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id stringlengths 40 40	title stringlengths 15 120	text stringlengths 41 3.14k	source stringclasses 2 values
d93c6a1ee13340082b9fb944401c09f596180600	the models used in 2d computer graphics usually	the models used in 2d computer graphics usually do not provide for three-dimensional shapes, or three-dimensional optical phenomena such as lighting, shadows, reflection, refraction, etc. however, they usually can model multiple layers (conceptually of ink, paper, or film; opaque, translucent, or transparent — stacked ...	wikipedia
56558ecfed8dfa15151e57995ca6213abcca9854	painting a pixel with a given color usually	painting a pixel with a given color usually replaces its previous color. however, many systems support painting with transparent and translucent colors, which only modify the previous pixel values. the two colors may also be combined in more complex ways, e.g. by computing their bitwise exclusive or. this technique is ...	wikipedia
34bce85078623cdb13358891fec9192293214ef1	text, shapes and lines are rendered with a	text, shapes and lines are rendered with a client-specified color. many libraries and cards provide color gradients, which are handy for the generation of smoothly-varying backgrounds, shadow effects, etc. (see also gouraud shading). the pixel colors can also be taken from a texture, e.g. a digital image (thus emulatin...	wikipedia
a443842de0d2ff26b1ea69b615209ae040825b2f	a convenient way to create a complex image	a convenient way to create a complex image is to start with a blank "canvas" raster map (an array of pixels, also known as a bitmap) filled with some uniform background color and then "draw", "paint" or "paste" simple patches of color onto it, in an appropriate order. in particular the canvas may be the frame buffer fo...	wikipedia
e3cc3aacb5c34c275e7ae2cc752be0df44ecd1f7	in projective geometry, often used in computer graphics,	in projective geometry, often used in computer graphics, points are represented using homogeneous coordinates. to scale an object by a vector v = (v, v, v), each homogeneous coordinate vector p = (p, p, p, 1) would need to be multiplied with this projective transformation matrix:	wikipedia
15b1725a77da336daf66c4f24a044d4cab56af2f	scaling in the most general sense is any	scaling in the most general sense is any affine transformation with a diagonalizable matrix. it includes the case that the three directions of scaling are not perpendicular. it includes also the case that one or more scale factors are equal to zero (projection), and the case of one or more negative scale factors. the l...	wikipedia
bc55117d06f7a6b440cc706b41c9daa3ed8cd51c	more general is scaling with a separate scale	more general is scaling with a separate scale factor for each axis direction. non-uniform scaling (anisotropic scaling, inhomogeneous dilation) is obtained when at least one of the scaling factors is different from the others; a special case is directional scaling or stretching (in one direction). non-uniform scaling c...	wikipedia
60f56f64ec7218643f7cca373fb84570a4b22ad6	in euclidean geometry, uniform scaling (isotropic scaling, homogeneous	in euclidean geometry, uniform scaling (isotropic scaling, homogeneous dilation, homothety) is a linear transformation that enlarges (increases) or shrinks (diminishes) objects by a scale factor that is the same in all directions. the result of uniform scaling is similar (in the geometric sense) to the original. a scal...	wikipedia
5d15c857ed423f4b3c8119d31b3422ac8d2456ca	if a standard right-handed cartesian coordinate system is	if a standard right-handed cartesian coordinate system is used, with the x axis to the right and the y axis up, the rotation r(θ) is counterclockwise. if a left-handed cartesian coordinate system is used, with x directed to the right but y directed down, r(θ) is clockwise. such non-standard orientations are rarely used...	wikipedia
4aecc59b0d8a0ccbcf315dece45eeac7c9524225	rotation matrices provide a simple algebraic description of	rotation matrices provide a simple algebraic description of such rotations, and are used extensively for computations in geometry, physics, and computer graphics. in 2-dimensional space, a rotation can be simply described by an angle θ of rotation, but it can be also represented by the 4 entries of a rotation matrix wi...	wikipedia
0a68e64561b110fbdbc8da8998d2c675141a0d1c	rotates points in the xy - cartesian plane	rotates points in the xy - cartesian plane counterclockwise through an angle θ about the origin of the cartesian coordinate system. to perform the rotation using a rotation matrix r, the position of each point must be represented by a column vector v, containing the coordinates of the point. a rotated vector is obtaine...	wikipedia
0edac82aa8c12d8746dbf51348cb9f20c74b79a7	since a translation is an affine transformation but	since a translation is an affine transformation but not a linear transformation, homogeneous coordinates are normally used to represent the translation operator by a matrix and thus to make it linear. thus we write the 3-dimensional vector w = (w, w, w) using 4 homogeneous coordinates as w = (w, w, w, 1).	wikipedia
31e2b4d9a9bb29dc93d08f10ba22e0be8ba7efba	in a euclidean space, any translation is an	in a euclidean space, any translation is an isometry. the set of all translations forms the translation group t, which is isomorphic to the space itself, and a normal subgroup of euclidean group e (n). the quotient group of e (n) by t is isomorphic to the orthogonal group o (n):	wikipedia
3ccae864db9b02cdda038b28d3c0d1027d425cf0	in euclidean geometry, a translation (geometry) moves every	in euclidean geometry, a translation (geometry) moves every point a constant distance in a specified direction. a translation can be described as a rigid motion: other rigid motions include rotations and reflections. a translation can also be interpreted as the addition of a constant vector to every point, or as shifti...	wikipedia
b77d61895d81ec23b1ed5b3cd8d0cba82b917cc7	2d graphics models may combine geometric models (also	2d graphics models may combine geometric models (also called vector graphics), digital images (also called raster graphics), text to be typeset (defined by content, font style and size, color, position, and orientation), mathematical functions and equations, and more. these components can be modified and manipulated by...	wikipedia
17fd0fa7b752f464aceeeec52a7e8cac4d4d70f6	in many domains, such as desktop publishing, engineering,	in many domains, such as desktop publishing, engineering, and business, a description of a document based on 2d computer graphics techniques can be much smaller than the corresponding digital image — often by a factor of 1/1000 or more. this representation is also more flexible since it can be rendered at different res...	wikipedia
ceb7ffe614848e07b3b9a76392521432f03def28	2d computer graphics are mainly used in applications	2d computer graphics are mainly used in applications that were originally developed upon traditional printing and drawing technologies, such as typography, cartography, technical drawing, advertising, etc. in those applications, the two-dimensional image is not just a representation of a real-world object, but an indep...	wikipedia
4e40781d432134c8408dccc50848bf3f4e6c6784	2d computer graphics is the computer-based generation of	2d computer graphics is the computer-based generation of digital images — mostly from two-dimensional models (such as 2d geometric models, text, and digital images) and by techniques specific to them. it may refer to the branch of computer science that comprises such techniques or to the models themselves.	wikipedia
bad5a08d82cda335150033137e3c18e42f2c2ff0	the 2008–09 sheffield shield season was the 107th	the 2008–09 sheffield shield season was the 107th season of official first-class domestic cricket in australia. after nine seasons of being named the pura cup, it was announced that the australian interstate trophy would return to its previous name of the sheffield shield as part of a new sponsorship agreement with wee...	wikipedia
bad5a08d82cda335150033137e3c18e42f2c2ff0	the 2008–09 sheffield shield season was the 107th	the 2008–09 sheffield shield season was the 107th season of official first-class domestic cricket in australia. after nine seasons of being named the pura cup, it was announced that the australian interstate trophy would return to its previous name of the sheffield shield as part of a new sponsorship agreement with wee...	wikipedia
5a4ac031cdb8d6192ab65d7137c7c28e4b6e5979	the 2008–09 senior women's challenger trophy was the	the 2008–09 senior women's challenger trophy was the inaugural edition of india's 50 over women's challenger trophy. three teams made up of the best players in india competed in a round-robin group, with the top two advancing to the final. matches were held at the sardar patel stadium, ahmedabad across four days in oct...	wikipedia
bf58087b9cf4d75a5a254f1e88abac5f5bda9a58	the 2008–09 senior women's challenger trophy was the	the 2008–09 senior women's challenger trophy was the inaugural edition of india 's 50 over women's challenger trophy. three teams made up of the best players in india competed in a round-robin group, with the top two advancing to the final. matches were held at the sardar patel stadium, ahmedabad across four days in oc...	wikipedia
1e60722351fc24cff8c91657fddf929d6255a8df	the 2017 caa women's soccer tournament was the	the 2017 caa women's soccer tournament was the postseason women's soccer tournament for the colonial athletic association held from october 29 through november 5, 2017. the tournament quarterfinals were held at campus sites, while the semifinals and final took place at hofstra university soccer stadium in hempstead, ne...	wikipedia
1e60722351fc24cff8c91657fddf929d6255a8df	the 2017 caa women's soccer tournament was the	the 2017 caa women's soccer tournament was the postseason women's soccer tournament for the colonial athletic association held from october 29 through november 5, 2017. the tournament quarterfinals were held at campus sites, while the semifinals and final took place at hofstra university soccer stadium in hempstead, ne...	wikipedia
b31293d8e402ca43771555fac57be037c84fd241	the 2016–17 arizona state sun devils men's ice	the 2016–17 arizona state sun devils men's ice hockey season was the 2nd season of play for the program at the division i level. the sun devils represented arizona state university and were coached by greg powers, in his 8th season.	wikipedia
f299309afda4314f9de9f6abb795a0affd5e19f3	for the program's second varsity season, the team	for the program's second varsity season, the team began by running a gauntlet of ranked teams. as a result, arizona state's record was very poor to start the season. after a small reprieve in the middle of the year the team ran through another slate of ranked programs to end the season, however, the early-season diffic...	wikipedia
b31293d8e402ca43771555fac57be037c84fd241	the 2016–17 arizona state sun devils men's ice	the 2016–17 arizona state sun devils men's ice hockey season was the 2nd season of play for the program at the division i level. the sun devils represented arizona state university and were coached by greg powers, in his 8th season.	wikipedia
0279e0819a87acefb297740626d0a2537b57b37a	the 2007 kansas city wizards season was the	the 2007 kansas city wizards season was the 12th for the club in major league soccer. the wizards finished fifth in the eastern conference and eighth overall with 40 points, their best points total since 2004 and, resultantly, as an eastern conference team. curt onalfo took over as head coach this season. the club also...	wikipedia
83d277039bf6c38ff6b3fe4352b3f8c27ed21e7c	curt onalfo took over as head coach this	curt onalfo took over as head coach this season. the club also acquired kevin hartman from the la galaxy, where the goalkeeper had made a name for himself in the league. for kansas city, 2007 was mostly defined on-field by eddie johnson, who scored 15 league goals including back to back hat tricks to end may and begin ...	wikipedia
c484991c467bf3dbbcb207c9cfe39cd2a0263ac7	the 2007 kansas city wizards season was the	the 2007 kansas city wizards season was the 12th for the club in major league soccer. the wizards finished fifth in the eastern conference and eighth overall with 40 points (11w 12l 7d), their best points total since 2004 and, resultantly, as an eastern conference team.	wikipedia
8c57f304c2acd3a4045a2c4a3790b15c48ad3610	the 2001–02 national division two was the second	the 2001–02 national division two was the second version of the third division of the english domestic rugby union competition using the name national division two. new teams to the division included orrell and waterloo who were relegated from the 2000–01 national division one while stourbridge (champions) and sedgley ...	wikipedia
a79877f2784b0000b9cc1aa3411b0bfd8b42c339	the title race was extremely tight and went	the title race was extremely tight and went to the last game with orrell winning their rescheduled game away to nottingham to draw dead level with plymouth albion at the top of the table and take the title by virtue of a better points difference – the fact orrell had won both of their games against plymouth was largely...	wikipedia
8e6e2896fd40413cc21d3da5a07da9a4a1b76f8e	the 2001–02 national division two was the second	the 2001–02 national division two was the second version (fifteenth overall) of the third division of the english domestic rugby union competition using the name national division two. new teams to the division included orrell and waterloo who were relegated from the 2000–01 national division one while stourbridge (cha...	wikipedia
4de979daa5d19ed75103ea032a18a30dbd38a153	on 19 july 2014, fenerbahçe unveiled its new	on 19 july 2014, fenerbahçe unveiled its new adidas 2014–15 home, away and third kits, which will feature no sponsor logo for the first time in 36 years. adidas and fenerbahçe extended their kit deal in february 2014 at least until 2018–19, while it is reported that the adidas–fenerbahçe deal is worth $8.5 million per ...	wikipedia
48b0f597fd596d0d1152bb399532b11bf8160e49	the 2020 north carolina fc season was the	the 2020 north carolina fc season was the 14th season for north carolina fc and its second in the usl championship, the second-tier professional soccer league in the united states. the season was suspended march 12 after the opening week because of the covid-19 pandemic. it restarted july 11 with a restructured format ...	wikipedia
1595c1e7dbe7c465c495da7ce993def2734fea8c	as a usl championship club, north carolina fc	as a usl championship club, north carolina fc was scheduled to enter the competition in the second round, which was to be played april 7–9. pairings for that round were announced on january 29. the first three rounds of the tournament were postponed on march 13, 2020, amid the covid-19 pandemic. on august 17, the tourn...	wikipedia
1066cf9022ecd23feed6fcbc463224b92b4408f7	the 2020–21 women's t20 super league was the	the 2020–21 women's t20 super league was the third women's t20 super league competition that took place in south africa. it took place in december 2020, with 4 teams taking part made up of the best players in south africa. coronations won the competition, winning their second title.	wikipedia
1066cf9022ecd23feed6fcbc463224b92b4408f7	the 2020–21 women's t20 super league was the	the 2020–21 women's t20 super league was the third women's t20 super league competition that took place in south africa. it took place in december 2020, with 4 teams taking part made up of the best players in south africa. coronations won the competition, winning their second title.	wikipedia
d224f8813603a4fe592da521ce76ac67c53c99c5	michael doudoroff (1911–1975) was an american microbiologist. with	michael doudoroff (1911–1975) was an american microbiologist. with nathan entner, he discovered the entner–doudoroff pathway. he was born in st. petersburg, russian empire but moved to san francisco when he was 12 years old. he entered stanford university (1929) where he completed his phd under the supervision of corne...	wikipedia
5a22b3d7d0b389c7af31d81f97b0b052f03a326e	michael doudoroff (1911 – 1975) was an american	michael doudoroff (1911 – 1975) was an american microbiologist. with nathan entner, he discovered the entner–doudoroff pathway. he was born in st. petersburg, russian empire but moved to san francisco when he was 12 years old. he entered stanford university (1929) where he completed his phd under the supervision of cor...	wikipedia