Staircase in two-point perspective.

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Graphical projection
Planar Parallel projection Orthographic projection Multiviews Plan, or floor plan Section Elevation Auxiliary Axonometric projection (i.e. pictorials) Isometric projection Dimetric projection Trimetric projection Oblique projection Cavalier projection Cabinet projection Perspective projection Linear perspective One-point perspective Two-point perspective Three-point perspective Zero-point perspective Curvilinear perspective Reverse perspective
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Views Bird's-eye view/Aerial view Detail view 3/4 perspective Cutaway drawing Exploded view drawing Fisheye Fixed 3D Panorama Top-down perspective Worm's-eye view Zoom
Topics Computer graphics Computer-aided design Descriptive geometry Engineering drawing Foreshortening Map projection Projective geometry Technical drawing Vanishing point Video game graphics
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Perspective (from Latin perspicere, to see through) in the graphic arts, such as drawing, is an approximate representation, on a flat surface (such as paper), of an image as it is seen by the eye. The two most characteristic features of perspective are that objects are drawn:

• Smaller as their distance from the observer increases
• Foreshortened: the size of an object's dimensions along the line of sight are relatively shorter than dimensions across the line of sight

Overview[link]

A cube in two-point perspective.

Linear perspective always works by representing the light that passes from a scene through an imaginary rectangle (the painting), to the viewer's eye. It is similar to a viewer 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 a flat, scaled down version of the object on the other side of the window.^[1] 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 cannot perceive (sans depth perception) any difference between the painted scene on the windowpane and the view of the real scene. All perspective drawings assume the viewer is a certain distance away from the drawing. Objects are scaled relative to that viewer. Additionally, an object is often not scaled evenly: a circle often 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, which is often implied. This line, directly opposite the viewer's eye, represents objects infinitely far away. They have shrunk, in the distance, to the infinitesimal thickness of a line. It is analogous to (and named after) 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, usually (though not necessarily) directly opposite the viewer's eye and usually (though not necessarily) 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 often when drawing architecture (architecture frequently uses lines parallel to the x, y, and z axes). Because it is rare to have a scene consisting solely of lines parallel to the three Cartesian axes (x, y, and z), it is rare to see perspectives in practice with only one, two, or three vanishing points; even a simple house frequently has a peaked roof which results in a minimum of six sets of parallel lines, in turn corresponding to up to six vanishing points.

In contrast, natural scenes often do not have any sets of parallel lines. Such a perspective would thus have no vanishing points.

History[link]

Early history[link]

The earliest art paintings and drawings typically sized objects and characters hierarchically according to their spiritual or thematic importance, not their distance from the viewer, and did not use foreshortening. The most important figures are often shown as the highest in a composition, also from hieratic motives, leading to the "vertical perspective", common in the art of Ancient Egypt, where a group of "nearer" figures are shown below the larger figure or figures. The only method to indicate the relative position of elements in the composition was by overlapping, of which much use is made in works like the Parthenon Marbles.

15th century illustration from the Old French translation of William of Tyre's Histoire d'Outremer. There is clearly a general attempt to reduce the size of more distant elements, but unsystematically. Sections of the composition are at a similar scale, with relative distance shown by overlapping, foreshortening, and further objects being higher than nearer ones, though the workmen at left do show finer adjustment of size. But this is abandoned on the right where the most important figure is much larger than the mason. Rectangular buildings, and the blocks of stone are shown obliquely.

Geometrically incorrect attempt at perspective in a 1614 painting of Old St Paul's Cathedral. (Society of Antiquaries)

Systematic attempts to evolve a system of perspective are usually considered to have begun around the 5th century B.C. in the art of Ancient Greece, as part of a developing interest in illusionism allied to theatrical scenery and detailed within Aristotle's Poetics as 'skenographia': Using flat panels on a stage to give the illusion of depth.^[2] The philosophers Anaxagoras and Democritus worked out geometric theories of perspective for use with skenographia. Alcibiades had paintings in his house designed based on skenographia, thus this art was not confined merely to the stage. Euclid's Optics introduced a mathematical theory of perspective; however, there is some debate over the extent to which Euclid's perspective coincides with a modern mathematical definition of perspective.

By the later periods of antiquity, artists, especially those in less popular traditions, were well aware that distant objects could be shown smaller than those close at hand for increased illusionism, but whether this convention was actually used in a work depended on many factors. Some of the paintings found in the ruins of Pompeii show a remarkable realism and perspective for their time;^[3] it has been claimed that comprehensive systems of perspective were evolved in antiquity, but most scholars do not accept this. Hardly any of the many works where such a system would have been used have survived. A passage in Philostratus suggests that classical artists and theorists thought in terms of "circles" at equal distance from the viewer, like a classical semi-circular theatre seen from the stage.^[4] The roof beams in rooms in the Vatican Virgil, from about 400 AD, are shown converging, more or less, on a common vanishing point, but this is not systematically related to the rest of the composition.^[5] In the Late Antique period use of perspective techniques declined. The art of the new cultures of the Migration Period had no tradition of attempting compositions of large numbers of figures and Early Medieval art was slow and inconsistent in relearning the convention from classical models, though the process can be seen underway in Carolingian art.

European Medieval artists were aware of the general principle of varying the relative size of elements according to distance, but even more than classical art was perfectly ready to override it for other reasons. Buildings were often shown obliquely according to a particular convention. The use and sophistication of attempts to convey distance increased steadily during the period, but without a basis in a systematic theory. Byzantine art was also aware of these principles, but also had the reverse perspective convention for the setting of principal figures.

Giotto attempted drawings in perspective using an algebraic method to determine the placement of distant lines. The problem with using a linear ratio in this manner is that the apparent distance between a series of evenly spaced lines actually falls off with a sine dependence. To determine the ratio for each succeeding line, a recursive ratio must be used.^[6]

One of Giotto's first uses of his algebraic method of perspective was Jesus Before Caiaphas. Although the picture does not conform to the modern, geometrical method of perspective, it does give a considerable illusion of depth, and was a large step forward in Western art.^{[citation needed]}

With the exception of dice,^[7] heraldry typically ignores perspective in the treatment of charges, though sometimes in later centuries charges are specified as in perspective.

Perspective study of a vase by Paolo Uccello (Galleria degli Uffizi, Gabinetto dei Disegni)

Renaissance : Mathematical basis[link]

This section may contain inappropriate or misinterpreted citations that do not verify the text. Please help improve this article by checking for inaccuracies. (help, talk, get involved!) (September 2010)

Prior to the Renaissance, Alhazen (al-Hasan Ibn al-Haytham, d. ca. 1041 AD), in his Book of Optics (Kitab al-manazir; known in Latin as De aspectibus or Perspectiva, written in 1021), explained that light projects conically into the eye.^[8] Alhazen's geometrical, physical, physio-psychological optics resolved in this the ancient dispute between the mathematicians (Ptolemaic and Euclidean) and the physicists (Aristotelian) over the nature of vision and light. He also showed that vision is not merely a phenomenon of pure sensation (namely what results from the introduction of light rays into the eyes), but that it involves the faculties of judgment, imagination and memory.^[9] Alhazen's geometrical model of the cone of vision was theoretically sufficient to translate visible objects within a given setting into a painting, and this was also supported by his experimental affirmation of the visibility of spatial depth; hence of offering a proper ground for the idea of perspective.^[10] Moreover, Alhazen presented a geometrical conception of place as spatial extension (a postulated void), and he refuted the Aristotelian account of topos as a surface of containment. Alhazen's mathematical definition of place was more akin to Plato's notion of Khôra or Chora as 'space', yet conceived on pure geometric grounds to facilitate the use of projections.^[11] In all of this, Alhazen was concerned with optics, with vision, light and the nature of colour, as well as with experimentation and the use of optical instruments, and not with painting as such. Conical translations are mathematically difficult, so a drawing constructed using them would be incredibly time consuming. However, what Alhazen named a cone of vision (makhrut al-shu'a') corresponded also with the idea of a pyramid of vision, hence, offering a model that can be more easily projected in orthogonal drawings of side views and top views that are needed in the geometric construction of perspective.

By the 14th century, Alhazen's Book of Optics was available in Italian translation, entitled Deli Aspecti. The Renaissance artist Lorenzo Ghiberti relied heavily upon this work, quoting it "verbatim and at length" while framing his account of art and its aesthetic imperatives in the “Commentario terzo.” Alhazen’s work was thus "central to the development of Ghiberti’s thought about art and visual aesthetics" and "may well have been central to the development of artificial perspective in early Renaissance Italian painting."^{[12][citation needed]}

In about 1413 a contemporary of Ghiberti, Filippo Brunelleschi, demonstrated the geometrical method of perspective, used today by artists, by painting the outlines of various Florentine buildings onto a mirror. When the building's outline was continued, he noticed that all of the lines converged on the horizon line. According to Vasari, he then set up a demonstration of his painting of the Baptistery in the incomplete doorway of the Duomo. He had the viewer look through a small hole on the back of the painting, facing the Baptistery. He would then set up a mirror, facing the viewer, which reflected his painting. To the viewer, the painting of the Baptistery and the Baptistery itself were nearly indistinguishable.

Soon after, nearly every artist in Florence and in Italy used geometrical perspective in their paintings,^[13] notably Masolino da Panicale and Donatello. Donatello started sculpting elaborate checkerboard floors into the simple manger portrayed in the birth of Christ. Although hardly historically accurate, these checkerboard floors obeyed the primary laws of geometrical perspective: the lines converged approximately to a vanishing point, and the rate at which the horizontal lines receded into the distance was graphically determined. This became an integral part of Quattrocento art. Melozzo da Forlì first used the technique of upward foreshortening (in Rome, Loreto, Forlì and others), and was celebrated for that. Not only was perspective a way of showing depth, it was also a new method of composing a painting. Paintings began to show a single, unified scene, rather than a combination of several.

Melozzo's usage of upward foreshortening in his frescoes at Loreto.

Pietro Perugino's usage of perspective in this fresco at the Sistine Chapel (1481–82) helped bring the Renaissance to Rome.

As shown by the quick proliferation of accurate perspective paintings in Florence, Brunelleschi likely understood (with help from his friend the mathematician Toscanelli),^[14] but did not publish, the mathematics behind perspective. Decades later, his friend Leon Battista Alberti wrote De pictura (1435/1436), a treatise on proper methods of showing distance in painting. Alberti's primary breakthrough was not to show the mathematics in terms of conical projections, as it actually appears to the eye. Instead, he formulated the theory based on planar projections, or how the rays of light, passing from the viewer's eye to the landscape, would strike the picture plane (the painting). He was then able to calculate the apparent height of a distant object using two similar triangles. The mathematics behind similar triangles is relatively simple, having been long ago formulated by Euclid. In viewing a wall, for instance, the first triangle has a vertex at the user's eye, and vertices at the top and bottom of the wall. The bottom of this triangle is the distance from the viewer to the wall. The second, similar triangle, has a point at the viewer's eye, and has a length equal to the viewer's eye from the painting. The height of the second triangle can then be determined through a simple ratio, as proven by Euclid. Alberti was also trained in the science of optics through the school of Padua and under the influence of Biagio Pelacani da Parma who studied Alhazen's Optics (see what was noted above in this regard with respect to Ghiberti).

Piero della Francesca elaborated on Della Pittura in his De Prospectiva Pingendi in the 1470s. Alberti had limited himself to figures on the ground plane and giving an overall basis for perspective. Della Francesca fleshed it out, explicitly covering solids in any area of the picture plane. Della Francesca also started the now common practice of using illustrated figures to explain the mathematical concepts, making his treatise easier to understand than Alberti's. Della Francesca was also the first to accurately draw the Platonic solids as they would appear in perspective.

Perspective remained, for a while, the domain of Florence. Jan van Eyck, among others, was unable to create a consistent structure for the converging lines in paintings, as in London's The Arnolfini Portrait, because he was unaware of the theoretical breakthrough just then occurring in Italy. However he achieved very subtle effects by manipulations of scale in his interiors. Gradually, and partly through the movement of academies of the arts, the Italian techniques became part of the training of artists across Europe, and later other parts of the world.

Present : Computer graphics[link]

3-D computer games and ray-tracers often use a modified version of perspective. Like the painter, the computer program is generally not concerned with every ray of light that is in a scene. Instead, the program simulates rays of light traveling backwards from the monitor (one for every pixel), and checks to see what it hits. In this way, the program does not have to compute the trajectories of millions of rays of light that pass from a light source, hit an object, and miss the viewer.

CAD software, and some computer games (especially games using 3-D polygons) use linear algebra, and in particular matrix multiplication, to create a sense of perspective. The scene is a set of points, and these points are projected to a plane (computer screen) in front of the view point (the viewer's eye). The problem of perspective is simply finding the corresponding coordinates on the plane corresponding to the points in the scene. By the theories of linear algebra, a matrix multiplication directly computes the desired coordinates, thus bypassing any descriptive geometry theorems used in perspective drawing.

Types of perspective[link]

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.

One-point perspective[link]

One-Point Perspective.

One vanishing point is typically used for 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 (the railroad slats) can be represented with one-point perspective.

One-point perspective exists when the painting plate (also known as the picture plane) is parallel to two axes of a rectilinear (or Cartesian) scene — a scene which is composed entirely of linear elements that intersect only at right angles. If one axis is parallel with the picture plane, then all elements are either parallel to the painting plate (either horizontally or vertically) or perpendicular to it. All elements that are parallel to the painting plate are drawn as parallel lines. All elements that are perpendicular to the painting plate converge at a single point (a vanishing point) on the horizon.

Some examples:

• Perspectivephoto.jpg
• 
• 

Two-point perspective[link]

Two-Point Perspective.

Two-point perspective can be used to draw the same objects as one-point perspective, rotated: looking at the corner of a house, or looking at two forked roads shrink into the distance, for example. One point represents one set of parallel lines, the other point represents the other. Looking at a house from the corner, one wall would recede towards one vanishing point, the other wall would recede towards the opposite vanishing point.

Two-point perspective exists when the painting plate is parallel to a Cartesian scene in one axis (usually the z-axis) but not to the other two axes. If the scene being viewed consists solely of a cylinder sitting on a horizontal plane, no difference exists in the image of the cylinder between a one-point and two-point perspective.

Two-point perspective has one set of lines parallel to the picture plane and two sets oblique to it. Parallel lines oblique to the picture plane converge to a vanishing point,which means that this set-up will require two vanishing points.

Three-point perspective[link]

Three-Point Perspective

Three-point perspective rendered from computer model by "Noel" from Google 3D Warehouse.
Rendered using IRender nXt.

Three-point perspective is usually used for buildings seen from above (or below). In addition to the two vanishing points from before, one for each wall, there is now one for how those walls recede into the ground. This third vanishing point will be below the ground. Looking up at a tall building is another common example of the third vanishing point. This time the third vanishing point is high in space.

Three-point perspective exists when the perspective is a view of a Cartesian scene where the picture plane is not parallel to any of the scene's three axes. Each of the three vanishing points corresponds with one of the three axes of the scene. Image constructed using multiple vanishing points.

One-point, two-point, and three-point perspectives appear to embody different forms of calculated perspective. The methods required to generate these perspectives by hand are different. Mathematically, however, all three are identical: The difference is simply in the relative orientation of the rectilinear scene to the viewer.

Four-point perspective[link]

Four-point perspective, also called infinite-point perspective, is the curvilinear variant of two-point perspective. As the result when made into an infinite point version (i.e. when the amount of vanishing points exceeds the minimum amount required), a four point perspective image becomes a panorama that can go to a 360 degree view and beyond - when going beyond the 360 degree view the artist might depict an "impossible" room as the artist might depict something new when it's supposed to show part of what already exists within those 360 degrees. This elongated frame can be used both horizontally and vertically and when used vertically can be described as an image that depicts both a worm's- and bird's-eye view of a scene at the same time.

As all other foreshortened variants of perspective (respectively one- to six-point perspective), it starts off with a horizon line, followed by four equally spaced vanishing points to delineate four vertical lines created in a 90 degree relation to the horizon line.

The vanishing points made to create the curvilinear orthogonals are thus made ad hoc on the four vertical lines placed on the opposite side of the horizon line. The only dimension not foreshortened in this type of perspective being the rectilinear and parallel lines at a 90 degree angle to the horizon line - similar to the vertical lines used in two-point perspective.

Zero-point perspective[link]

Because vanishing points exist only when parallel lines are present in the scene, a perspective without any vanishing points ("zero-point" perspective) occurs if the viewer is observing a nonlinear scene. The most common example of a nonlinear scene is a natural scene (e.g., a mountain range) which frequently does not contain any parallel lines. A perspective without vanishing points can still create a sense of "depth," as is clearly apparent in a photograph of a mountain range (more distant mountains have smaller scale features).

Other varieties of linear perspective[link]

One-point, two-point, and three-point perspective are dependent on the structure of the scene being viewed. These only exist for strict Cartesian (rectilinear) scenes. By inserting into a Cartesian scene a set of parallel lines that are not parallel to any of the three axes of the scene, a new distinct vanishing point is created. Therefore, it is possible to have an infinite-point perspective if the scene being viewed is not a Cartesian scene but instead consists of infinite pairs of parallel lines, where each pair is not parallel to any other pair.

A: No perspective foreshortening, and B: Perspective foreshortening

Foreshortening[link]

Foreshortening refers to the visual effect or optical illusion that an object or distance appears shorter than it actually is because it is angled toward the viewer.

Although foreshortening is an important element in art where visual perspective is being depicted, foreshortening occurs in other types of two-dimensional representations of three-dimensional scenes. Some other types where foreshortening can occur include oblique parallel projection drawings.

Figure F1 shows two different projections of a stack of two cubes, illustrating oblique parallel projection foreshortening ("A") and perspective foreshortening ("B").

Foreshortening also occurs when imaging rugged terrain using Synthetic Aperture Radar systems.

This technique was often used in Renaissance paintings.

Methods of construction[link]

Several methods of constructing perspectives exist, including:

• Freehand sketching (common in art)
• Graphically constructing (once common in architecture)
• Using a perspective grid
• Computing a perspective transform (common in 3D computer applications)
• Mimicry using tools such as a proportional divider (sometimes called a variscaler)

Example[link]

One of the most common, and earliest, uses of geometrical perspective is a checkerboard floor. It is a simple but striking application of one-point perspective. Many of the properties of perspective drawing are used while drawing a checkerboard. The checkerboard floor is, essentially, just a combination of a series of squares. Once a single square is drawn, it can be widened or subdivided into a checkerboard. Where necessary, lines and points will be referred to by their colors in the diagram.

To draw a square in perspective, the artist starts by drawing a horizon line (black) and determining where the vanishing point (green) should be. The higher up the horizon line is, the lower the viewer will appear to be looking, and vice versa. The more off-center the vanishing point, the more tilted the square will be. Because the square is made up of right angles, the vanishing point should be directly in the middle of the horizon line. A rotated square is drawn using two-point perspective, with each set of parallel lines leading to a different vanishing point.

The foremost edge of the (orange) square is drawn near the bottom of the painting. Because the viewer's picture plane is parallel to the bottom of the square, this line is horizontal. Lines connecting each side of the foremost edge to the vanishing point are drawn (in grey). These lines give the basic, one point "railroad tracks" perspective. The closer it is the horizon line, the farther away it is from the viewer, and the smaller it will appear. The farther away from the viewer it is, the closer it is to being perpendicular to the picture plane.

A new point (the eye) is now chosen, on the horizon line, either to the left or right of the vanishing point. The distance from this point to the vanishing point represents the distance of the viewer from the drawing. If this point is very far from the vanishing point, the square will appear squashed, and far away. If it is close, it will appear stretched out, as if it is very close to the viewer.

A line connecting this point to the opposite corner of the square is drawn. Where this (blue) line hits the side of the square, a horizontal line is drawn, representing the farthest edge of the square. The line just drawn represents the ray of light traveling from the farthest edge of the square to the viewer's eye. This step is key to understanding perspective drawing. The light that passes through the picture plane obviously can not be traced. Instead, lines that represent those rays of light are drawn on the picture plane. In the case of the square, the side of the square also represents the picture plane (at an angle), so there is a small shortcut: when the line hits the side of the square, it has also hit the appropriate spot in the picture plane. The (blue) line is drawn to the opposite edge of the foremost edge because of another shortcut: since all sides are the same length, the foremost edge can stand in for the side edge.

Original formulations used, instead of the side of the square, a vertical line to one side, representing the picture plane. Each line drawn through this plane was identical to the line of sight from the viewer's eye to the drawing, only rotated around the y-axis ninety degrees. It is, conceptually, an easier way of thinking of perspective. It can be easily shown that both methods are mathematically identical, and result in the same placement of the farthest side (see Panofsky).

Limitations[link]

Plato was one of the first to discuss the problems of perspective. "Thus (through perspective) every sort of confusion is revealed within us; and this is that weakness of the human mind on which the art of conjuring and of deceiving by light and shadow and other ingenious devices imposes, having an effect upon us like magic... And the arts of measuring and numbering and weighing come to the rescue of the human understanding—there is the beauty of them—and the apparent greater or less, or more or heavier, no longer have the mastery over us, but give way before calculation and measure and weight?"^[15]

Satire on false perspective by Hogarth.

Perspective images are calculated assuming a particular vanishing point. In order for the resulting image to appear identical to the original scene, a viewer of the perspective must view the image from the exact vantage point used in the calculations relative to the image. This cancels out what would appear to be distortions in the image when viewed from a different point. These apparent distortions are more pronounced away from the center of the image as the angle between a projected ray (from the scene to the eye) becomes more acute relative to the picture plane. In practice, unless the viewer chooses an extreme angle, like looking at it from the bottom corner of the window, the perspective normally looks more or less correct. This is referred to as "Zeeman's Paradox."^[16] It has been suggested that a drawing in perspective still seems to be in perspective at other spots because we still perceive it as a drawing, because it lacks depth of field cues.^[17]

For a typical perspective, however, the field of view is narrow enough (often only 60 degrees) that the distortions are similarly minimal enough that the image can be viewed from a point other than the actual calculated vantage point without appearing significantly distorted. When a larger angle of view is required, the standard method of projecting rays onto a flat picture plane becomes impractical. As a theoretical maximum, the field of view of a flat picture plane must be less than 180 degrees (as the field of view increases towards 180 degrees, the required breadth of the picture plane approaches infinity).

In order to create a projected ray image with a large field of view, one can project the image onto a curved surface. In order to have a large field of view horizontally in the image, a surface that is a vertical cylinder (i.e., the axis of the cylinder is parallel to the z-axis) will suffice (similarly, if the desired large field of view is only in the vertical direction of the image, a horizontal cylinder will suffice). A cylindrical picture surface will allow for a projected ray image up to a full 360 degrees in either the horizontal or vertical dimension of the perspective image (depending on the orientation of the cylinder). In the same way, by using a spherical picture surface, the field of view can be a full 360 degrees in any direction (note that for a spherical surface, all projected rays from the scene to the eye intersect the surface at a right angle).

Just as a standard perspective image must be viewed from the calculated vantage point for the image to appear identical to the true scene, a projected image onto a cylinder or sphere must likewise be viewed from the calculated vantage point for it to be precisely identical to the original scene. If an image projected onto a cylindrical surface is "unrolled" into a flat image, different types of distortions occur: For example, many of the scene's straight lines will be drawn as curves. An image projected onto a spherical surface can be flattened in various ways, including:

• an image equivalent to an unrolled cylinder
• a portion of the sphere can be flattened into an image equivalent to a standard perspective
• an image similar to a fisheye photograph

See also[link]

Notes[link]

References[link]

• Panofsky, Erwin (1960). Renaissance and Renascences in Western Art. Stockholm: Almqvist & Wiksell. ISBN 0-06-430026-9. 

Further reading[link]

• Kemp, Martin (1992). The Science of Art: Optical Themes in Western Art from Brunelleschi to Seurat. Yale University Press. 
• Pérez-Gómez, Alberto, and Pelletier, Louise (1997). Architectural Representation and the Perspective Hinge. Cambridge, Mass.: MIT Press. 
• Damisch, Hubert (1994). The Origin of Perspective, Translated by John Goodman. Cambridge, Mass.: MIT Press. 
• Hyman, Isabelle, comp (1974). Brunelleschi in Perspective. Englewood Cliffs, New Jersey: Prentice-Hall. 
• Vasari, Giorgio (1568). The Lives of the Artists. Florence, Italy. http://easyweb.easynet.co.uk/giorgio.vasari/. 
• Andersen, Kirsti (2007). The Geometry of an Art: The History of the Mathematical Theory of Perspective from Alberti to Monge. Springer. 

External links[link]

Wikimedia Commons has media related to: Perspective

Wikimedia Commons has media related to: Evolution of Perspective

• Teaching Perspective in Art and Mathematics through Leonardo da Vinci's Work at Convergence
• Mathematics of Perspective Drawing
• Drawing Comics - Perspective
• Quadrilateral Perspective by Yvonne Tessuto Tavares
• The Perspective Page A short interactive introduction to the geometry of perspective drawing
• Perspective Drawing Video
• The Despotic Eye: An Illustration of Metabletic Phenomenology and Its Implications by Robert D. Romanyshyn. An essay on the link between Western culture and linear perspective drawing, published in Janus Head
• Perspective in Ancient Roman-Wall Painting (c.50BC)

This biographical article needs additional citations for verification. Please help by adding reliable sources. Contentious material about living persons that is unsourced or poorly sourced must be removed immediately, especially if potentially libelous or harmful. (May 2010)

The Basics
The Basics at the Oxford Art Factory, 2010
Background information
Origin	Melbourne, Australia
Genres	Rock
Years active	2002–present
Labels	Independent, Albert Records
Associated acts	Gotye, Down Hills Home, Dog With Wheels, Blood Red Bird
Website	The Basics Official Website
Members
Wally De Backer Kris Schroeder Tim Heath
Past members
Michael Hubbard
Notable instruments
Lead guitar, drums, bass guitar.

The Basics ( /ˈbæzɪtʃ/ BAZZ-ich) are a three-piece band from Melbourne, Australia, formed by Wally De Backer and Kris Schroeder in 2002. Their style has been described as anything from 'indie-pop' to 'rock'n'roll' to 'pop-rock', though their records show they span a wide range of genres, including reggae, ska, country, and electro-pop. They are "recognised as one of Australia's hardest-working bands".^[1]

With close to 1000 shows in their ten-year career, their live performances are well-known for their sense of humour and energy.^[2]

Formation[link]

The Basics were formed after Kris met Wally at a party in Melbourne.^[3] The event was to see off the young aspiring producer, who was about to depart for Los Angeles, and together with a number of musician friends, the two jammed on some blues-rock standards. Later that night, they bonded over a mutual love of The Beatles, 70s and 80s cartoon theme songs and old Sierra adventure games.

Initially, they played around Melbourne as an acoustic guitar/drums combo, starting at The Opposition in Frankston and the House of Fools in Footscray, where in late 2002 they met Michael Hubbard and later invited him to join them on electric guitar.^[4] Though lacking any real experience with the instrument, Kris willingly purchased his first bass guitar, and the trio was born. During this time, the group start performing songs with more complicated three-part harmony.

During late 2002 and early 2003, The Basics recorded and released an album called Get Back through MGM Distribution. They began what was to become regular tours of the East and West coasts of Australia.

2004-2005: Current lineup[link]

Tim Heath joined the group in June 2004, after Michael decided to pursue his solo career, which has included being one half of Down Hills Home.^[4] Tim was reportedly the only person to reply to an advertisement in Melbourne's Beat Magazine looking for a new guitarist. Tim apparently answered the advertisement - which said the applicant "must have a love of 50s and 60s rock'n'roll" - thinking that he would be meeting "a couple of old guys to play with on the weekends over some beers". They soon recorded For Girls Like You.

The Basics in 2005 continued to tour and play small festivals, and after releasing For Girls Like You through MGM Distribution, they departed for a national tour of Australia, which lasted for two months and took them to every Australian state and territory. Stuart Padbury, a young Melbourne sound engineer, joined them on much of this tour. On returning, the band began demonstrating songs for a new album.

2006-2009: Touring and soundtracks[link]

In 2006, The Basics began recording what was to become known as Stand Out/Fit In. Taking several months, it was not completed until the end of the year, despite intentions to have it released in June. Instead, they held a successful 'album preview', where each of the tracks was demonstrated in 'rough form' accompanied by a music video for each (produced by Melbourne photographic artist James Bryans). The band also talked about the origins of the songs. This event brought a lot of attention to the band for the idea's originality. They pre-released a radio single 'Just Hold On' from the album. The band were invited to play the hugely popular Homebake Festival in Sydney, where they received a great response, after being introduced onto the stage by a short stocky Asian guy with big calves ("one of the highlights" wrote The Daily Telegraph).

In 2007, the band departed on a tri-state residency which saw them play Melbourne, Sydney and Brisbane every week for the month of April - a bold move which brought further attention to the band for its original idea.^[5] Riding on the wave of this tour, Schroeder, De Backer and Heath departed on their first overseas tour which saw them performing 26 shows around Japan, Norway and the United Kingdom.^[6] They also toured twice more up the East Coast, one of which was with popular Japanese band The Bawdies. Their song 'Rattle My Chain' was used in a series of commercials for Volvo Australia. The song 'Hey There!' featured in the British film The Bank Job - starring Jason Statham - and was used as the backing for a February 2007 short film directed by Tim Longhurst called The Rip. Their song 'Better' was featured in a surfing documentary about the invention of the shortboard in 1967.

In 2008, the band appeared on Australia's Channel 9 for Australia Day celebrations, performing two of their songs - 'Just Hold On' and 'Hey There!' - to an estimated audience of 2 million. Securing an Australian Government grant, they embarked on a two-month tour of Australia, specifically targeting "culturally underprivileged groups" in rural and regional schoolchildren and Indigenous communities. The programme had them holding masterclasses and performing alongside Indigenous groups in the remote Northern Territory and Queensland.^[7][8] Their initiative also had them raising money for the charity Lifeline^{[disambiguation needed ]}, their contribution to which was recognised with a plaque at the end of the tour. Season two of Californication starring David Duchovny featured their cover of the classic 'Have Love, Will Travel', most famously covered by 'The Sonics'.

In 2009, The Basics for the first time enjoyed the support of Australian radio network Triple J, which had reportedly snubbed the band's previous material.^[9] The singles 'With This Ship' and 'Like A Brother' were added to the station's playlist, and momentum carried The Basics overseas for a second tour of the United Kingdom and Norway, and also a series of shows in Dublin, Ireland. They were joined by the longtime front-of-house engineer Stuart Padbury, who had been mixing them since 2005. The band was often seen in the Grafton Street Mall in Dublin, busking to promote their concerts there. Their second show in Oslo, Norway, saw the band perform with Hot Tub, one of the members of the Norwegian boy band "Boyzvoice", in his first performance for several years. Season Eight of Scrubs featured the song 'Lookin' Over My Shoulder'.

Despite all this promise, the band's album Keep Your Friends Close - produced and part-recorded by Peter Cobbin at London's Abbey Road Studios - though enjoying many favourable reviews,^{[10][11][12][13]} failed to impress Richard Kingsmill, music director of Triple J. This effectively ended the band's apparent upward spiral and the resulting album launch tour was reportedly "trying".

2010: Hiatus and live album[link]

In 2010, following the band's fourth stint at the Tamworth Country Music Festival, and the recording of a yet-unreleased live album, an indefinite hiatus was announced on the band's websites. This was in part due to the impending release of a new album produced by Wally for his Gotye project, and also to reported tensions within the band following the previous year's disappointments.

However, this hiatus was soon broken with a two-month residency at the Northcote Social Club in Melbourne, which saw an apparent return to form.^[14] The band's EP "Wait For You" enjoys airplay on Triple J.^[15] The Basics also played a one-off show at Sydney's Oxford Art Factory.^[16]

On 20 August 2010, The Basics released their fourth LP /ðəˈbæzɪtʃ/, available free and exclusively from their website for digital download^[17]. The band had reportedly moved to expand their listenership through this free giveaway, though 300 "Deluxe" CD/vinyl versions have been printed. /ðəˈbæzɪtʃ/ was recorded at the Northcote Social Club on 6 February, "in front of a live studio audience", and like the previous record, was mixed by Peter Cobbin at Abbey Road Studios. Technically a self-titled album, the phonetics spell out the accurate pronunciation of the band’s name. Kris Schroeder: "For years we’ve worked at bringing our live energy into the studio and thus far it’s been a bit hit-and-miss. Our trick this time was to pull a switcheroo and bring the studio to us instead; the result is the best and closest to us we’ve sounded yet."

Melbourne thespian and Dog With Wheels bassist David Bramble - friends with Heath from university days - has occasionally joined the band on tour, playing keys, often while sporting a large moustache. Other guests have included Jake Mason (saxophone), also of Cookin' on 3 Burners and The Bamboos^{[disambiguation needed ]}, Gideon Brazil (saxophone, flute), Simon Imrei (guitar and vocals) and Monty MacKenzie (saxophone).

Covers have often made an appearance from various sources: to date, some of the bands covered have been Cream, The Kinks, The Rolling Stones, The Police, Neil Young, Bob Dylan, New Kids on the Block, Richard Berry, Sonny Curtis and The Crickets, JJ Cale, Harry Nilsson, Bill Scott, Ryan Adams and The Coasters (via The Beatles for their cover of Three Cool Cats).

Members[link]

Current

• Wally De Backer - drums, vocals (2002-present)
• Kris Schroeder - bass, vocals (2002-present)
• Tim Heath - guitar, vocals (2004-present)

Former

• Michael Hubbard - guitar, vocals (2002-2004)

Discography[link]

Albums[link]

• Get Back (15 January 2004)
• Stand Out/Fit In (5 May 2007)
• Keep Your Friends Close (25 September 2009)
• /ðəˈbæzɪtʃ/ (20 August 2010)

EP[link]

• For Girls Like You (11 July 2005)
• Lookin' Over My Shoulder (10 February 2007)
• Like A Brother (5 June 2009)
• Wait For You (21 May 2010)

Singles[link]

• Call It Rhythm & Blues (20 August 2004)
• Just Hold On
• With This Ship (22 February 2009)

Upcoming projects[link]

The band is taking a three year hiatus, with an announced return to the stage together in early 2014. Wally De Backer launched Making Mirrors under his Gotye act in August 2011, Tim Heath will be touring and recording with Blood Red Bird, and Kris Schroeder recorded a solo EP titled, Patience in the Face of Control, before leaving Australia to work with the Red Cross in Kenya for a two year sabbatical.

References[link]

External links[link]

• Official Website
• Myspace Website

Filippo Brunelleschi 1377–1446
Presumed depiction in Resurrection of the Son of Theophilus, Masaccio
Birth name	Filippo di ser Brunellesco di Lippo Lapi[1]
Born	1377 Florence, Italy
Died	April 15, 1446 (aged 68–69) unknown
Nationality	Italian
Field	Architecture, Sculpture, Mechanical engineering
Movement	Early Renaissance
Works	Dome of Santa Maria del Fiore

Brunelleschi's dome for the Duomo of Florence, Santa Maria del Fiore

Section of the dome

Nave of the Santo Spirito, 1441–1481

Chapel of the Pazzi family, one of his last works

Sculpture of Brunelleschi looking at his cathedral dome

Filippo Brunelleschi (Italian pronunciation: [fiˈlippo brunelˈleski]; 1377 – April 15, 1446) was one of the foremost architects and engineers of the Italian Renaissance. He is perhaps most famous for his studies of linear perspective and engineering the dome of the Florence Cathedral, but his accomplishments also include other architectural works, sculpture, mathematics, engineering and even ship design. His principal surviving works are to be found in Florence, Italy.

Early life[link]

Little is known about the early life of Brunelleschi, the only sources being Antonio Manetti and Giorgio Vasari.^[2] According to these sources, Filippo's father was Brunellesco di Lippo, a lawyer, and his mother was Giuliana Spini. Filippo was the middle of their three children. The young Filippo was given a literary and mathematical education intended to enable him to follow in the footsteps of his father, a civil servant. Being artistically inclined, however, Filippo enrolled in the Arte della Seta, the silk merchants' Guild, which also included goldsmiths, metalworkers, and bronze workers. He became a master goldsmith in 1398. It was thus not a coincidence that his first important building commission, the Ospedale degli Innocenti, came from the guild to which he belonged.^[3]

In 1401, Brunelleschi entered a competition to design a new set of bronze doors for the baptistery in Florence. Seven competitors each produced a gilded bronze panel, depicting the Sacrifice of Isaac. Brunelleschi's entry, which, with that of Lorenzo Ghiberti, is one of only two to have survived, made reference to the Greco-Roman Boy with Thorn, whilst Ghiberti used a naked torso in the Classical style for his figure of Isaac. In 1403, Ghiberti was announced the victor, largely because of his superior technical skill: his panel showed a more sophisticated knowledge of bronze-casting being cast as a single piece. Brunelleschi's panel, by contrast, consisted of several pieces bolted to the back plate. Ghiberti went on to complete a second set of bronze doors for the baptistery, whose beauty Michelangelo extolled a hundred years later, saying "surely these must be the "Gates of Paradise".^[4]

As an architect[link]

There is little biographical information about Brunelleschi's life to explain his transition from goldsmith to architect and, no less importantly, from his training in the gothic or medieval manner to the new classicism in architecture and urbanism that we now loosely call the Renaissance and of which Brunelleschi is considered the seminal figure. By 1400 there emerged an interest in humanitas which contrasted with the formalism of the medieval period, but initially this new interest in Roman antiquity was restricted to a few scholars, writers and philosophers; it did not at first influence the visual arts. Apparently it was in this period (1402–1404) that Brunelleschi and his friend Donatello visited Rome to study the ancient Roman ruins. Donatello, like Brunelleschi, had received his training in a goldsmith's workshop, and had then worked in Ghiberti's studio. Although in previous decades the writers and philosophers had discussed the glories of ancient Rome, it seems that until Brunelleschi and Donatello made their journey, no-one had studied the physical fabric of these ruins in any great detail. They gained inspiration too from ancient Roman authors, especially Vitruvius whose De Architectura provided an intellectual framework for the standing structures still visible.

Commissions[link]

Brunelleschi's first architectural commission was the Ospedale degli Innocenti‎ (1419–ca.1445), or Foundling Hospital. Its long loggia would have been a rare sight in the tight and curving streets of Florence, not to mention its impressive arches, each about 8 meters high. The building was dignified and sober; there were no displays of fine marble or decorative inlays.^[5] It was also the first building in Florence to make clear reference—in its columns and capitals—to classical antiquity.

Soon other commissions came, such as the Ridolfi Chapel in the church of San Jacopo sopr'Arno, now lost, and the Barbadori Chapel in Santa Trinita, also modified since its building. For both Brunelleschi devised elements already used in the Ospedale degli Innocenti, and which would also be used in the Pazzi Chapel and the Sagrestia Vecchia. At the same time he was using such smaller works as a sort of feasibility study for his most famous work, the dome of the Cathedral of Florence.

Of the two churches that Brunelleschi designed, the Basilica of San Lorenzo, (1419-1480s) and Santo Spirito (1441–1481), both of which are considered landmarks in Renaissance architecture, the latter is seen as conforming most closely to his ideas.

Santa Maria del Fiore: The Florence Cathedral[link]

Santa Maria del Fiore was the new cathedral of the city, and by 1418 the dome had yet to be defined. When the building was designed in the previous century, no one had any idea about how such a dome was to be built, given that it was to be even larger than the Pantheon's dome in Rome and that no dome of that size had been built since antiquity. Because buttresses were forbidden by the city fathers, and clearly was impossible to obtain rafters for scaffolding long and strong enough (and in sufficient quantity) for the task, it was unclear how a dome of that size could be built, or just avoid collapse. It must be considered also that the stresses of compression were not clearly understood at the time, and the mortars used in the periods would only set after several days, keeping the strain on the scaffolding for a very long time.^[6] In 1419, the Arte della Lana, the wool merchants' guild, held a competition to solve the problem. The two main competitors were Ghiberti and Brunelleschi, with Brunelleschi winning and receiving the commission.

The competition consisted of the great architects attempting to stand an egg upright on a piece of marble. None could do it but Brunelleschi, who, according to Vasari^[7]:

...giving one end a blow on the flat piece of marble, made it stand upright...The architects protested that they could have done the same; but Filippo answered, laughing, that they could have made the dome, if they had seen his design.

The dome, the lantern (built 1446–ca.1461) and the exedra (built 1439-1445) would occupy most of Brunelleschi’s life.^[8] Brunelleschi's success can be attributed to no small degree to his technical and mathematical genius.^[9] Brunelleschi used more than 4 million bricks in the construction of the dome. He invented a new hoisting machine for raising the masonry needed for the dome, a task no doubt inspired by republication of Vitruvius' De Architectura, which describes Roman machines used in the first century AD to build large structures such as the Pantheon and the Baths of Diocletian, structures still standing which he would have seen for himself. He also issued one of the first patents for the hoist in an attempt to prevent theft of his ideas. Brunelleschi was granted the first modern patent for his invention of a river transport vessel.^[10]

Brunelleschi kept his workers up in the building during their breaks and brought food and wine up to them. He felt the trip up and down the hundreds of stairs would exhaust them and reduce their productivity. In a further attempt to motivate the workers, he gave them diluted wine, similar to that given to pregnant women at the time.^[11]

Other work[link]

This unreferenced section requires citations to ensure verifiability.

Brunelleschi's interests extended to mathematics and engineering and the study of ancient monuments. He invented hydraulic machinery and elaborate clockwork, none of which survives.

Brunelleschi also designed fortifications used by Florence in its military struggles against Pisa and Siena. In 1424, he did work in Lastra a Signa, a village protecting the route to Pisa, and in 1431 he did work to the south, on the walls of the village of Staggia. The latter walls are still preserved, but whether these are specifically by Brunelleschi is uncertain.

He also had a brief appearance in the world of shipmaking, when, in 1427, he built a monstrous ship called Il Badalone to transport marble to Florence from Pisa up the Arno River. The ship sank on its first voyage, along with a sizable chunk of Brunelleschi's personal fortune.

Besides accomplishments in architecture, Brunelleschi is also credited with inventing one-point linear perspective which revolutionized painting and allowed for naturalistic styles to develop as the Renaissance digressed from the stylized figures of medieval art. In addition, he was somewhat involved in urban planning: he strategically positioned several of his buildings in relation to the nearby squares and streets for "maximum visibility". For example, demolitions in front of San Lorenzo were approved in 1433 in order to create a piazza facing the church. At Santo Spirito, he suggested that the façade be turned either towards the Arno so travelers would see it, or to the north, to face a large, prospective piazza.

Invention of linear perspective[link]

Brunelleschi is famous for two panel paintings illustrating geometric optical linear perspective made in the early 1400s. His biographer, Antonio Manetti, described this famous experiment in which Brunelleschi painted two panels: the first of the Florentine Baptistery as viewed frontally from the western portal of the unfinished cathedral, and second the Palazzo Vecchio as seen obliquely from its northwest corner. These were not, however, the first paintings with accurate linear perspective, which may be attributed to Ambrogio Lorenzetti (Annunciation, 1344 File:Lorenzetti Ambrogio annunciation- 1344..jpg).

The first Baptistery panel was constructed with a hole drilled through the centric vanishing point. Curiously, Brunelleschi intended that it only be observed by the viewer holding the unpainted back of the picture against his/her eye with one hand, and a mirror in the other hand facing and reflecting the painted side. In other words, Brunelleschi wanted his new perspective "realism" to be tested not by comparing the painted image to the actual Baptistery but to its reflection in a mirror according to the Euclidean laws of geometric optics. This feat showed artists vividly how they might paint their images, not merely as flat two-dimensional shapes, but looking more like three-dimensional structures just as mirrors reflect them. Unfortunately, both panels have since been lost.^[12]

Around this time, linear perspective as a novel artistic tool spread not only in Italy but throughout western Europe, and quickly became standard studio practice up to and including present time.

Theatrical machinery[link]

Brunelleschi's tomb

Another of Brunelleschi’s activities was the designing of the machinery in churches for theatrical, religious performances that re-enacted Biblical miracle stories. Contrivances were created by which characters and angels were made to fly through the air in the midst of spectacular explosions of lights and fireworks. These events took place during state and ecclesiastical visits. Though it is not known for certain how many of these Brunelleschi designed, but it seems that at least one, for the church of San Felice, is confirmed in the records.^[3]

Death[link]

Brunelleschi's body lies in the crypt of the Cathedral of Florence. As explained by Antonio Manetti, who knew Brunelleschi and who wrote his biography, Brunelleschi "was granted such honors as to be buried in the Basilica di Santa Maria del Fiore, and with a marble bust, which they say was carved from life, and placed there in perpetual memory with such a splendid epitaph."^[13] Inside the cathedral entrance is this epitaph: "Both the magnificent dome of this famous church and many other devices invented by Filippo the architect, bear witness to his superb skill. Therefore, in tribute to his exceptional talents, a grateful country that will always remember buries him here in the soil below."

Principal works[link]

The principal buildings and works designed by Brunelleschi or which included his involvement:

• Dome of the Cathedral of Florence, (1419–1436)
• Ospedale degli Innocenti,‎ (1419–ca.1445)
• Basilica di San Lorenzo di Firenze, (1419–1480s)
• Meeting Hall of the Palazzo di Parte Guelfa, (1420s–1445)
• Sagrestia Vecchia, or Old Sacristy of S. Lorenzo, (1421–1440)
• Santa Maria degli Angeli: unfinished, (begun 1434)
• The lantern of the Florence Cathedral, (1436–ca.1450)
• The exedrae of the Florence Cathedral, (1439–1445)
• Santo Spirito di Firenze, (1441–1481)
• Pazzi Chapel, (1441–1460s)

See also[link]

• Paolo dal Pozzo Toscanelli

References[link]

Further reading[link]

• Argan, Giulio Carlo; Robb, Nesca A (1946). "The Architecture of Brunelleschi and the Origins of Perspective Theory in the Fifteenth Century". J. Warburg and Courtauld Institutes 9: 96–121. DOI:10.2307/750311. JSTOR 750311. 
• Fanelli, Giovanni (2004). Brunelleschi’s Cupola: Past and Present of an Architectural Masterpiece. Florence: Mandragora. 
• Heydenreich, Ludwig H. (1996). Architecture in Italy, 1400-1500. New Haven/London: Yale University Press. ISBN 978-0-300-06467-4. 
• Kemp, Martin (1978). "Science, Non-science and Nonsense: The Interpretation of Brunelleschi's Perspective". Art History 1 (2): 134–161. 
• Prager, F. D. (1950). "Brunelleschi's Inventions and the 'Renewal of Roman Masonry Work'". Osiris 9: 457–554. DOI:10.1086/368537. 
• Millon, Henry A.; Lampugnani, Vittorio Magnago, eds. (1994). The Renaissance from Brunelleschi to Michelangelo: the Representation of Architecture. London: Thames and Hudson. 
• Trachtenberg, Marvin (1988). What Brunelleschi Saw: Monument and Site at the Palazzo Vecchio in Florence. New York. 
• King, Ross (2000). Brunelleschi's Dome: How a Renaissance Genius Reinvented Architecture. New York: Walker. ISBN 0-8027-1366-1. 

External links[link]

Wikimedia Commons has media related to: Filippo Brunelleschi

Wikisource has the text of the 1911 Encyclopædia Britannica article Brunelleschi, Filippo.

• Free audio guide of Brunelleschi's Dome
• O'Connor, John J.; Robertson, Edmund F., "Filippo Brunelleschi", MacTutor History of Mathematics archive, University of St Andrews, http://www-history.mcs.st-andrews.ac.uk/Biographies/Brunelleschi.html .