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Parallel Projection
In three-dimensional geometry, a parallel projection (or axonometric projection) is a projection of an object in three-dimensional space onto a fixed plane, known as the ''projection plane'' or ''image plane'', where the '' rays'', known as '' lines of sight'' or ''projection lines'', are parallel to each other. It is a basic tool in descriptive geometry. The projection is called '' orthographic'' if the rays are perpendicular (orthogonal) to the image plane, and '' oblique'' or '' skew'' if they are not. Overview A parallel projection is a particular case of ''projection'' in mathematics and ''graphical projection'' in technical drawing. Parallel projections can be seen as the limit of a central or perspective projection, in which the rays pass through a fixed point called the ''center'' or ''viewpoint'', as this point is moved towards infinity. Put differently, a parallel projection corresponds to a perspective projection with an infinite focal length (the distance between ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Three-dimensional Geometry
Solid geometry or stereometry is the geometry of three-dimensional Euclidean space (3D space). A solid figure is the region of 3D space bounded by a two-dimensional closed surface; for example, a solid ball consists of a sphere and its interior. Solid geometry deals with the measurements of volumes of various solids, including pyramids, prisms (and other polyhedrons), cubes, cylinders, cones (and truncated cones). History The Pythagoreans dealt with the regular solids, but the pyramid, prism, cone and cylinder were not studied until the Platonists. Eudoxus established their measurement, proving the pyramid and cone to have one-third the volume of a prism and cylinder on the same base and of the same height. He was probably also the discoverer of a proof that the volume enclosed by a sphere is proportional to the cube of its radius.Paraphrased and taken in part from the ''1911 Encyclopædia Britannica''. Topics Basic topics in solid geometry and stereometry include: ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Graphical Projection
A 3D projection (or graphical projection) is a design technique used to display a three-dimensional (3D) object on a two-dimensional (2D) surface. These projections rely on visual perspective and aspect analysis to project a complex object for viewing capability on a simpler plane. 3D projections use the primary qualities of an object's basic shape to create a map of points, that are then connected to one another to create a visual element. The result is a graphic that contains conceptual properties to interpret the figure or image as not actually flat (2D), but rather, as a solid object (3D) being viewed on a 2D display. 3D objects are largely displayed on two-dimensional mediums (such as paper and computer monitors). As such, graphical projections are a commonly used design element; notably, in engineering drawing, drafting, and computer graphics. Projections can be calculated through employment of mathematical analysis and formulae, or by using various geometric and op ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Circle
A circle is a shape consisting of all point (geometry), points in a plane (mathematics), plane that are at a given distance from a given point, the Centre (geometry), centre. The distance between any point of the circle and the centre is called the radius. The length of a line segment connecting two points on the circle and passing through the centre is called the diameter. A circle bounds a region of the plane called a Disk (mathematics), disc. The circle has been known since before the beginning of recorded history. Natural circles are common, such as the full moon or a slice of round fruit. The circle is the basis for the wheel, which, with related inventions such as gears, makes much of modern machinery possible. In mathematics, the study of the circle has helped inspire the development of geometry, astronomy and calculus. Terminology * Annulus (mathematics), Annulus: a ring-shaped object, the region bounded by two concentric circles. * Circular arc, Arc: any Connected ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Centroid
In mathematics and physics, the centroid, also known as geometric center or center of figure, of a plane figure or solid figure is the arithmetic mean position of all the points in the figure. The same definition extends to any object in n-dimensional Euclidean space. In geometry, one often assumes uniform mass density, in which case the '' barycenter'' or ''center of mass'' coincides with the centroid. Informally, it can be understood as the point at which a cutout of the shape (with uniformly distributed mass) could be perfectly balanced on the tip of a pin. In physics, if variations in gravity are considered, then a '' center of gravity'' can be defined as the weighted mean of all points weighted by their specific weight. In geography, the centroid of a radial projection of a region of the Earth's surface to sea level is the region's geographical center. History The term "centroid" was coined in 1814. It is used as a substitute for the older terms "center of grav ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Midpoint
In geometry, the midpoint is the middle point of a line segment. It is equidistant from both endpoints, and it is the centroid both of the segment and of the endpoints. It bisects the segment. Formula The midpoint of a segment in ''n''-dimensional space whose endpoints are A = (a_1, a_2, \dots , a_n) and B = (b_1, b_2, \dots , b_n) is given by :\frac. That is, the ''i''th coordinate of the midpoint (''i'' = 1, 2, ..., ''n'') is :\frac 2. Construction Given two points of interest, finding the midpoint of the line segment they determine can be accomplished by a compass and straightedge construction. The midpoint of a line segment, embedded in a plane, can be located by first constructing a lens using circular arcs of equal (and large enough) radii centered at the two endpoints, then connecting the cusps of the lens (the two points where the arcs intersect). The point where the line connecting the cusps intersects the segment is then the midpoint of the segment. It i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Ratio
In mathematics, a ratio () shows how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six (that is, 8:6, which is equivalent to the ratio 4:3). Similarly, the ratio of lemons to oranges is 6:8 (or 3:4) and the ratio of oranges to the total amount of fruit is 8:14 (or 4:7). The numbers in a ratio may be quantities of any kind, such as counts of people or objects, or such as measurements of lengths, weights, time, etc. In most contexts, both numbers are restricted to be Positive integer, positive. A ratio may be specified either by giving both constituting numbers, written as "''a'' to ''b''" or "''a'':''b''", or by giving just the value of their quotient Equal quotients correspond to equal ratios. A statement expressing the equality of two ratios is called a ''proportion''. Consequently, a ratio may be considered as an ordered pair of numbers, a Fraction (mathematic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Axonometry
Axonometry is a graphical procedure belonging to descriptive geometry that generates a Planar graph, planar image of a three-dimensional object. The term "axonometry" means "to measure along Cartesian coordinate system, axes", and indicates that the Dimension, dimensions and Scaling (geometry), scaling of the coordinate axes play a crucial role. The result of an axonometric procedure is a uniformly-scaled parallel projection of the object. In general, the resulting parallel projection is oblique projection, oblique (the rays are not perpendicular to the image plane); but in special cases the result is orthographic projection, orthographic (the rays are perpendicular to the image plane), which in this context is called an Orthogonality, orthogonal axonometry. In technical drawing and in architecture, axonometric perspective is a form of Two-dimensional space, two-dimensional representation of Three-dimensional space, three-dimensional objects whose goal is to preserve the impressi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Human Vision
Visual perception is the ability to detect light and use it to form an image of the surrounding Biophysical environment, environment. Photodetection without image formation is classified as ''light sensing''. In most vertebrates, visual perception can be enabled by photopic vision (daytime vision) or scotopic vision (night vision), with most vertebrates having both. Visual perception detects light (photons) in the visible spectrum reflected by objects in the environment or emitted by light sources. The light, visible range of light is defined by what is readily perceptible to humans, though the visual perception of non-humans often extends beyond the visual spectrum. The resulting perception is also known as vision, sight, or eyesight (adjectives ''visual'', ''optical'', and ''ocular'', respectively). The various physiological components involved in vision are referred to collectively as the visual system, and are the focus of much research in linguistics, psychology, cognitive s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Zooming (filmmaking)
In filmmaking and television production, zooming is the technique of changing the focal length of a zoom lens (and hence the angle of view) during a shot – this technique is also called a zoom. The technique allows a change from close-up to wide shot (or vice versa) during a shot, giving a cinematographic degree of freedom. But unlike changes in camera position, zooming does not change the perspective (the relative sizes of near and far objects); it only magnifies or reduces the size of the entire image as a whole. Zooming can either be performed towards longer focal lengths, giving a "zoom in" effect: The filmed object will then increase in apparent size, and fewer objects become visible on film. Or it is performed towards shorter focal lengths, giving a "zoom out" effect: The filmed object will shrink in apparent size, and more objects come into view. The speed of the zoom allows for a further degree of cinematographic freedom. Combined with a dolly camera move it is poss ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Photography
Photography is the visual arts, art, application, and practice of creating images by recording light, either electronically by means of an image sensor, or chemically by means of a light-sensitive material such as photographic film. It is employed in many fields of science, manufacturing (e.g., photolithography), and business, as well as its more direct uses for art, film and video production, recreational purposes, hobby, and mass communication. A person who operates a camera to capture or take Photograph, photographs is called a photographer, while the captured image, also known as a photograph, is the result produced by the camera. Typically, a lens is used to focus (optics), focus the light reflected or emitted from objects into a real image on the light-sensitive surface inside a camera during a timed Exposure (photography), exposure. With an electronic image sensor, this produces an Charge-coupled device, electrical charge at each pixel, which is Image processing, electro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Focal Length
The focal length of an Optics, optical system is a measure of how strongly the system converges or diverges light; it is the Multiplicative inverse, inverse of the system's optical power. A positive focal length indicates that a system Convergence (optics), converges light, while a negative focal length indicates that the system Divergence (optics), diverges light. A system with a shorter focal length bends the Ray (optics), rays more sharply, bringing them to a focus in a shorter distance or diverging them more quickly. For the special case of a thin lens in air, a positive focal length is the distance over which initially Collimated beam, collimated (parallel) rays are brought to a Focus (optics), focus, or alternatively a negative focal length indicates how far in front of the lens a point source must be located to form a collimated beam. For more general optical systems, the focal length has no intuitive meaning; it is simply the inverse of the system's optical power. In mos ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
