distance between evenly spaced linears.sineDependently decreasing, to determine each linear ratioInductionIt is indispensable to apply the ratio.This is in the 20th centuryErwin PanofskyIt was solved for the first time by.Giotto wrote his work, "Jesus in front of High Priest Kayafa.^{[5]}I used my perspective for the first time.It was not the same as modern descriptive geometry, but it represented a decent sense of depth and was a major step forward in Western painting.Giotto's perspective is becoming more precise ("View of the Oratory")^{[6]}^{[7]}")^{[8]}Also, I accepted GiottoAmbrogio LorenzettiDraws the distant parallel lines disappearing at one point ("The Annunciation"^{[9]}")^{[10]}.

Expressions such as small drawings of things in the distance or parallel lines moving away from the painter approaching each other are also accepted in regions other than Italy ("Robert Campin"Melode altar painting"Yang van ake"Mr. and Mrs. Arnolfini statue""Lucca Madonna'^{[11]}).Early NetherlandishWas exported to Italy and influenced the Renaissance perspective of Florence.

### Mathematical basics

100 years after Giottothe 1400sbeginning,建築 家BrunelleschiOn the mirror surfaceFlorence OfbuildingI succeeded in demonstrating the perspective method by a geometrical method by copying the outline of.He noticed that the contours of every building were all concentrated on the horizon.So heCathedral of Santa Maria del FioreThe unfinished painting was depicted in accurate perspective, the painting was placed facing the entrance to the baptistery, and a mirror was placed in the opposite position.There is a small hole in the painting, and when you look into the small hole from the back of the painting, the inside of the baptistery "which should be unfinished" is reflected in the front mirror.It just looked like the real thing.

Shortly thereafter, all Florentine painters began to use geometric perspective.Above allDonatelloThe checkered floor of the stables, which he drew in "The Birth of Christ," is noteworthy.It was not strictly accurate, but was drawn in line with the basic principles of geometric perspective.All the straight lines converged to the vanishing point, and the straight line width narrowed by the distance was drawn accurately.This technique15st centuryIt has become an indispensable technique in Western art.Perspective has made it possible for paintings, which were previously a combination of disparate elements, to represent a unified scene.

As an actual work,彫刻Relief(1425 - )orMasaccioPainting (1426 -) Is the fastest.The perspective method has made it possible to express deeply while moving the three-dimensional world to the two-dimensional world.

Perspective art flourished rapidly in Florence, and some painters, such as Brunelleschi, understood its mathematical theory, but did not open it up.He is a mathematician to a friendToscanelliIt seems that it also helped to understand mathematics.Decades later Brunelleschi's friend and humanistAlbertiWrote a detailed dissertation on perspective drawing, "Painting Theory" (1435).The greatest achievement of this paper isConic projectionIt was not to show the difficult mathematical formula of, but to formulate and theorize the path of the projection plane and the light spot passing through it.He has two similarity triangles and an old-fashionedEuclidean geometryIt was shown that the coordinates to the projection plane can be calculated using.

1474,Piero della FrancescaIn his book, he showed how to apply perspective to all objects in the field of view.His book was the first to explain Alberti's mathematical commentary in a more understandable and illustrated manner.

The principle of perspective discovered in Florence has not left this place for a while,ItalyIt will be a little later that this great discovery that is happening in Japan will spread to painters in other countries.

### Leonardo da Vinci

Brunelleschi's perspective did not take into account objects that were very close to the point of view.Da VinciHe himself recalculated the trajectory of the ray exactly and built a more accurate one.Not only that, Da Vinci also made new discoveries.He combined geometric perspective with the concept of aerial perspective that "distant objects change color and blur boundaries."He realized that understanding of perspective was very important to art, "practice is built only on a strong theory. Perspective is its guide and entrance. Without perspective. There is nothing you can expect from painting. "

However, his perspective is erroneous because it has a stronger perspective when compared to the correct one.

### Changes in perspective before and after the Renaissance

Tokyo University of the ArtsHonorary professorIsShigeru TsujiIn his book "Discovery of Perspective", he named the perspective without a distance point before the Renaissance "Angel's Perspective" and the perspective with a distance point after the Renaissance "Earth Perspective".^{[10]}.

## Various projections

A perspective view using perspective can be drawn by the following method (projection).

- Sketch by hand (in art)
- Point perspective
- Use grid paper (grid) for fluoroscopy
- Perspective projectionOperation (eg: Three-dimensional computer graphics）
- Proportional compassUse tools such as (also with a ball scaler)

### Point perspective

Point-projection perspective is a technique that creates a sense of perspective by converging parallel lines to the vanishing point.A straight line with an angle (a straight line that is not parallel to the plane) with a perspective plane (a fictitious canvas placed in front of the viewpoint) has a depth, so it converges to the vanishing point when projected onto the perspective view.Then, the straight line group having the same angle, that is, the parallel straight line group converges to the same vanishing point.The point perspective projection is a projection that converges parallel lines to the vanishing point based on this fact.

#### One-point perspective

One-point perspective (British: one-point perspective) Is a projection that converges a group of parallel lines to one vanishing point.^{[12]}..Parallel lines are drawn so that they converge radially to one vanishing point.The one-point perspective method is used when there is a surface parallel to the perspective plane and the parallel line group extends from that surface to the back side.

Seiyo CityThe vanishing point is on the left side of the center of the US Museum.

#### Two-point perspective

Two-point perspective (two-point perspective)British: two-point perspective) Is a projection that converges two parallel lines with different angles to the vanishing point.It is used when one side is parallel to the perspective plane and the two straight lines intersecting it have an angle.When the viewpoint is rotated by one axis from the one-point perspective (example: when the building is viewed diagonally from the side), the two-point perspective is used.The vanishing point of a straight line parallel to the eye level (line of sight) exists on the eye level.

Former Main Building of Ministry of Justice There is a vanishing point outside the photo

#### Three-point perspective

Three-point perspective (British: three-point perspective) Is a projection that converges three parallel lines with different angles to the vanishing point.If none of the sides of the cube are parallel to the perspective plane, then three-point perspective is used (eg, looking at the building diagonally from the side, with additional elevation and depression).

Century Park Tower..View the object from diagonally below.

#### Zero perspective

The vanishing point exists when there is a straight line in the field of view that is not parallel to the screen.Therefore, even if a non-linear scene is copied on the canvas, there is no vanishing point, and a zero point perspective projection occurs.A typical example is the scenery of mountains.

As is clear from landscape photographs, the farther the mountain is, the smaller it is drawn to give a sense of perspective even in perspective projection with no vanishing point.

Shizuoka CityLandscape

#### Example: Rectangle in perspective view

As soon as you have a chess board, you'll know where the horizon and vanishing points of one-point perspective are.Chessboards provide a simple but effective technique.If you look horizontally into the squares of the chess board, it is the world of one-point perspective, and if you tilt the board a little to the left or right, the world of two-point perspective expands.If you tilt the board up and down, you can get a three-point perspective.

## Abbreviation method

The shortening method is a visual effect (or) that the object looks shorter than it actually is as it becomes diagonal to the line of sight.Optical illusion) Is used to project to two dimensions. The shortening method is a very important factor when perspectively projecting a three-dimensional object into two dimensions.However, there is also a shortening method that does not use the perspective projection method, for example.**Parallel projection**Is mentioned.

One of the parallel projection methods.Isometric projection (Isometric projection).

## Architectural perspective

BuildingConceptual drawingA bird's-eye view or a bird's-eye view drawn according to perspective is called an "architectural perspective" or "architectural perspective".Design drawingDraw a sketch based on, and in some cases even color it.You need to get the vanishing point exactly,Architectural course,Department of DesignRequires specialized knowledge such as.In recent years, CG perspectives created by 3D-CAD software have been widely used.

## Related concepts

### Aerial perspective

On the other hand, such parallel lines do not exist in natural landscapes, and even if the vanishing point is set, an accurate painting cannot be drawn.One of the effective methods for drawing nature is that the farther the object is, the more hazy it looks, instead of the linear perspective method (perspective method) as described above.**Aerial perspective**(Aerial perspective) (Example:Leonardo da VinciWork "Mona Lisa』Background).this isRenaissance periodPaintings and orientalInk paintingThis is a technique that is often seen in such cases.It is often confused with the aerial perspective, but in reality, the color perspective is used as part of the aerial perspective (eg, due to the influence of the atmosphere, the farther it is, the more bluish it is). It's a technique that is, not the same.

To get the same visual effect as when a human actually sees a solid,parallax,Depth of fieldIf the influences such as are excluded, it is sufficient to reproduce which color is visible in which direction (which light is incident from which direction).This effect can be completely obtained only when the picture drawn in perspective is placed on a plane and viewed from the same viewpoint as when the perspective is drawn.On the other hand, the outer peripheral portion of the perspective view drawn with a particularly large angle of view looks greatly distorted when viewed from different viewpoints.This is justCardiogramIt looks like the outer circumference of the is distorted.

A common misconception is that perspective is incomplete because it does not reproduce the distortion of the image on the retina by the human lens, which is incorrect.Distortion of the retina also occurs when viewing a picture, so if the picture reproduces the distortion of the retina, it will be doubly distorted when the picture is viewed.

Conducted a visual study of pilots in the 1950sJames GibsonRevealed that pilots must first perceive the background ground in order to fly.Based on Gibson's ground theory, thenFlight simulationAlongside angle perspective in computer graphics**Exercise perspective**Is used^{[13]}..In addition to depicting landscapes, motion perspective slows the movement of distant views such as mountains and clouds according to the focal point of the vector of the aircraft, and quickly draws the flow of the ground and targets in the near view, so that the observer can see his own speed. It gives perceptual information to judge the direction and so on.

### Reverse perspective, etc.

Perspective has changed from responding to vision to the act of representing vision in an interesting way by sandwiching a perspective map.The reverse perspective method, in which a distant object is large and a nearby object is small, a mixed perspective method with multiple vanishing points using 5 or 6 points, and the reverse vanishing point when drawing an object on the ceiling. So I started to increase the points,Hyperbola (hyperbola),parabola The hyperbola perspective method using (parabola) etc., the horizon curve division type angel perspective method, the straight line division type ground perspective method, etc. are currently showing the extent of expansion.In addition, a new perspective method based on the relationship between the Chinese perspective "San-en" (high distance = looking up high in the sky), (deep = looking deep into space), (heien = looking around the horizon), and compounding is also considered.In addition, the line structure state of perspective that is accidentally created from the imagination after drawing a line like a grid is also called (prospettiva accidentale), and it is also a pursuit of the fun of testing the imagination of perspective.

## References

**^**In a broad sense, this term is a general term for many other perspective expressions such as air perspective, color perspective, vanishing perspective, curved perspective, vertical perspective, superimposed perspective, and oblique perspective. It will be used. Perspective-Musashino Art University modeling file**^**In a narrow sense, it refers to the "line perspective" established during the Renaissance.Perspective-Musashino Art University modeling file**^**Ognissanti Madonna**^**Birth of Our Lady**^**Jesus before High Priest Kayafa**^**1**^**2**^**Hoffmann, Volker (2010) "Giotto and Renaissance Perspective",*Nexus Network Journal*, 12-1, pp.5-32, Basel: Springer.**^**Annunciation- ^
^{a}^{b}Shigeru Tsuji, "Discovery of Perspective", Gendai Kikakushitsu Office 1996 ISBN 978-4-7738-9615-2 **^**Elkins, James (1991) "On the Arnolfini Portrait and the Lucca Madonna: Did Jan van Eyck Have a Perspectival System?",*The Art Bulletin*, 73-1, pp.53-62, College Art Association.**^**"One-point perspective" with one vanishing point Perspective-MAU modeling file**^**Norihisa Kakinuma Hisao Ishizuka ・Akihito Suzuki(Edit) "Vision of Flight Simulator" "Physical Medicine Culture Theory: Senses and Desires" Keio University Press 2002,ISBN-4 7664-0924-8 pp. 421-433.

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