Perspective (graphical) From Wikipedia, the free encyclopedia. Perspective (French: perspective from Latin perspicere, to see clearly) in the graphic arts, such as drawing, is an approximate representation on a flat surface (such as paper) of an image as it is perceived by the eye. The two most characteristic features of this representation are these: - Objects are drawn smaller on the drawing as their distance from the observer increases
- Spatial foreshortening, which is the distortion of items when viewed at an angle (see discussion at the end of this article)
In art, the term "foreshortening" is often used synonymously with perspective, even though foreshortening can occur in other types of non-perspective drawing representations (such as oblique parallel projection). Producing a perspective drawing on a flat surface, whether sketched or calculated, is always an approximation. It necessarily incurs some distortion from what would be perceived by the eye due to the nature of the geometric transforms involved. A perspective drawing, whether roughly sketched (ie, intuitively by freehand) or precisely calculated (ie, using matrix multiplication on a computer or other means), is usually a combination of two geometric transforms: - First is a perspective transform, which is a perspective projection onto a typically flat picture plane (or painting plate) of a scene from the viewpoint of an observer
- Second is a similarity transform, which is simply a scaling of the picture plane from the first transform onto an actual drawing of a usually smaller size.
An exact replication of the image perceived by the eye is only possible when the picture plane is a spherical surface or portion of a spherical surface (with the center of the sphere located at the observer's eye). The distortion that occurs is similar to the distortions that occur when attempting to represent the globe (approximately spherical) on a flat surface (see perspective projection distortion).
// History of perspective That the two most characteristic features of perspective (see above) are not self-evident in art is apparent from even a casual perusal of the art of other cultures and eras - most frequently objects are drawn or painted a certain size for reasons that have nothing to do with their position in space. The optical basis of perspective went undefined until the year 1000 when the Arabian mathematician and philosopher, Alhazen, in his Perspectiva, first explained that light projects conically into the eye. A method for projecting a scene onto a plane surface (known as the picture plane) was unknown for another 300 years. The artist Giotto di Bondone may have been the first to recognize that the image beheld by the eye is distorted, viz. that the projections of lines that are parallel to each other (but are not parallel to the picture plane) intersect on the picture plane (in the manner of receding railroad tracks). One of the first uses of perspective was in Giotto's Jesus Before the Caïf, more than 100 years before Filippo Brunelleschi's perspectival demonstrations galvanized the widespread use of convergent perspective of the Renaissance proper.
Artificial and natural Artificial perspective projection is the name given by Leonardo da Vinci to what today is called classical perspective projection. Natural perspective projection is the name given by Leonardo to the projection that produces the image beheld by the human eye. Both types of projection involve a distortion; parallel lines never intersect in nature, but they always intersect in perspective projections (with the exception in classical perspective projection where the parallel lines are parallel to the picture plane). However, differences exist in the types of distortion between the images of the same object produced by artificial perspective projection and by natural perspective projection. These differences are called perspective projection distortion. Mathematically, artificial perspective projection is a perspective projection onto a flat surface. Because drawings are typically flat, this is the type of projection utilized in most perspective drawings. Natural perspective projection, in contrast, is a perspective projection onto a spherical surface. Thus from a geometric point of view, the differences between artificial and natural perspectives can be thought of as similar to the distortion that occurs when representing the earth (approximately spherical) as a map (typically flat).
Early attempts at perspective Prior to perspective becoming the accepted manner of representation of images, drawings did not associate the represented size of objects with distance. In medieval Last Judgement paintings, for example, the relative scale of the various figures is determined only by their sacred significance; the most important are the largest. Once the diminishment of scale with distance is noted, it is an easy step to understanding why the space between parallel lines must also appear to diminish. A wall retreating from the observer will appear to get progressively shorter, and the top and bottom edges of the wall will thus appear to move closer together. However, it was an enormous conceptual leap when artists concluded that sets of parallel lines, if extended indefinitely, would appear to meet at a single point on the horizon. These points are called vanishing points. This idea was likely made from a theoretical analysis of the process of seeing rather than direct observation. Jan van Eyck, for example, was unable to create a consistent structure for the converging lines in paintings like London's The Arnolfini Portrait because he was not aware of the theoretical breakthrough just then occurring in Italy.
Varieties of perspective drawings 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. Strictly speaking, these types can only exist for scenes being represented that are rectilinear. The difference between the three lies not in the mathematical definition of the perspectives (it is the same for all three), but at what angle (both side-to-side and up-and-down) that the scene is being viewed.
One-point perspective If the viewpoint is pointing directly into a linear object like a building or a road, one would use one vanishing point, that is the principal focus. All lines perpendicular to the painting plate would vanish in the vanishing point. More precisely, 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 (see also Cartesian coordinate system) --- a scene which is composed entirely of linear elements that intersect only at right angles. Therefore, 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.
Two-point perspective A vanishing point exists for every set of parallel lines that are not parallel to the picture plane. (If the lines of a rectilinear scene have angles to the painting plate, they would vanish in other vanishing points. There are lot of vanishing points homologous to different angles. But all vanishing points should be located in the same horizontal line with the focus.) A two-point (ie, two vanishing points) perspective is derived from one-point perspective by yawing (typically) the line of vision so that the line of vision will be at an angle away from the focus (the view may be pitched as well to create a two-point perspective along the vertical axis). Then the lines which used to be horizontal and parallel will now be concurrent, intersecting at the horizon. Interpreted according to projective geometry, the horizontal parallel lines of one-point perspective are actually concurrent, intersecting at the point at infinity [1:0:1]. When the head is turned by a slight angle, these lines no longer intersect at an ideal point, but at an affine point on the horizon, so they are no longer parallel. In other words, two-point perspective exists when the painting plate is parallel to a "Cartesian scene" (a scene composed entirely of linear elements intersecting only at right angles) in one axis (usually the z-axis) but not parallel 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.
Three-point perspective If the lines have angles from the painting plate up or down, one would use the other kind vanishing points. Those vanishing points must be located in the same vertical line with the focus. Looking at the object from above or below, the horizontal line with the focus and all other 2nd VPs would left the horizon up or down. Three-point perspective exists when the perspective is a view of a rectilinear (Cartesian) scene (a scene composed entirely of linear elements intersecting at right angles) where the painting plate is not parallel to any of the scene's three axes. Linear elements in the scene that are parallel to one of the three axes will converge on one of three vanishing points. Each of the three vanishing points corresponds with one of the three axes of the scene.
Other varieties of linear perspective 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. Due to the fact that vanishing points exist only when parallel lines are present in the scene, a zero-point perspective is also possible if the viewer is observing a nonlinear scene. One example is a random (ie, not aligned in a three-dimensional Cartesian coordinate system) arrangement of spherical objects. Another would be a scene composed entirely of three-dimensionally curvilinear strings. A third example would be a scene consisting of lines where no two are parallel to each other.
Varieties of nonlinear perspective Typically, mathematically constructed perspectives are "linear" in that the ratio at which more distant objects decrease in size is constant (ie, graphing the drawn size of a one-foot object versus the distant from viewer will form a straight line). It is conceivable to have non-linear perspectives --- those in which the graph of the ratio mentioned above does not form a straight line. A panorama is a perspective projected onto a cylinder. The actual drawing can be drawn onto a cylinder (typically on the interior surface and viewed from the inside the cylinder) or onto a flat surface, equivalent to "unrolling" the cylinder. A panorama (projection onto a cylinder) removes one of the differences between artificial perspective projection (projection onto a flat surface) and natural perspective projection (projection onto a spherical surface). A standard Mercator map projection is similar to a panorama.
Methods of constructing perspectives 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)
Foreshortening Foreshortening refers to the visual effect or optical illusion that an object or distance is 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").
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