1902:
2408:
7967:
1440:
7977:
2732:
77:
524:
179:
36:
4662:
3952:
4399:
464:
1107:
3331:
3414:), and the case of one or more negative scale factors. The latter corresponds to a combination of scaling proper and a kind of reflection: along lines in a particular direction we take the reflection in the point of intersection with a plane that need not be perpendicular; therefore it is more general than ordinary reflection in the plane.
3645:
2169:
4132:
1435:{\displaystyle T_{\mathbf {v} }\mathbf {p} ={\begin{bmatrix}1&0&0&v_{x}\\0&1&0&v_{y}\\0&0&1&v_{z}\\0&0&0&1\end{bmatrix}}{\begin{bmatrix}p_{x}\\p_{y}\\p_{z}\\1\end{bmatrix}}={\begin{bmatrix}p_{x}+v_{x}\\p_{y}+v_{y}\\p_{z}+v_{z}\\1\end{bmatrix}}=\mathbf {p} +\mathbf {v} }
1096:
5126:
operations. They typically use a direct-painting paradigm, where the user controls virtual pens, brushes, and other free-hand artistic instruments to apply paint to a virtual canvas. Some image editors support a multiple-layer model; however, in order to support signal-processing operations like
3075:
4102:
3634:
2863:(in the geometric sense) to the original. A scale factor of 1 is normally allowed, so that congruent shapes are also classed as similar. (Some school text books specifically exclude this possibility, just as some exclude squares from being rectangles or circles from being ellipses.)
4762:
which is then painted over the canvas, pixel by pixel. Fully transparent parts of a layer need not be rendered, of course. The rendering and painting may be done in parallel, i.e., each layer pixel may be painted on the canvas as soon as it is produced by the rendering procedure.
3947:{\displaystyle S_{v}p={\begin{bmatrix}v_{x}&0&0&0\\0&v_{y}&0&0\\0&0&v_{z}&0\\0&0&0&1\end{bmatrix}}{\begin{bmatrix}p_{x}\\p_{y}\\p_{z}\\1\end{bmatrix}}={\begin{bmatrix}v_{x}p_{x}\\v_{y}p_{y}\\v_{z}p_{z}\\1\end{bmatrix}}.}
4394:{\displaystyle S_{v}p={\begin{bmatrix}1&0&0&0\\0&1&0&0\\0&0&1&0\\0&0&0&{\frac {1}{s}}\end{bmatrix}}{\begin{bmatrix}p_{x}\\p_{y}\\p_{z}\\1\end{bmatrix}}={\begin{bmatrix}p_{x}\\p_{y}\\p_{z}\\{\frac {1}{s}}\end{bmatrix}}}
2396:
2009:
4720:-D computer graphics". They make it possible to mimic traditional drafting and printing techniques based on film and paper, such as cutting and pasting; and allow the user to edit any layer without affecting the others. For these reasons, they are used in most
2029:
1705:
3064:
664:
1770:, but it can be also represented by the 4 entries of a rotation matrix with 2 rows and 2 columns. In 3-dimensional space, every rotation can be interpreted as a rotation by a given angle about a single fixed axis of rotation (see
341:, 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
2897:
of the object; e.g. a square may change into a rectangle, or into a parallelogram if the sides of the square are not parallel to the scaling axes (the angles between lines parallel to the axes are preserved, but not all angles).
948:
3326:{\displaystyle S_{v}p={\begin{bmatrix}v_{x}&0&0\\0&v_{y}&0\\0&0&v_{z}\\\end{bmatrix}}{\begin{bmatrix}p_{x}\\p_{y}\\p_{z}\end{bmatrix}}={\begin{bmatrix}v_{x}p_{x}\\v_{y}p_{y}\\v_{z}p_{z}\end{bmatrix}}.}
2635:
2715:
1579:
2552:
3967:
1778:
with 3 entries. However, it can also be represented by the 9 entries of a rotation matrix with 3 rows and 3 columns. The notion of rotation is not commonly used in dimensions higher than 3; there is a notion of a
3485:
5084:; and some even support procedural models. The illustration is usually represented internally as a layered model, often with a hierarchical structure to make editing more convenient. These editors generally output
5037:
to aid the user in conceptually distinguishing between different applications. The user interface within individual software applications is typically 2D in nature as well, due in part to the fact that most common
4495:
317:
is not just a representation of a real-world object, but an independent artifact with added semantic value; two-dimensional models are therefore preferred, because they give more direct control of the image than
5127:
blurring each layer is normally represented as a digital image. Therefore, any geometric primitives that are provided by the editor are immediately converted to pixels and painted onto the canvas. The name
1747:. Since matrix multiplication has no effect on the zero vector (i.e., on the coordinates of the origin), rotation matrices can only be used to describe rotations about the origin of the coordinate system.
1505:
2290:
2232:
2302:
1919:
2164:{\displaystyle {\begin{bmatrix}x'\\y'\\\end{bmatrix}}={\begin{bmatrix}\cos \theta &-\sin \theta \\\sin \theta &\cos \theta \\\end{bmatrix}}{\begin{bmatrix}x\\y\\\end{bmatrix}}}
1864:
1624:
593:
2952:
4750:
In a layer-based model, the target image is produced by "painting" or "pasting" each layer, in order of decreasing depth, on the virtual canvas. Conceptually, each layer is first
2450:) is clockwise. Such non-standard orientations are rarely used in mathematics but are common in 2D computer graphics, which often have the origin in the top left corner and the
5112:. There are also many 2D graphics editors specialized for certain types of drawings such as electrical, electronic and VLSI diagrams, topographic maps, computer fonts, etc.
276:
4959:
4653:
for highlighting, rubber-band drawing, and other volatile painting—since re-painting the same shapes with the same color will restore the original pixel values.
5171:
With the resurgence of 2D animation, free and proprietary software packages have become widely available for amateurs and professional animators. With software like
5033:, are primarily based on 2D graphical concepts. Such software provides a visual environment for interacting with the computer, and commonly includes some form of
3410:. 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 (
598:
7356:
1091:{\displaystyle T_{\mathbf {v} }={\begin{bmatrix}1&0&0&v_{x}\\0&1&0&v_{y}\\0&0&1&v_{z}\\0&0&0&1\end{bmatrix}}}
7095:
6993:
6978:
3957:
Since the last component of a homogeneous coordinate can be viewed as the denominator of the other three components, a uniform scaling by a common factor
7938:
7911:
6522:
4823:, due to the relatively low cost of raster-based video hardware as compared with vector graphic hardware. Most graphic hardware has internal support for
2559:
2642:
1516:
4679:
The models used in 2D computer graphics usually do not provide for three-dimensional shapes, or three-dimensional optical phenomena such as lighting,
2479:
5205:
5049:
2D graphics are very important in the control peripherals such as printers, plotters, sheet cutting machines, etc. They were also used in most early
4097:{\displaystyle S_{v}={\begin{bmatrix}1&0&0&0\\0&1&0&0\\0&0&1&0\\0&0&0&{\frac {1}{s}}\end{bmatrix}}.}
7182:
6193:
4739:
Layered models are also used to allow the user to suppress unwanted information when viewing or printing a document, e.g. roads or railways from a
3629:{\displaystyle S_{v}={\begin{bmatrix}v_{x}&0&0&0\\0&v_{y}&0&0\\0&0&v_{z}&0\\0&0&0&1\end{bmatrix}}.}
5208:
allow the user to do either 3D animation, 2D animation or combine both in its software allowing experimentation with multiple forms of animation.
7933:
6163:
5362:
4410:
7906:
7187:
6492:
5434:
4634:
colors, which only modify the previous pixel values. The two colors may also be combined in more complex ways, e.g. by computing their
518:
7948:
7135:
7079:
7197:
7177:
5262:
4806:
2796:
141:
4526:
and then "draw", "paint" or "paste" simple patches of color onto it, in an appropriate order. In particular the canvas may be the
7234:
7192:
7091:
5872:
5072:
are application-level software for the creation of images, diagrams and illustrations by direct manipulation (through the mouse,
2768:
113:
1451:
2296:
The direction of vector rotation is counterclockwise if θ is positive (e.g. 90°), and clockwise if θ is negative (e.g. -90°).
7943:
7928:
6998:
5823:
5796:
2749:
545:: other rigid motions include rotations and reflections. A translation can also be interpreted as the addition of a constant
94:
49:
2775:
120:
7896:
7165:
7160:
7084:
6644:
5839:
5443:
2391:{\displaystyle R(-\theta )={\begin{bmatrix}\cos \theta &\sin \theta \\-\sin \theta &\cos \theta \\\end{bmatrix}}\,}
17:
7207:
6988:
6764:
5334:
4782:, respectively), which are then painted as separate layers, in some order. However, this solution may create undesirable
1750:
Rotation matrices provide a simple algebraic description of such rotations, and are used extensively for computations in
2004:{\displaystyle R(\theta )={\begin{bmatrix}\cos \theta &-\sin \theta \\\sin \theta &\cos \theta \\\end{bmatrix}}}
6857:
6634:
6577:
6183:
5563:
5376:
2782:
2239:
2181:
1588:, multiplication of translation matrices is therefore also commutative (unlike multiplication of arbitrary matrices).
127:
8011:
7074:
2815:
240:
222:
160:
63:
204:
7202:
6983:
6905:
7125:
6188:
5427:
2764:
489:
109:
5185:
Various approaches have been developed to aid and speed up the process of digital 2D animation. For example, by
7140:
7069:
6965:
6935:
6915:
5686:
5487:
4674:
2753:
1700:{\displaystyle R={\begin{bmatrix}\cos \theta &-\sin \theta \\\sin \theta &\cos \theta \\\end{bmatrix}}}
189:
98:
3059:{\displaystyle S_{v}={\begin{bmatrix}v_{x}&0&0\\0&v_{y}&0\\0&0&v_{z}\\\end{bmatrix}}.}
7583:
7352:
7150:
6940:
6920:
5896:
5811:
5801:
5691:
5510:
4751:
1810:
432:
342:
569:
7474:
7145:
6970:
6960:
6945:
6925:
6178:
5806:
5671:
5611:
5303:
Robot manipulators: mathematics, programming, and control : the computer control of robot manipulators
4885:
4790:
7106:
6955:
6930:
5865:
3411:
2423:
1771:
1723:
1715:
447:
6107:
8006:
7479:
7432:
5599:
5420:
4828:
4810:
2885:) is obtained when at least one of the scaling factors is different from the others; a special case is
282:
257:
7442:
7155:
7052:
6910:
6817:
5931:
4819:
displays almost overwhelmingly use raster techniques, dividing the screen into a rectangular grid of
4767:
4703:—stacked in a specific order. The ordering is usually defined by a single number (the layer's
4599:, which are handy for the generation of smoothly-varying backgrounds, shadow effects, etc. (See also
3476:
2848:
1775:
435:
428:
408:
289:
2D computer graphics are mainly used in applications that were originally developed upon traditional
55:
5096:
line of computers, was an early example of this class; recent examples are the commercial products
4626:
with a given color usually replaces its previous color. However, many systems support painting with
4595:
Text, shapes and lines are rendered with a client-specified color. Many libraries and cards provide
541:
moves every point a constant distance in a specified direction. A translation can be described as a
7721:
7701:
7101:
5956:
5951:
5916:
5881:
5115:
5018:
4968:
4854:
4802:
4650:
1883:
424:
2789:
134:
7816:
7676:
7130:
6757:
4955:
4907:
3431:
3395:
2742:
1781:
855:
493:
200:
87:
5006:
7716:
7494:
7447:
6862:
6837:
6527:
6079:
5966:
5858:
5818:
5768:
5733:
5711:
5706:
5315:
5272:
5186:
5077:
4700:
4627:
1611:
718:
564:
537:
527:
A translation moves every point of a figure or a space by the same amount in a given direction.
479:
412:
400:
6143:
1445:
The inverse of a translation matrix can be obtained by reversing the direction of the vector:
268:, text, and digital images) and by techniques specific to them. It may refer to the branch of
196:
7842:
7811:
7801:
7726:
7686:
7457:
7226:
6792:
6421:
6234:
6158:
5976:
5661:
5640:
5584:
4924:
4775:
4725:
3407:
3403:
2860:
2852:
2458:
2020:
1738:
851:
847:
442:
by an arbitrary algorithm. Complex models can be built by combining simpler objects, in the
7985:
7791:
7639:
7623:
7484:
7414:
7384:
7297:
7286:
7032:
6897:
6887:
6847:
6701:
6592:
6416:
6366:
6274:
6259:
6203:
6168:
6064:
5961:
5936:
5544:
5530:
5247:
5222:
5085:
4684:
2461:
for other alternative conventions which may change the sense of the rotation produced by a
1607:
859:
550:
354:
319:
5131:
is sometimes used to contrast this approach to that of general editors which also handle
8:
7864:
7706:
7644:
6872:
6827:
6797:
6681:
6436:
6371:
6208:
6069:
6019:
6014:
5850:
5676:
5604:
5492:
5277:
5179:
5160:
5076:, or similar device) of 2D computer graphics primitives. These editors generally provide
4937:
3423:
2420:
1879:
710:
659:{\displaystyle T_{\mathbf {\delta } }f(\mathbf {v} )=f(\mathbf {v} +\mathbf {\delta } ).}
483:
5159:. This class too includes many specialized editors—for medicine, remote sensing,
4933:
7970:
7891:
7821:
7766:
7598:
7588:
7571:
7489:
7347:
7059:
7037:
6882:
6852:
6842:
6812:
6750:
6721:
6381:
6376:
6330:
6320:
6254:
5946:
5921:
5911:
5738:
5726:
5573:
5568:
5520:
5227:
5201:
4994:
4920:
4870:
4744:
3435:
3370:). If all except one of the scale factors are equal to 1, we have directional scaling.
3344:
by a factor between the smallest and the largest product of two scale factors, and the
2902:
2829:
532:
420:
380:
330:
265:
6587:
7976:
7576:
7303:
7244:
7025:
6867:
6832:
6802:
6716:
6666:
6639:
6567:
6446:
6426:
6269:
6074:
5971:
5788:
5681:
5666:
5482:
5372:
5366:
5242:
5123:
5097:
5026:
4985:
4972:
4911:
4733:
4635:
3427:
3399:
by a factor k, increasing the area by a factor of k and the volume by a factor of k.
1871:
1797:
1763:
1759:
1737:, containing the coordinates of the point. A rotated vector is obtained by using the
928:
554:
353:. For these reasons, documents and illustrations are often stored or transmitted as
306:
7980:
7923:
7806:
7781:
7548:
7521:
7437:
7320:
7293:
7047:
6950:
6726:
6711:
6706:
6686:
6537:
6512:
6476:
6471:
6406:
6340:
6244:
6148:
6138:
6112:
6059:
5986:
5926:
5901:
5773:
5763:
5645:
5633:
5175:
5054:
4862:
4759:
4538:
4531:
4523:
804:
346:
269:
6153:
4556:
write a string of characters with a specified font, at a given position and angle;
2630:{\displaystyle R(180^{\circ })={\begin{bmatrix}-1&0\\0&-1\\\end{bmatrix}}}
2438:) is counterclockwise. If a left-handed Cartesian coordinate system is used, with
7918:
7837:
7786:
7776:
7731:
7462:
7379:
7308:
7172:
6807:
6731:
6671:
6582:
6507:
6451:
6401:
6044:
5941:
5594:
5459:
5451:
5302:
5267:
5093:
5088:
where the layers and primitives are separately preserved in their original form.
5073:
5030:
4858:
4721:
4600:
4560:
4511:
2710:{\displaystyle R(270^{\circ })={\begin{bmatrix}0&1\\-1&0\\\end{bmatrix}}}
2462:
1615:
1602:
1574:{\displaystyle T_{\mathbf {u} }T_{\mathbf {v} }=T_{\mathbf {u} +\mathbf {v} }.\!}
777:
773:
761:
542:
497:
473:
407:, and more. These components can be modified and manipulated by two-dimensional
388:
384:
373:
365:
361:
279:
5393:"blender.org - Home of the Blender project - Free and Open 3D Creation Software"
4537:
Some programs will set the pixel colors directly, but most will rely on some 2D
2547:{\displaystyle R(90^{\circ })={\begin{bmatrix}0&-1\\1&0\\\end{bmatrix}}}
1901:
1785:, which can be represented by a matrix, but no associated single axis or angle.
7847:
7736:
7618:
7593:
7452:
7404:
7394:
7259:
6877:
6696:
6661:
6602:
6557:
6456:
6441:
6335:
6310:
6264:
6218:
6213:
6049:
5981:
5743:
5156:
5136:
5043:
5034:
4980:
4976:
4916:
4596:
4579:
3352:
2943:
1597:
1510:
Similarly, the product of translation matrices is given by adding the vectors:
788:
559:
4946:
8000:
7603:
7536:
7389:
7282:
7249:
6656:
6542:
6466:
6431:
6411:
6315:
6279:
6133:
6117:
6102:
5906:
5748:
5622:
5552:
5257:
5232:
5119:
5081:
4893:
4874:
4850:
4816:
4755:
4728:
of complex drawings and provide a sound model for certain techniques such as
4604:
4550:
4542:
4510:
A convenient way to create a complex image is to start with a blank "canvas"
2016:
1789:
1731:
350:
261:
496:
to the section by replacing the section with a link and a summary or by
7901:
7770:
7711:
7691:
7671:
7613:
7566:
7467:
7399:
7064:
7042:
6691:
6651:
6572:
6552:
6517:
6502:
6396:
6391:
6361:
6239:
5753:
5716:
5701:
5696:
5616:
5557:
5039:
5002:
4998:
4832:
4779:
4638:
4575:
4527:
2901:
A scaling can be represented by a scaling matrix. To scale an object by a
2856:
546:
7869:
7649:
7427:
7269:
7254:
6676:
6624:
6562:
6532:
6461:
6386:
6356:
6294:
6249:
5721:
5589:
5525:
5190:
4929:
4881:
4866:
4696:
4666:
4631:
2876:
2407:
1801:
1793:
1585:
938:(written in homogeneous coordinates) would need to be multiplied by this
392:
334:
323:
310:
302:
4490:{\displaystyle {\begin{bmatrix}sp_{x}\\sp_{y}\\sp_{z}\\1\end{bmatrix}}.}
7874:
7741:
7654:
7337:
7332:
7277:
6547:
6325:
6289:
6284:
6034:
5050:
4688:
4608:
369:
298:
2717:(270° counterclockwise rotation, the same as a 90° clockwise rotation)
7884:
7854:
7664:
7608:
7558:
7526:
7325:
7313:
7239:
6773:
6629:
6597:
6198:
6173:
6054:
6039:
5282:
5152:
5101:
4902:
2859:
that is the same in all directions. The result of uniform scaling is
2838:
443:
5412:
3961:(uniform scaling) can be accomplished by using this scaling matrix:
2731:
2402:
207:. Statements consisting only of original research should be removed.
76:
7879:
7746:
7696:
7681:
7659:
7531:
7508:
7020:
6742:
6024:
5579:
5252:
5237:
5194:
5140:
5109:
5062:
4783:
4771:
4564:
3337:
1762:. In 2-dimensional space, a rotation can be simply described by an
1751:
862:
and thus to make it linear. Thus we write the 3-dimensional vector
765:
416:
404:
396:
338:
290:
3639:
As shown below, the multiplication will give the expected result:
3069:
As shown below, the multiplication will give the expected result:
2175:
So the coordinates (x',y') of the point (x,y) after rotation are:
1101:
As shown below, the multiplication will give the expected result:
6497:
6009:
5628:
5144:
5089:
4989:
4841:
4616:
2473:
Particularly useful are the matrices for 90° and 180° rotations:
1755:
523:
294:
4661:
1913:
In two dimensions every rotation matrix has the following form:
399:
style and size, color, position, and orientation), mathematical
7541:
7516:
7422:
5758:
5515:
4898:
4836:
4824:
4680:
4568:
4519:
3345:
2855:
that enlarges (increases) or shrinks (diminishes) objects by a
4603:). The pixel colors can also be taken from a texture, e.g. a
2673:
2590:
2510:
7796:
6822:
6004:
5778:
5464:
5172:
5058:
5022:
4951:
4889:
4820:
4623:
4515:
2894:
858:
are normally used to represent the translation operator by a
439:
314:
5193:
an artist may employ software-driven automatic coloring and
272:
that comprises such techniques or to the models themselves.
7374:
5502:
5392:
5316:"Scalable Vector Graphics -- the initial coordinate system"
5217:
5148:
5105:
4964:
3341:
275:
5880:
4766:
Layers that consist of complex geometric objects (such as
1500:{\displaystyle T_{\mathbf {v} }^{-1}=T_{-\mathbf {v} }.\!}
768:. The set of all translations forms the translation group
7859:
6029:
4942:
4740:
4786:
artifacts wherever two elements overlap the same pixel.
3340:
of an object by a factor between the scale factors, the
1796:
entries. More specifically they can be characterized as
5053:; and are still used for card and board games such as
4419:
4328:
4264:
4157:
3989:
3855:
3791:
3670:
3507:
3241:
3184:
3100:
2974:
2870:
with a separate scale factor for each axis direction.
2329:
2140:
2077:
2038:
1943:
1905:
A counterclockwise rotation of a vector through angle
1730:, the position of each point must be represented by a
1639:
1321:
1257:
1136:
972:
5182:, coloring and compositing can be done in less time.
4747:
diagram, or hand annotations from a business letter.
4413:
4135:
3970:
3648:
3488:
3078:
2955:
2645:
2562:
2482:
2305:
2242:
2184:
2032:
1922:
1813:
1627:
1519:
1454:
1110:
951:
601:
572:
5122:, mainly by means of free-hand drawing/painting and
4545:, which usually implement the following operations:
2893:(in one direction). Non-uniform scaling changes the
438:—a procedure that assigns colors to the image
360:
2D computer graphics started in the 1950s, based on
7939:
List of animated television series by episode count
2756:. Unsourced material may be challenged and removed.
313:, etc. In those applications, the two-dimensional
264:—mostly from two-dimensional models (such as
101:. Unsourced material may be challenged and removed.
4489:
4393:
4096:
3946:
3628:
3325:
3058:
2709:
2629:
2546:
2390:
2284:
2226:
2163:
2003:
1909:. The vector is initially aligned with the x-axis.
1858:
1726:. To perform the rotation using a rotation matrix
1699:
1573:
1499:
1434:
1090:
658:
587:
376:protocol were landmark developments in the field.
5046:, are constrained to two dimensions of movement.
2637:(180° rotation in either direction – a half-turn)
2403:Non-standard orientation of the coordinate system
1570:
1496:
772:, which is isomorphic to the space itself, and a
7998:
4691:, etc. However, they usually can model multiple
3417:
2285:{\displaystyle y'=x\sin \theta +y\cos \theta \,}
2227:{\displaystyle x'=x\cos \theta -y\sin \theta \,}
1843:
7934:List of animated films by box office admissions
5135:. One of the first popular image editors was
4695:(conceptually of ink, paper, or film; opaque,
6758:
5866:
5428:
4774:) may be broken down into simpler elements (
3475:, 1) would need to be multiplied with this
1774:), and hence it can be simply described by
519:Rotations and reflections in two dimensions
64:Learn how and when to remove these messages
27:Computer-based generation of digital images
6765:
6751:
5873:
5859:
5435:
5421:
5166:
427:, the image is described indirectly by an
3402:Scaling in the most general sense is any
2816:Learn how and when to remove this message
2387:
2281:
2223:
1855:
241:Learn how and when to remove this message
223:Learn how and when to remove this message
161:Learn how and when to remove this message
5332:
5263:List of home computers by video hardware
5118:are specialized for the manipulation of
4807:List of home computers by video hardware
4660:
4590:
2942:) would need to be multiplied with this
2406:
1900:
672:is a fixed vector, then the translation
522:
453:
274:
5340:. Massachusetts Institute of Technology
1859:{\displaystyle R^{T}=R^{-1},\det R=1\,}
14:
7999:
5357:
5355:
4710:Layered models are sometimes called "2
4553:at a specified offset onto the canvas;
3456:), each homogeneous coordinate vector
588:{\displaystyle T_{\mathbf {\delta } }}
6746:
5854:
5442:
5416:
893:) using 4 homogeneous coordinates as
7907:Films with live action and animation
6772:
5840:List of computer graphics algorithms
5361:
5151:editor, and the commercial products
4857:of the late 1970s to 1980s, used in
2754:adding citations to reliable sources
2725:
1896:
457:
172:
99:adding citations to reliable sources
70:
29:
5501:
5352:
4724:. Layered models also allow better
4615:which used to be available only in
2468:
549:to every point, or as shifting the
364:. These were largely supplanted by
24:
4505:
1718:counterclockwise through an angle
25:
8023:
6999:Modern TV cable and streaming era
5368:2D Graphics Programming for Games
4743:, certain process layers from an
45:This article has multiple issues.
7975:
7966:
7965:
5147:. Modern examples are the free
4707:, or distance from the viewer).
4669:with 3D backgrounds using layers
3389:, the scaling is also called an
2730:
1561:
1553:
1538:
1526:
1487:
1461:
1428:
1420:
1124:
1117:
958:
638:
621:
462:
322:(whose approach is more akin to
177:
75:
34:
5104:, and the free editors such as
4791:Portable Document Format#Layers
4567:defined by three corners, or a
3430:, points are represented using
3355:the scaling factors are equal (
2741:needs additional citations for
2554:(90° counterclockwise rotation)
2454:-axis down the screen or page.
1584:Because addition of vectors is
387:), digital images (also called
379:2D graphics models may combine
86:needs additional citations for
53:or discuss these issues on the
5385:
5326:
5308:
5295:
5092:, introduced in 1984 with the
4675:Layers (digital image editing)
4641:. This technique is known as
4404:which would be homogenized to
2662:
2649:
2579:
2566:
2499:
2486:
2318:
2309:
1932:
1926:
841:
650:
634:
625:
617:
368:in the following decades. The
13:
1:
7929:Most expensive animated films
7584:Direct manipulation animation
7235:Barrier-grid and stereography
5897:Biological data visualization
5797:3D computer graphics software
5288:
4571:with given center and radius;
4500:
3418:Using homogeneous coordinates
3348:by the product of all three.
1874:of all such matrices of size
7475:Non-photorealistic rendering
5612:Hidden-surface determination
927:To translate an object by a
7:
7107:International Animation Day
5371:. New York, NY: CRC Press.
5211:
5012:
4796:
4522:) filled with some uniform
3336:Such a scaling changes the
2424:Cartesian coordinate system
1724:Cartesian coordinate system
1591:
709:is a translation, then the
476:the scope of other articles
448:object-oriented programming
203:the claims made and adding
10:
8028:
7577:Linear Animation Generator
7480:Physically based animation
5937:Mathematical visualization
5305:, MIT Press, Cambridge, MA
4811:Sprite (computer graphics)
4800:
4672:
3434:. To scale an object by a
2721:
2442:directed to the right but
2430:axis to the right and the
2019:by means of the following
1610:that is used to perform a
934:, each homogeneous vector
846:Since a translation is an
516:
7961:
7830:
7759:
7632:
7557:
7507:
7413:
7365:
7346:
7268:
7225:
7218:
7166:Children's animated films
7115:
7013:
6896:
6788:
6781:
6615:
6485:
6349:
6303:
6227:
6126:
6095:
6088:
5995:
5932:Information visualization
5917:Educational visualization
5889:
5832:
5787:
5654:
5543:
5473:
5450:
5187:generating vector artwork
5019:graphical user interfaces
4855:graphics processing units
4656:
4651:graphical user interfaces
4582:, or simple curve with a
3477:projective transformation
2411:A rotation through angle
409:geometric transformations
329:In many domains, such as
8012:Euclidean plane geometry
7075:Animation film festivals
6108:Charles-René de Fourcroy
5957:Scientific visualization
5884:of technical information
5273:Transparency in graphics
4803:Video display controller
4665:A 2D animated character
2434:axis up, the rotation R(
1884:special orthogonal group
1772:Euler's rotation theorem
1722:about the origin of the
764:, any translation is an
425:object-oriented graphics
7897:Twelve basic principles
7817:Instructional animation
5824:Vector graphics editors
5819:Raster graphics editors
5167:Developmental animation
5068:2D graphics editors or
4754:on its own, yielding a
4649:, and is often used in
4607:(thus emulating rub-on
3432:homogeneous coordinates
3351:The scaling is uniform
1782:rotational displacement
856:homogeneous coordinates
362:vector graphics devices
7495:Virtual cinematography
7092:Highest-grossing films
6994:Early TV broadcast era
6528:Christopher R. Johnson
6080:Technical illustration
5967:Software visualization
5707:Checkerboard rendering
5129:raster graphics editor
4670:
4491:
4395:
4098:
3948:
3630:
3327:
3060:
2883:inhomogeneous dilation
2765:"2D computer graphics"
2711:
2631:
2548:
2416:
2415:with non-standard axes
2392:
2286:
2228:
2165:
2005:
1910:
1860:
1788:Rotation matrices are
1710:rotates points in the
1701:
1575:
1501:
1436:
1092:
660:
589:
538:translation (geometry)
528:
480:Translation (geometry)
297:technologies, such as
286:
110:"2D computer graphics"
7812:Independent animation
7802:Educational animation
6422:Lawrence J. Rosenblum
6235:Edward Walter Maunder
6159:Charles Joseph Minard
5977:User interface design
5952:Product visualization
5662:Affine transformation
5641:Surface triangulation
5585:Anisotropic filtering
4726:spatial anti-aliasing
4664:
4591:Extended color models
4492:
4396:
4099:
3949:
3631:
3408:diagonalizable matrix
3404:affine transformation
3328:
3061:
2853:linear transformation
2712:
2632:
2549:
2410:
2393:
2287:
2229:
2166:
2021:matrix multiplication
2006:
1904:
1861:
1776:an angle and a vector
1739:matrix multiplication
1702:
1576:
1502:
1437:
1093:
852:linear transformation
848:affine transformation
803:is isomorphic to the
736:. The translation of
661:
590:
526:
517:Further information:
498:splitting the content
492:and help introduce a
454:Background (geometry)
395:(defined by content,
326:than to typography).
278:
7792:Animated documentary
7624:Whiteboard animation
7517:Traditional puppetry
7161:Adult animated films
7070:Biologist simulators
7033:Animation department
6702:Scientific modelling
6677:Information graphics
6417:Clifford A. Pickover
6367:William S. Cleveland
6275:Henry Norris Russell
6260:Howard G. Funkhouser
6204:Florence Nightingale
6169:Francis Amasa Walker
6065:Statistical graphics
5987:Volume visualization
5962:Social visualization
5301:Richard Paul, 1981,
5248:Graphic art software
5223:3D computer graphics
5078:geometric primitives
4947:μPD7220 and μPD72120
4411:
4133:
3968:
3646:
3486:
3076:
2953:
2845:homogeneous dilation
2750:improve this article
2643:
2560:
2480:
2303:
2240:
2182:
2030:
1920:
1811:
1625:
1517:
1452:
1108:
949:
599:
570:
560:translation operator
431:endowed with a self-
366:raster-based devices
320:3D computer graphics
254:2D computer graphics
95:improve this article
18:2d computer graphics
7865:Character animation
7645:Character animation
7183:Children's animated
6682:Information science
6645:in computer science
6437:Sheelagh Carpendale
6372:George G. Robertson
6209:Karl Wilhelm Pohlke
6144:André-Michel Guerry
6020:Graph of a function
6015:Engineering drawing
5677:Collision detection
5605:Global illumination
5278:Palette (computing)
5180:Adobe After Effects
5161:digital photography
4871:video game consoles
4126:, 1) we would have
3424:projective geometry
2887:directional scaling
2872:Non-uniform scaling
1798:orthogonal matrices
1474:
500:into a new article.
484:Rotation (geometry)
266:2D geometric models
7892:Creature animation
7822:Virtual newscaster
7767:Abstract animation
7599:Ink-wash animation
7589:Humanoid animation
7572:Audio-Animatronics
7136:Lost or unfinished
7060:Animation database
7038:Animation director
6722:Volume cartography
6486:Early 21st century
6382:Catherine Plaisant
6377:Bruce H. McCormick
6331:Mary Eleanor Spear
6321:Arthur H. Robinson
6255:Arthur Lyon Bowley
6228:Early 20th century
6075:Technical drawings
5947:Molecular graphics
5922:Flow visualization
5912:Data visualization
5727:Scanline rendering
5521:Parallax scrolling
5511:Isometric graphics
5228:Computer animation
5021:(GUIs), including
4745:integrated circuit
4671:
4518:, also known as a
4487:
4478:
4391:
4385:
4314:
4253:
4094:
4085:
3944:
3935:
3841:
3780:
3626:
3617:
3373:In the case where
3323:
3314:
3227:
3173:
3056:
3047:
2830:Euclidean geometry
2707:
2701:
2627:
2621:
2544:
2538:
2426:is used, with the
2417:
2388:
2381:
2282:
2224:
2161:
2155:
2129:
2063:
2001:
1995:
1911:
1856:
1697:
1691:
1571:
1497:
1455:
1432:
1410:
1307:
1246:
1088:
1082:
940:translation matrix
656:
585:
533:Euclidean geometry
529:
490:discuss this issue
349:to suit different
331:desktop publishing
287:
188:possibly contains
8007:Computer graphics
7994:
7993:
7755:
7754:
7682:Erasure animation
7503:
7502:
7245:Limited animation
7188:Computer-animated
7126:Computer-animated
7048:Animation studios
7009:
7008:
6740:
6739:
6717:Visual perception
6667:Graphic organizer
6640:Computer graphics
6611:
6610:
6593:Martin Wattenberg
6568:Hanspeter Pfister
6523:Martin Krzywinski
6447:Jock D. Mackinlay
6427:Thomas A. DeFanti
6350:Late 20th century
6270:Ejnar Hertzsprung
5972:Technical drawing
5848:
5847:
5789:Graphics software
5682:Planar projection
5667:Back-face culling
5539:
5538:
5483:Alpha compositing
5444:Computer graphics
5335:"Transformations"
5243:Computer graphics
5124:signal processing
5098:Adobe Illustrator
5027:Microsoft Windows
4986:Texas Instruments
4981:315-5196/315-5197
4977:315-5011/315-5012
4758:with the desired
4541:or the machine's
4381:
4249:
4081:
3428:computer graphics
2826:
2825:
2818:
2800:
2446:directed down, R(
1897:In two dimensions
1760:computer graphics
749:is often written
555:coordinate system
515:
514:
372:language and the
307:technical drawing
251:
250:
243:
233:
232:
225:
190:original research
171:
170:
163:
145:
68:
16:(Redirected from
8019:
7979:
7969:
7968:
7949:anime franchises
7924:Cartoon violence
7912:highest grossing
7807:Erotic animation
7782:Animated cartoon
7549:Supermarionation
7522:Digital puppetry
7443:Facial animation
7363:
7362:
7223:
7222:
7096:Opening weekends
6786:
6785:
6767:
6760:
6753:
6744:
6743:
6727:Volume rendering
6712:Visual analytics
6707:Spatial analysis
6687:Misleading graph
6538:David McCandless
6513:Gordon Kindlmann
6477:Alfred Inselberg
6472:Leland Wilkinson
6407:Michael Friendly
6341:Howard T. Fisher
6304:Mid 20th century
6245:W. E. B. Du Bois
6149:William Playfair
6139:Adolphe Quetelet
6113:Joseph Priestley
6096:Pre-19th century
6093:
6092:
6060:Skeletal formula
5927:Geovisualization
5902:Chemical imaging
5875:
5868:
5861:
5852:
5851:
5774:Volume rendering
5646:Wire-frame model
5499:
5498:
5437:
5430:
5423:
5414:
5413:
5407:
5406:
5404:
5403:
5389:
5383:
5382:
5359:
5350:
5349:
5347:
5345:
5339:
5333:Durand; Cutler.
5330:
5324:
5323:
5312:
5306:
5299:
5176:UbiArt Framework
5070:drawing programs
4815:Modern computer
4722:graphics editors
4719:
4718:
4714:
4539:graphics library
4532:computer display
4524:background color
4496:
4494:
4493:
4488:
4483:
4482:
4468:
4467:
4451:
4450:
4434:
4433:
4400:
4398:
4397:
4392:
4390:
4389:
4382:
4374:
4368:
4367:
4354:
4353:
4340:
4339:
4319:
4318:
4304:
4303:
4290:
4289:
4276:
4275:
4258:
4257:
4250:
4242:
4145:
4144:
4107:For each vector
4103:
4101:
4100:
4095:
4090:
4089:
4082:
4074:
3980:
3979:
3953:
3951:
3950:
3945:
3940:
3939:
3925:
3924:
3915:
3914:
3901:
3900:
3891:
3890:
3877:
3876:
3867:
3866:
3846:
3845:
3831:
3830:
3817:
3816:
3803:
3802:
3785:
3784:
3750:
3749:
3716:
3715:
3682:
3681:
3658:
3657:
3635:
3633:
3632:
3627:
3622:
3621:
3587:
3586:
3553:
3552:
3519:
3518:
3498:
3497:
3426:, often used in
3332:
3330:
3329:
3324:
3319:
3318:
3311:
3310:
3301:
3300:
3287:
3286:
3277:
3276:
3263:
3262:
3253:
3252:
3232:
3231:
3224:
3223:
3210:
3209:
3196:
3195:
3178:
3177:
3170:
3169:
3141:
3140:
3112:
3111:
3088:
3087:
3065:
3063:
3062:
3057:
3052:
3051:
3044:
3043:
3015:
3014:
2986:
2985:
2965:
2964:
2866:More general is
2821:
2814:
2810:
2807:
2801:
2799:
2758:
2734:
2726:
2716:
2714:
2713:
2708:
2706:
2705:
2661:
2660:
2636:
2634:
2633:
2628:
2626:
2625:
2578:
2577:
2553:
2551:
2550:
2545:
2543:
2542:
2498:
2497:
2469:Common rotations
2397:
2395:
2394:
2389:
2386:
2385:
2291:
2289:
2288:
2283:
2250:
2233:
2231:
2230:
2225:
2192:
2170:
2168:
2167:
2162:
2160:
2159:
2134:
2133:
2068:
2067:
2060:
2048:
2010:
2008:
2007:
2002:
2000:
1999:
1892:
1865:
1863:
1862:
1857:
1839:
1838:
1823:
1822:
1706:
1704:
1703:
1698:
1696:
1695:
1580:
1578:
1577:
1572:
1566:
1565:
1564:
1556:
1543:
1542:
1541:
1531:
1530:
1529:
1506:
1504:
1503:
1498:
1492:
1491:
1490:
1473:
1465:
1464:
1441:
1439:
1438:
1433:
1431:
1423:
1415:
1414:
1400:
1399:
1387:
1386:
1373:
1372:
1360:
1359:
1346:
1345:
1333:
1332:
1312:
1311:
1297:
1296:
1283:
1282:
1269:
1268:
1251:
1250:
1221:
1220:
1192:
1191:
1163:
1162:
1127:
1122:
1121:
1120:
1097:
1095:
1094:
1089:
1087:
1086:
1057:
1056:
1028:
1027:
999:
998:
963:
962:
961:
805:orthogonal group
665:
663:
662:
657:
649:
641:
624:
613:
612:
611:
594:
592:
591:
586:
584:
583:
582:
510:
507:
501:
466:
465:
458:
381:geometric models
355:2D graphic files
285:(left) and masks
270:computer science
246:
239:
228:
221:
217:
214:
208:
205:inline citations
181:
180:
173:
166:
159:
155:
152:
146:
144:
103:
79:
71:
60:
38:
37:
30:
21:
8027:
8026:
8022:
8021:
8020:
8018:
8017:
8016:
7997:
7996:
7995:
7990:
7957:
7919:Cartoon physics
7838:Animation music
7826:
7787:Animated sitcom
7777:Adult animation
7751:
7732:Special effects
7628:
7553:
7499:
7409:
7350:
7342:
7264:
7214:
7193:Direct-to-video
7111:
7005:
6892:
6777:
6771:
6741:
6736:
6732:Information art
6672:Imaging science
6617:
6607:
6588:Fernanda Viégas
6583:Moritz Stefaner
6508:Jessica Hullman
6481:
6452:Alan MacEachren
6402:Ben Shneiderman
6345:
6299:
6223:
6122:
6084:
5997:
5991:
5942:Medical imaging
5885:
5879:
5849:
5844:
5828:
5783:
5650:
5595:Fluid animation
5535:
5497:
5469:
5460:Diffusion curve
5452:Vector graphics
5446:
5441:
5411:
5410:
5401:
5399:
5391:
5390:
5386:
5379:
5360:
5353:
5343:
5341:
5337:
5331:
5327:
5314:
5313:
5309:
5300:
5296:
5291:
5268:Turtle graphics
5214:
5206:Adobe Substance
5189:in a tool like
5169:
5143:, companion to
5133:vector graphics
5074:graphics tablet
5031:X Window System
5015:
4903:CPS-A and CPS-B
4813:
4799:
4716:
4712:
4711:
4677:
4659:
4647:color inversion
4643:inverting color
4611:and the fabled
4601:Gouraud shading
4597:color gradients
4593:
4586:of given width.
4561:geometric shape
4559:paint a simple
4508:
4506:Direct painting
4503:
4477:
4476:
4470:
4469:
4463:
4459:
4453:
4452:
4446:
4442:
4436:
4435:
4429:
4425:
4415:
4414:
4412:
4409:
4408:
4384:
4383:
4373:
4370:
4369:
4363:
4359:
4356:
4355:
4349:
4345:
4342:
4341:
4335:
4331:
4324:
4323:
4313:
4312:
4306:
4305:
4299:
4295:
4292:
4291:
4285:
4281:
4278:
4277:
4271:
4267:
4260:
4259:
4252:
4251:
4241:
4239:
4234:
4229:
4223:
4222:
4217:
4212:
4207:
4201:
4200:
4195:
4190:
4185:
4179:
4178:
4173:
4168:
4163:
4153:
4152:
4140:
4136:
4134:
4131:
4130:
4124:
4120:
4116:
4084:
4083:
4073:
4071:
4066:
4061:
4055:
4054:
4049:
4044:
4039:
4033:
4032:
4027:
4022:
4017:
4011:
4010:
4005:
4000:
3995:
3985:
3984:
3975:
3971:
3969:
3966:
3965:
3934:
3933:
3927:
3926:
3920:
3916:
3910:
3906:
3903:
3902:
3896:
3892:
3886:
3882:
3879:
3878:
3872:
3868:
3862:
3858:
3851:
3850:
3840:
3839:
3833:
3832:
3826:
3822:
3819:
3818:
3812:
3808:
3805:
3804:
3798:
3794:
3787:
3786:
3779:
3778:
3773:
3768:
3763:
3757:
3756:
3751:
3745:
3741:
3739:
3734:
3728:
3727:
3722:
3717:
3711:
3707:
3705:
3699:
3698:
3693:
3688:
3683:
3677:
3673:
3666:
3665:
3653:
3649:
3647:
3644:
3643:
3616:
3615:
3610:
3605:
3600:
3594:
3593:
3588:
3582:
3578:
3576:
3571:
3565:
3564:
3559:
3554:
3548:
3544:
3542:
3536:
3535:
3530:
3525:
3520:
3514:
3510:
3503:
3502:
3493:
3489:
3487:
3484:
3483:
3473:
3469:
3465:
3454:
3450:
3446:
3420:
3386:
3382:
3378:
3368:
3364:
3360:
3313:
3312:
3306:
3302:
3296:
3292:
3289:
3288:
3282:
3278:
3272:
3268:
3265:
3264:
3258:
3254:
3248:
3244:
3237:
3236:
3226:
3225:
3219:
3215:
3212:
3211:
3205:
3201:
3198:
3197:
3191:
3187:
3180:
3179:
3172:
3171:
3165:
3161:
3159:
3154:
3148:
3147:
3142:
3136:
3132:
3130:
3124:
3123:
3118:
3113:
3107:
3103:
3096:
3095:
3083:
3079:
3077:
3074:
3073:
3046:
3045:
3039:
3035:
3033:
3028:
3022:
3021:
3016:
3010:
3006:
3004:
2998:
2997:
2992:
2987:
2981:
2977:
2970:
2969:
2960:
2956:
2954:
2951:
2950:
2940:
2936:
2932:
2921:
2917:
2913:
2834:uniform scaling
2822:
2811:
2805:
2802:
2759:
2757:
2747:
2735:
2724:
2700:
2699:
2694:
2685:
2684:
2679:
2669:
2668:
2656:
2652:
2644:
2641:
2640:
2620:
2619:
2611:
2605:
2604:
2599:
2586:
2585:
2573:
2569:
2561:
2558:
2557:
2537:
2536:
2531:
2525:
2524:
2516:
2506:
2505:
2493:
2489:
2481:
2478:
2477:
2471:
2463:rotation matrix
2405:
2380:
2379:
2368:
2353:
2352:
2341:
2325:
2324:
2304:
2301:
2300:
2243:
2241:
2238:
2237:
2185:
2183:
2180:
2179:
2154:
2153:
2147:
2146:
2136:
2135:
2128:
2127:
2116:
2104:
2103:
2089:
2073:
2072:
2062:
2061:
2053:
2050:
2049:
2041:
2034:
2033:
2031:
2028:
2027:
1994:
1993:
1982:
1970:
1969:
1955:
1939:
1938:
1921:
1918:
1917:
1899:
1886:
1882:, known as the
1831:
1827:
1818:
1814:
1812:
1809:
1808:
1790:square matrices
1716:Cartesian plane
1690:
1689:
1678:
1666:
1665:
1651:
1635:
1634:
1626:
1623:
1622:
1616:Euclidean space
1603:rotation matrix
1594:
1560:
1552:
1551:
1547:
1537:
1536:
1532:
1525:
1524:
1520:
1518:
1515:
1514:
1486:
1482:
1478:
1466:
1460:
1459:
1453:
1450:
1449:
1427:
1419:
1409:
1408:
1402:
1401:
1395:
1391:
1382:
1378:
1375:
1374:
1368:
1364:
1355:
1351:
1348:
1347:
1341:
1337:
1328:
1324:
1317:
1316:
1306:
1305:
1299:
1298:
1292:
1288:
1285:
1284:
1278:
1274:
1271:
1270:
1264:
1260:
1253:
1252:
1245:
1244:
1239:
1234:
1229:
1223:
1222:
1216:
1212:
1210:
1205:
1200:
1194:
1193:
1187:
1183:
1181:
1176:
1171:
1165:
1164:
1158:
1154:
1152:
1147:
1142:
1132:
1131:
1123:
1116:
1115:
1111:
1109:
1106:
1105:
1081:
1080:
1075:
1070:
1065:
1059:
1058:
1052:
1048:
1046:
1041:
1036:
1030:
1029:
1023:
1019:
1017:
1012:
1007:
1001:
1000:
994:
990:
988:
983:
978:
968:
967:
957:
956:
952:
950:
947:
946:
923:
914:
905:
892:
883:
874:
844:
778:Euclidean group
774:normal subgroup
762:Euclidean space
748:
689:
680:
645:
637:
620:
607:
606:
602:
600:
597:
596:
578:
577:
573:
571:
568:
567:
521:
511:
505:
502:
487:
478:, specifically
467:
463:
456:
389:raster graphics
385:vector graphics
374:X Window System
247:
236:
235:
234:
229:
218:
212:
209:
194:
182:
178:
167:
156:
150:
147:
104:
102:
92:
80:
39:
35:
28:
23:
22:
15:
12:
11:
5:
8025:
8015:
8014:
8009:
7992:
7991:
7989:
7988:
7983:
7973:
7962:
7959:
7958:
7956:
7955:
7954:
7953:
7952:
7951:
7936:
7931:
7926:
7921:
7916:
7915:
7914:
7904:
7899:
7894:
7889:
7888:
7887:
7882:
7877:
7872:
7862:
7857:
7852:
7851:
7850:
7848:Mickey Mousing
7845:
7834:
7832:
7831:Related topics
7828:
7827:
7825:
7824:
7819:
7814:
7809:
7804:
7799:
7794:
7789:
7784:
7779:
7774:
7763:
7761:
7757:
7756:
7753:
7752:
7750:
7749:
7744:
7739:
7734:
7729:
7724:
7722:Straight ahead
7719:
7714:
7709:
7704:
7702:Paint-on-glass
7699:
7694:
7689:
7684:
7679:
7674:
7669:
7668:
7667:
7662:
7657:
7652:
7642:
7636:
7634:
7630:
7629:
7627:
7626:
7621:
7619:Squigglevision
7616:
7611:
7606:
7601:
7596:
7594:Idle animation
7591:
7586:
7581:
7580:
7579:
7574:
7563:
7561:
7555:
7554:
7552:
7551:
7546:
7545:
7544:
7539:
7534:
7529:
7519:
7513:
7511:
7505:
7504:
7501:
7500:
7498:
7497:
7492:
7487:
7482:
7477:
7472:
7471:
7470:
7465:
7460:
7453:Motion capture
7450:
7445:
7440:
7435:
7430:
7425:
7419:
7417:
7411:
7410:
7408:
7407:
7405:Onion skinning
7402:
7397:
7392:
7387:
7382:
7377:
7371:
7369:
7360:
7344:
7343:
7341:
7340:
7335:
7330:
7329:
7328:
7318:
7317:
7316:
7306:
7301:
7291:
7290:
7289:
7274:
7272:
7266:
7265:
7263:
7262:
7260:Exposure sheet
7257:
7252:
7247:
7242:
7237:
7231:
7229:
7220:
7216:
7215:
7213:
7212:
7211:
7210:
7205:
7200:
7195:
7190:
7185:
7180:
7178:Adult animated
7170:
7169:
7168:
7163:
7158:
7153:
7148:
7143:
7138:
7133:
7131:Feature-length
7128:
7119:
7117:
7113:
7112:
7110:
7109:
7104:
7099:
7089:
7088:
7087:
7082:
7072:
7067:
7062:
7057:
7056:
7055:
7045:
7040:
7035:
7030:
7029:
7028:
7017:
7015:
7011:
7010:
7007:
7006:
7004:
7003:
7002:
7001:
6996:
6991:
6986:
6984:The Golden Age
6981:
6975:United States
6973:
6971:United Kingdom
6968:
6963:
6958:
6953:
6948:
6943:
6938:
6933:
6928:
6923:
6918:
6913:
6908:
6902:
6900:
6894:
6893:
6891:
6890:
6885:
6880:
6875:
6870:
6865:
6860:
6855:
6850:
6845:
6840:
6835:
6830:
6825:
6820:
6815:
6810:
6805:
6800:
6795:
6789:
6783:
6779:
6778:
6770:
6769:
6762:
6755:
6747:
6738:
6737:
6735:
6734:
6729:
6724:
6719:
6714:
6709:
6704:
6699:
6697:Patent drawing
6694:
6689:
6684:
6679:
6674:
6669:
6664:
6662:Graphic design
6659:
6654:
6649:
6648:
6647:
6637:
6632:
6627:
6621:
6619:
6613:
6612:
6609:
6608:
6606:
6605:
6603:Hadley Wickham
6600:
6595:
6590:
6585:
6580:
6575:
6570:
6565:
6560:
6558:Tamara Munzner
6555:
6550:
6545:
6540:
6535:
6530:
6525:
6520:
6515:
6510:
6505:
6500:
6495:
6489:
6487:
6483:
6482:
6480:
6479:
6474:
6469:
6464:
6459:
6457:David Goodsell
6454:
6449:
6444:
6442:Cynthia Brewer
6439:
6434:
6429:
6424:
6419:
6414:
6409:
6404:
6399:
6394:
6389:
6384:
6379:
6374:
6369:
6364:
6359:
6353:
6351:
6347:
6346:
6344:
6343:
6338:
6336:Edgar Anderson
6333:
6328:
6323:
6318:
6313:
6311:Jacques Bertin
6307:
6305:
6301:
6300:
6298:
6297:
6292:
6287:
6282:
6277:
6272:
6267:
6265:John B. Peddle
6262:
6257:
6252:
6247:
6242:
6237:
6231:
6229:
6225:
6224:
6222:
6221:
6219:Francis Galton
6216:
6214:Toussaint Loua
6211:
6206:
6201:
6196:
6194:Georg von Mayr
6191:
6186:
6184:Matthew Sankey
6181:
6176:
6171:
6166:
6161:
6156:
6151:
6146:
6141:
6136:
6130:
6128:
6124:
6123:
6121:
6120:
6115:
6110:
6105:
6099:
6097:
6090:
6086:
6085:
6083:
6082:
6077:
6072:
6067:
6062:
6057:
6052:
6050:Sankey diagram
6047:
6042:
6037:
6032:
6027:
6022:
6017:
6012:
6007:
6001:
5999:
5993:
5992:
5990:
5989:
5984:
5982:Visual culture
5979:
5974:
5969:
5964:
5959:
5954:
5949:
5944:
5939:
5934:
5929:
5924:
5919:
5914:
5909:
5904:
5899:
5893:
5891:
5887:
5886:
5878:
5877:
5870:
5863:
5855:
5846:
5845:
5843:
5842:
5836:
5834:
5830:
5829:
5827:
5826:
5821:
5816:
5815:
5814:
5809:
5804:
5793:
5791:
5785:
5784:
5782:
5781:
5776:
5771:
5766:
5761:
5756:
5751:
5746:
5744:Shadow mapping
5741:
5736:
5731:
5730:
5729:
5724:
5719:
5714:
5709:
5704:
5699:
5689:
5684:
5679:
5674:
5669:
5664:
5658:
5656:
5652:
5651:
5649:
5648:
5643:
5638:
5637:
5636:
5626:
5619:
5614:
5609:
5608:
5607:
5597:
5592:
5587:
5582:
5577:
5571:
5566:
5560:
5555:
5549:
5547:
5541:
5540:
5537:
5536:
5534:
5533:
5528:
5523:
5518:
5513:
5507:
5505:
5496:
5495:
5490:
5485:
5479:
5477:
5471:
5470:
5468:
5467:
5462:
5456:
5454:
5448:
5447:
5440:
5439:
5432:
5425:
5417:
5409:
5408:
5384:
5378:978-1466501898
5377:
5363:Pile, John Jr.
5351:
5325:
5307:
5293:
5292:
5290:
5287:
5286:
5285:
5280:
5275:
5270:
5265:
5260:
5255:
5250:
5245:
5240:
5235:
5230:
5225:
5220:
5213:
5210:
5200:Programs like
5168:
5165:
5157:Paint Shop Pro
5120:digital images
5086:graphics files
5082:digital images
5042:, such as the
5035:window manager
5014:
5011:
5010:
5009:
4992:
4983:
4962:
4949:
4940:
4927:
4917:MOS Technology
4914:
4905:
4896:
4875:home computers
4851:graphics chips
4839:is known as a
4827:operations or
4798:
4795:
4730:mitered joints
4673:Main article:
4658:
4655:
4592:
4589:
4588:
4587:
4572:
4557:
4554:
4549:paste a given
4507:
4504:
4502:
4499:
4498:
4497:
4486:
4481:
4475:
4472:
4471:
4466:
4462:
4458:
4455:
4454:
4449:
4445:
4441:
4438:
4437:
4432:
4428:
4424:
4421:
4420:
4418:
4402:
4401:
4388:
4380:
4377:
4372:
4371:
4366:
4362:
4358:
4357:
4352:
4348:
4344:
4343:
4338:
4334:
4330:
4329:
4327:
4322:
4317:
4311:
4308:
4307:
4302:
4298:
4294:
4293:
4288:
4284:
4280:
4279:
4274:
4270:
4266:
4265:
4263:
4256:
4248:
4245:
4240:
4238:
4235:
4233:
4230:
4228:
4225:
4224:
4221:
4218:
4216:
4213:
4211:
4208:
4206:
4203:
4202:
4199:
4196:
4194:
4191:
4189:
4186:
4184:
4181:
4180:
4177:
4174:
4172:
4169:
4167:
4164:
4162:
4159:
4158:
4156:
4151:
4148:
4143:
4139:
4122:
4118:
4114:
4105:
4104:
4093:
4088:
4080:
4077:
4072:
4070:
4067:
4065:
4062:
4060:
4057:
4056:
4053:
4050:
4048:
4045:
4043:
4040:
4038:
4035:
4034:
4031:
4028:
4026:
4023:
4021:
4018:
4016:
4013:
4012:
4009:
4006:
4004:
4001:
3999:
3996:
3994:
3991:
3990:
3988:
3983:
3978:
3974:
3955:
3954:
3943:
3938:
3932:
3929:
3928:
3923:
3919:
3913:
3909:
3905:
3904:
3899:
3895:
3889:
3885:
3881:
3880:
3875:
3871:
3865:
3861:
3857:
3856:
3854:
3849:
3844:
3838:
3835:
3834:
3829:
3825:
3821:
3820:
3815:
3811:
3807:
3806:
3801:
3797:
3793:
3792:
3790:
3783:
3777:
3774:
3772:
3769:
3767:
3764:
3762:
3759:
3758:
3755:
3752:
3748:
3744:
3740:
3738:
3735:
3733:
3730:
3729:
3726:
3723:
3721:
3718:
3714:
3710:
3706:
3704:
3701:
3700:
3697:
3694:
3692:
3689:
3687:
3684:
3680:
3676:
3672:
3671:
3669:
3664:
3661:
3656:
3652:
3637:
3636:
3625:
3620:
3614:
3611:
3609:
3606:
3604:
3601:
3599:
3596:
3595:
3592:
3589:
3585:
3581:
3577:
3575:
3572:
3570:
3567:
3566:
3563:
3560:
3558:
3555:
3551:
3547:
3543:
3541:
3538:
3537:
3534:
3531:
3529:
3526:
3524:
3521:
3517:
3513:
3509:
3508:
3506:
3501:
3496:
3492:
3471:
3467:
3463:
3452:
3448:
3444:
3419:
3416:
3384:
3380:
3376:
3366:
3362:
3358:
3353:if and only if
3334:
3333:
3322:
3317:
3309:
3305:
3299:
3295:
3291:
3290:
3285:
3281:
3275:
3271:
3267:
3266:
3261:
3257:
3251:
3247:
3243:
3242:
3240:
3235:
3230:
3222:
3218:
3214:
3213:
3208:
3204:
3200:
3199:
3194:
3190:
3186:
3185:
3183:
3176:
3168:
3164:
3160:
3158:
3155:
3153:
3150:
3149:
3146:
3143:
3139:
3135:
3131:
3129:
3126:
3125:
3122:
3119:
3117:
3114:
3110:
3106:
3102:
3101:
3099:
3094:
3091:
3086:
3082:
3067:
3066:
3055:
3050:
3042:
3038:
3034:
3032:
3029:
3027:
3024:
3023:
3020:
3017:
3013:
3009:
3005:
3003:
3000:
2999:
2996:
2993:
2991:
2988:
2984:
2980:
2976:
2975:
2973:
2968:
2963:
2959:
2944:scaling matrix
2938:
2934:
2930:
2923:), each point
2919:
2915:
2911:
2824:
2823:
2738:
2736:
2729:
2723:
2720:
2719:
2718:
2704:
2698:
2695:
2693:
2690:
2687:
2686:
2683:
2680:
2678:
2675:
2674:
2672:
2667:
2664:
2659:
2655:
2651:
2648:
2638:
2624:
2618:
2615:
2612:
2610:
2607:
2606:
2603:
2600:
2598:
2595:
2592:
2591:
2589:
2584:
2581:
2576:
2572:
2568:
2565:
2555:
2541:
2535:
2532:
2530:
2527:
2526:
2523:
2520:
2517:
2515:
2512:
2511:
2509:
2504:
2501:
2496:
2492:
2488:
2485:
2470:
2467:
2419:If a standard
2404:
2401:
2400:
2399:
2384:
2378:
2375:
2372:
2369:
2367:
2364:
2361:
2358:
2355:
2354:
2351:
2348:
2345:
2342:
2340:
2337:
2334:
2331:
2330:
2328:
2323:
2320:
2317:
2314:
2311:
2308:
2294:
2293:
2280:
2277:
2274:
2271:
2268:
2265:
2262:
2259:
2256:
2253:
2249:
2246:
2235:
2222:
2219:
2216:
2213:
2210:
2207:
2204:
2201:
2198:
2195:
2191:
2188:
2173:
2172:
2158:
2152:
2149:
2148:
2145:
2142:
2141:
2139:
2132:
2126:
2123:
2120:
2117:
2115:
2112:
2109:
2106:
2105:
2102:
2099:
2096:
2093:
2090:
2088:
2085:
2082:
2079:
2078:
2076:
2071:
2066:
2059:
2056:
2052:
2051:
2047:
2044:
2040:
2039:
2037:
2017:column vectors
2013:
2012:
1998:
1992:
1989:
1986:
1983:
1981:
1978:
1975:
1972:
1971:
1968:
1965:
1962:
1959:
1956:
1954:
1951:
1948:
1945:
1944:
1942:
1937:
1934:
1931:
1928:
1925:
1898:
1895:
1868:
1867:
1854:
1851:
1848:
1845:
1842:
1837:
1834:
1830:
1826:
1821:
1817:
1708:
1707:
1694:
1688:
1685:
1682:
1679:
1677:
1674:
1671:
1668:
1667:
1664:
1661:
1658:
1655:
1652:
1650:
1647:
1644:
1641:
1640:
1638:
1633:
1630:
1598:linear algebra
1593:
1590:
1582:
1581:
1569:
1563:
1559:
1555:
1550:
1546:
1540:
1535:
1528:
1523:
1508:
1507:
1495:
1489:
1485:
1481:
1477:
1472:
1469:
1463:
1458:
1443:
1442:
1430:
1426:
1422:
1418:
1413:
1407:
1404:
1403:
1398:
1394:
1390:
1385:
1381:
1377:
1376:
1371:
1367:
1363:
1358:
1354:
1350:
1349:
1344:
1340:
1336:
1331:
1327:
1323:
1322:
1320:
1315:
1310:
1304:
1301:
1300:
1295:
1291:
1287:
1286:
1281:
1277:
1273:
1272:
1267:
1263:
1259:
1258:
1256:
1249:
1243:
1240:
1238:
1235:
1233:
1230:
1228:
1225:
1224:
1219:
1215:
1211:
1209:
1206:
1204:
1201:
1199:
1196:
1195:
1190:
1186:
1182:
1180:
1177:
1175:
1172:
1170:
1167:
1166:
1161:
1157:
1153:
1151:
1148:
1146:
1143:
1141:
1138:
1137:
1135:
1130:
1126:
1119:
1114:
1099:
1098:
1085:
1079:
1076:
1074:
1071:
1069:
1066:
1064:
1061:
1060:
1055:
1051:
1047:
1045:
1042:
1040:
1037:
1035:
1032:
1031:
1026:
1022:
1018:
1016:
1013:
1011:
1008:
1006:
1003:
1002:
997:
993:
989:
987:
984:
982:
979:
977:
974:
973:
971:
966:
960:
955:
919:
910:
901:
888:
879:
870:
843:
840:
839:
838:
789:quotient group
744:
685:
676:
655:
652:
648:
644:
640:
636:
633:
630:
627:
623:
619:
616:
610:
605:
581:
576:
513:
512:
470:
468:
461:
455:
452:
391:), text to be
351:output devices
280:Raster graphic
262:digital images
260:generation of
258:computer-based
249:
248:
231:
230:
185:
183:
176:
169:
168:
83:
81:
74:
69:
43:
42:
40:
33:
26:
9:
6:
4:
3:
2:
8024:
8013:
8010:
8008:
8005:
8004:
8002:
7987:
7984:
7982:
7978:
7974:
7972:
7964:
7963:
7960:
7950:
7947:
7946:
7945:
7942:
7941:
7940:
7937:
7935:
7932:
7930:
7927:
7925:
7922:
7920:
7917:
7913:
7910:
7909:
7908:
7905:
7903:
7900:
7898:
7895:
7893:
7890:
7886:
7883:
7881:
7878:
7876:
7873:
7871:
7868:
7867:
7866:
7863:
7861:
7858:
7856:
7853:
7849:
7846:
7844:
7843:Bouncing ball
7841:
7840:
7839:
7836:
7835:
7833:
7829:
7823:
7820:
7818:
7815:
7813:
7810:
7808:
7805:
7803:
7800:
7798:
7795:
7793:
7790:
7788:
7785:
7783:
7780:
7778:
7775:
7772:
7768:
7765:
7764:
7762:
7758:
7748:
7745:
7743:
7740:
7738:
7735:
7733:
7730:
7728:
7725:
7723:
7720:
7718:
7715:
7713:
7710:
7708:
7705:
7703:
7700:
7698:
7695:
7693:
7690:
7688:
7687:Hydrotechnics
7685:
7683:
7680:
7678:
7677:Drawn-on-film
7675:
7673:
7670:
7666:
7663:
7661:
7658:
7656:
7653:
7651:
7648:
7647:
7646:
7643:
7641:
7638:
7637:
7635:
7633:Other methods
7631:
7625:
7622:
7620:
7617:
7615:
7612:
7610:
7607:
7605:
7604:Magic Lantern
7602:
7600:
7597:
7595:
7592:
7590:
7587:
7585:
7582:
7578:
7575:
7573:
7570:
7569:
7568:
7565:
7564:
7562:
7560:
7556:
7550:
7547:
7543:
7540:
7538:
7537:Virtual human
7535:
7533:
7530:
7528:
7525:
7524:
7523:
7520:
7518:
7515:
7514:
7512:
7510:
7506:
7496:
7493:
7491:
7488:
7486:
7483:
7481:
7478:
7476:
7473:
7469:
7466:
7464:
7463:hand tracking
7461:
7459:
7456:
7455:
7454:
7451:
7449:
7446:
7444:
7441:
7439:
7436:
7434:
7431:
7429:
7426:
7424:
7421:
7420:
7418:
7416:
7412:
7406:
7403:
7401:
7398:
7396:
7393:
7391:
7388:
7386:
7383:
7381:
7378:
7376:
7373:
7372:
7370:
7368:
7364:
7361:
7358:
7354:
7349:
7345:
7339:
7336:
7334:
7331:
7327:
7324:
7323:
7322:
7319:
7315:
7312:
7311:
7310:
7307:
7305:
7302:
7299:
7295:
7292:
7288:
7284:
7283:clay painting
7281:
7280:
7279:
7276:
7275:
7273:
7271:
7267:
7261:
7258:
7256:
7253:
7251:
7248:
7246:
7243:
7241:
7238:
7236:
7233:
7232:
7230:
7228:
7224:
7221:
7217:
7209:
7206:
7204:
7201:
7199:
7196:
7194:
7191:
7189:
7186:
7184:
7181:
7179:
7176:
7175:
7174:
7171:
7167:
7164:
7162:
7159:
7157:
7154:
7152:
7149:
7147:
7144:
7142:
7139:
7137:
7134:
7132:
7129:
7127:
7124:
7123:
7121:
7120:
7118:
7114:
7108:
7105:
7103:
7100:
7097:
7093:
7090:
7086:
7083:
7081:
7080:international
7078:
7077:
7076:
7073:
7071:
7068:
7066:
7063:
7061:
7058:
7054:
7051:
7050:
7049:
7046:
7044:
7041:
7039:
7036:
7034:
7031:
7027:
7024:
7023:
7022:
7019:
7018:
7016:
7012:
7000:
6997:
6995:
6992:
6990:
6987:
6985:
6982:
6980:
6977:
6976:
6974:
6972:
6969:
6967:
6964:
6962:
6959:
6957:
6954:
6952:
6949:
6947:
6944:
6942:
6939:
6937:
6934:
6932:
6929:
6927:
6924:
6922:
6919:
6917:
6914:
6912:
6909:
6907:
6904:
6903:
6901:
6899:
6895:
6889:
6886:
6884:
6883:United States
6881:
6879:
6876:
6874:
6871:
6869:
6866:
6864:
6861:
6859:
6856:
6854:
6851:
6849:
6846:
6844:
6841:
6839:
6836:
6834:
6831:
6829:
6826:
6824:
6821:
6819:
6816:
6814:
6811:
6809:
6806:
6804:
6801:
6799:
6796:
6794:
6791:
6790:
6787:
6784:
6780:
6775:
6768:
6763:
6761:
6756:
6754:
6749:
6748:
6745:
6733:
6730:
6728:
6725:
6723:
6720:
6718:
6715:
6713:
6710:
6708:
6705:
6703:
6700:
6698:
6695:
6693:
6690:
6688:
6685:
6683:
6680:
6678:
6675:
6673:
6670:
6668:
6665:
6663:
6660:
6658:
6657:Graph drawing
6655:
6653:
6650:
6646:
6643:
6642:
6641:
6638:
6636:
6633:
6631:
6628:
6626:
6623:
6622:
6620:
6614:
6604:
6601:
6599:
6596:
6594:
6591:
6589:
6586:
6584:
6581:
6579:
6578:Claudio Silva
6576:
6574:
6571:
6569:
6566:
6564:
6561:
6559:
6556:
6554:
6551:
6549:
6546:
6544:
6543:Mauro Martino
6541:
6539:
6536:
6534:
6531:
6529:
6526:
6524:
6521:
6519:
6516:
6514:
6511:
6509:
6506:
6504:
6501:
6499:
6496:
6494:
6491:
6490:
6488:
6484:
6478:
6475:
6473:
6470:
6468:
6467:Michael Maltz
6465:
6463:
6460:
6458:
6455:
6453:
6450:
6448:
6445:
6443:
6440:
6438:
6435:
6433:
6432:George Furnas
6430:
6428:
6425:
6423:
6420:
6418:
6415:
6413:
6412:Howard Wainer
6410:
6408:
6405:
6403:
6400:
6398:
6395:
6393:
6390:
6388:
6385:
6383:
6380:
6378:
6375:
6373:
6370:
6368:
6365:
6363:
6360:
6358:
6355:
6354:
6352:
6348:
6342:
6339:
6337:
6334:
6332:
6329:
6327:
6324:
6322:
6319:
6317:
6316:Rudolf Modley
6314:
6312:
6309:
6308:
6306:
6302:
6296:
6293:
6291:
6288:
6286:
6283:
6281:
6280:Max O. Lorenz
6278:
6276:
6273:
6271:
6268:
6266:
6263:
6261:
6258:
6256:
6253:
6251:
6248:
6246:
6243:
6241:
6238:
6236:
6233:
6232:
6230:
6226:
6220:
6217:
6215:
6212:
6210:
6207:
6205:
6202:
6200:
6197:
6195:
6192:
6190:
6189:Charles Booth
6187:
6185:
6182:
6180:
6177:
6175:
6172:
6170:
6167:
6165:
6164:Luigi Perozzo
6162:
6160:
6157:
6155:
6154:August Kekulé
6152:
6150:
6147:
6145:
6142:
6140:
6137:
6135:
6134:Charles Dupin
6132:
6131:
6129:
6125:
6119:
6118:Gaspard Monge
6116:
6114:
6111:
6109:
6106:
6104:
6103:Edmond Halley
6101:
6100:
6098:
6094:
6091:
6087:
6081:
6078:
6076:
6073:
6071:
6068:
6066:
6063:
6061:
6058:
6056:
6053:
6051:
6048:
6046:
6043:
6041:
6038:
6036:
6033:
6031:
6028:
6026:
6023:
6021:
6018:
6016:
6013:
6011:
6008:
6006:
6003:
6002:
6000:
5994:
5988:
5985:
5983:
5980:
5978:
5975:
5973:
5970:
5968:
5965:
5963:
5960:
5958:
5955:
5953:
5950:
5948:
5945:
5943:
5940:
5938:
5935:
5933:
5930:
5928:
5925:
5923:
5920:
5918:
5915:
5913:
5910:
5908:
5907:Crime mapping
5905:
5903:
5900:
5898:
5895:
5894:
5892:
5888:
5883:
5882:Visualization
5876:
5871:
5869:
5864:
5862:
5857:
5856:
5853:
5841:
5838:
5837:
5835:
5831:
5825:
5822:
5820:
5817:
5813:
5810:
5808:
5805:
5803:
5800:
5799:
5798:
5795:
5794:
5792:
5790:
5786:
5780:
5777:
5775:
5772:
5770:
5767:
5765:
5762:
5760:
5757:
5755:
5752:
5750:
5749:Shadow volume
5747:
5745:
5742:
5740:
5737:
5735:
5732:
5728:
5725:
5723:
5720:
5718:
5715:
5713:
5710:
5708:
5705:
5703:
5700:
5698:
5695:
5694:
5693:
5690:
5688:
5685:
5683:
5680:
5678:
5675:
5673:
5670:
5668:
5665:
5663:
5660:
5659:
5657:
5653:
5647:
5644:
5642:
5639:
5635:
5632:
5631:
5630:
5627:
5624:
5623:Triangle mesh
5620:
5618:
5615:
5613:
5610:
5606:
5603:
5602:
5601:
5598:
5596:
5593:
5591:
5588:
5586:
5583:
5581:
5578:
5575:
5572:
5570:
5567:
5565:
5561:
5559:
5556:
5554:
5553:3D projection
5551:
5550:
5548:
5546:
5542:
5532:
5529:
5527:
5524:
5522:
5519:
5517:
5514:
5512:
5509:
5508:
5506:
5504:
5500:
5494:
5493:Text-to-image
5491:
5489:
5486:
5484:
5481:
5480:
5478:
5476:
5472:
5466:
5463:
5461:
5458:
5457:
5455:
5453:
5449:
5445:
5438:
5433:
5431:
5426:
5424:
5419:
5418:
5415:
5398:
5394:
5388:
5380:
5374:
5370:
5369:
5364:
5358:
5356:
5336:
5329:
5321:
5317:
5311:
5304:
5298:
5294:
5284:
5281:
5279:
5276:
5274:
5271:
5269:
5266:
5264:
5261:
5259:
5258:Image scaling
5256:
5254:
5251:
5249:
5246:
5244:
5241:
5239:
5236:
5234:
5231:
5229:
5226:
5224:
5221:
5219:
5216:
5215:
5209:
5207:
5203:
5198:
5196:
5195:in-betweening
5192:
5188:
5183:
5181:
5177:
5174:
5164:
5162:
5158:
5154:
5150:
5146:
5142:
5138:
5134:
5130:
5125:
5121:
5117:
5116:Image editors
5113:
5111:
5107:
5103:
5099:
5095:
5091:
5087:
5083:
5079:
5075:
5071:
5066:
5064:
5060:
5056:
5052:
5047:
5045:
5041:
5040:input devices
5036:
5032:
5028:
5024:
5020:
5008:
5004:
5000:
4996:
4993:
4991:
4987:
4984:
4982:
4978:
4974:
4970:
4966:
4963:
4961:
4957:
4953:
4950:
4948:
4944:
4941:
4939:
4935:
4931:
4928:
4926:
4922:
4918:
4915:
4913:
4909:
4906:
4904:
4900:
4897:
4895:
4894:CTIA and GTIA
4891:
4887:
4883:
4880:
4879:
4878:
4876:
4872:
4868:
4864:
4860:
4856:
4852:
4847:
4845:
4843:
4838:
4835:dedicated to
4834:
4830:
4826:
4822:
4818:
4817:graphics card
4812:
4808:
4804:
4794:
4792:
4787:
4785:
4781:
4780:line segments
4777:
4773:
4769:
4764:
4761:
4757:
4756:digital image
4753:
4748:
4746:
4742:
4737:
4735:
4734:even–odd rule
4731:
4727:
4723:
4708:
4706:
4702:
4698:
4694:
4690:
4686:
4682:
4676:
4668:
4663:
4654:
4652:
4648:
4644:
4640:
4637:
4633:
4629:
4625:
4620:
4618:
4614:
4613:checker paint
4610:
4606:
4605:digital image
4602:
4598:
4585:
4581:
4577:
4573:
4570:
4566:
4562:
4558:
4555:
4552:
4548:
4547:
4546:
4544:
4543:graphics card
4540:
4535:
4533:
4529:
4525:
4521:
4517:
4514:(an array of
4513:
4484:
4479:
4473:
4464:
4460:
4456:
4447:
4443:
4439:
4430:
4426:
4422:
4416:
4407:
4406:
4405:
4386:
4378:
4375:
4364:
4360:
4350:
4346:
4336:
4332:
4325:
4320:
4315:
4309:
4300:
4296:
4286:
4282:
4272:
4268:
4261:
4254:
4246:
4243:
4236:
4231:
4226:
4219:
4214:
4209:
4204:
4197:
4192:
4187:
4182:
4175:
4170:
4165:
4160:
4154:
4149:
4146:
4141:
4137:
4129:
4128:
4127:
4125:
4110:
4091:
4086:
4078:
4075:
4068:
4063:
4058:
4051:
4046:
4041:
4036:
4029:
4024:
4019:
4014:
4007:
4002:
3997:
3992:
3986:
3981:
3976:
3972:
3964:
3963:
3962:
3960:
3941:
3936:
3930:
3921:
3917:
3911:
3907:
3897:
3893:
3887:
3883:
3873:
3869:
3863:
3859:
3852:
3847:
3842:
3836:
3827:
3823:
3813:
3809:
3799:
3795:
3788:
3781:
3775:
3770:
3765:
3760:
3753:
3746:
3742:
3736:
3731:
3724:
3719:
3712:
3708:
3702:
3695:
3690:
3685:
3678:
3674:
3667:
3662:
3659:
3654:
3650:
3642:
3641:
3640:
3623:
3618:
3612:
3607:
3602:
3597:
3590:
3583:
3579:
3573:
3568:
3561:
3556:
3549:
3545:
3539:
3532:
3527:
3522:
3515:
3511:
3504:
3499:
3494:
3490:
3482:
3481:
3480:
3478:
3474:
3459:
3455:
3440:
3437:
3433:
3429:
3425:
3415:
3413:
3409:
3405:
3400:
3398:
3397:
3392:
3388:
3371:
3369:
3354:
3349:
3347:
3343:
3339:
3320:
3315:
3307:
3303:
3297:
3293:
3283:
3279:
3273:
3269:
3259:
3255:
3249:
3245:
3238:
3233:
3228:
3220:
3216:
3206:
3202:
3192:
3188:
3181:
3174:
3166:
3162:
3156:
3151:
3144:
3137:
3133:
3127:
3120:
3115:
3108:
3104:
3097:
3092:
3089:
3084:
3080:
3072:
3071:
3070:
3053:
3048:
3040:
3036:
3030:
3025:
3018:
3011:
3007:
3001:
2994:
2989:
2982:
2978:
2971:
2966:
2961:
2957:
2949:
2948:
2947:
2945:
2941:
2926:
2922:
2907:
2904:
2899:
2896:
2892:
2888:
2884:
2880:
2878:
2873:
2869:
2864:
2862:
2858:
2854:
2850:
2846:
2842:
2840:
2835:
2831:
2820:
2817:
2809:
2798:
2795:
2791:
2788:
2784:
2781:
2777:
2774:
2770:
2767: –
2766:
2762:
2761:Find sources:
2755:
2751:
2745:
2744:
2739:This article
2737:
2733:
2728:
2727:
2702:
2696:
2691:
2688:
2681:
2676:
2670:
2665:
2657:
2653:
2646:
2639:
2622:
2616:
2613:
2608:
2601:
2596:
2593:
2587:
2582:
2574:
2570:
2563:
2556:
2539:
2533:
2528:
2521:
2518:
2513:
2507:
2502:
2494:
2490:
2483:
2476:
2475:
2474:
2466:
2464:
2460:
2455:
2453:
2449:
2445:
2441:
2437:
2433:
2429:
2425:
2422:
2414:
2409:
2382:
2376:
2373:
2370:
2365:
2362:
2359:
2356:
2349:
2346:
2343:
2338:
2335:
2332:
2326:
2321:
2315:
2312:
2306:
2299:
2298:
2297:
2278:
2275:
2272:
2269:
2266:
2263:
2260:
2257:
2254:
2251:
2247:
2244:
2236:
2220:
2217:
2214:
2211:
2208:
2205:
2202:
2199:
2196:
2193:
2189:
2186:
2178:
2177:
2176:
2156:
2150:
2143:
2137:
2130:
2124:
2121:
2118:
2113:
2110:
2107:
2100:
2097:
2094:
2091:
2086:
2083:
2080:
2074:
2069:
2064:
2057:
2054:
2045:
2042:
2035:
2026:
2025:
2024:
2022:
2018:
2015:This rotates
1996:
1990:
1987:
1984:
1979:
1976:
1973:
1966:
1963:
1960:
1957:
1952:
1949:
1946:
1940:
1935:
1929:
1923:
1916:
1915:
1914:
1908:
1903:
1894:
1890:
1885:
1881:
1877:
1873:
1852:
1849:
1846:
1840:
1835:
1832:
1828:
1824:
1819:
1815:
1807:
1806:
1805:
1803:
1799:
1795:
1791:
1786:
1784:
1783:
1777:
1773:
1769:
1767:
1761:
1757:
1753:
1748:
1746:
1743:
1740:
1736:
1733:
1732:column vector
1729:
1725:
1721:
1717:
1713:
1692:
1686:
1683:
1680:
1675:
1672:
1669:
1662:
1659:
1656:
1653:
1648:
1645:
1642:
1636:
1631:
1628:
1621:
1620:
1619:
1617:
1613:
1609:
1605:
1604:
1599:
1589:
1587:
1567:
1557:
1548:
1544:
1533:
1521:
1513:
1512:
1511:
1493:
1483:
1479:
1475:
1470:
1467:
1456:
1448:
1447:
1446:
1424:
1416:
1411:
1405:
1396:
1392:
1388:
1383:
1379:
1369:
1365:
1361:
1356:
1352:
1342:
1338:
1334:
1329:
1325:
1318:
1313:
1308:
1302:
1293:
1289:
1279:
1275:
1265:
1261:
1254:
1247:
1241:
1236:
1231:
1226:
1217:
1213:
1207:
1202:
1197:
1188:
1184:
1178:
1173:
1168:
1159:
1155:
1149:
1144:
1139:
1133:
1128:
1112:
1104:
1103:
1102:
1083:
1077:
1072:
1067:
1062:
1053:
1049:
1043:
1038:
1033:
1024:
1020:
1014:
1009:
1004:
995:
991:
985:
980:
975:
969:
964:
953:
945:
944:
943:
941:
937:
933:
930:
925:
922:
918:
913:
909:
904:
900:
896:
891:
887:
882:
878:
873:
869:
865:
861:
857:
853:
849:
836:
832:
828:
824:
820:
817:
816:
815:
813:
809:
806:
802:
798:
794:
790:
786:
782:
779:
775:
771:
767:
763:
758:
756:
752:
747:
743:
739:
735:
731:
727:
723:
720:
716:
712:
708:
703:
701:
697:
693:
688:
684:
681:will work as
679:
675:
671:
666:
653:
646:
642:
631:
628:
614:
608:
603:
579:
574:
566:
562:
561:
556:
552:
548:
544:
540:
539:
534:
525:
520:
509:
499:
495:
494:summary style
491:
485:
481:
477:
475:
471:This section
469:
460:
459:
451:
449:
445:
441:
437:
434:
430:
426:
422:
418:
414:
410:
406:
402:
398:
394:
390:
386:
383:(also called
382:
377:
375:
371:
367:
363:
358:
356:
352:
348:
345:at different
344:
340:
336:
332:
327:
325:
321:
316:
312:
308:
304:
300:
296:
292:
284:
281:
277:
273:
271:
267:
263:
259:
255:
245:
242:
227:
224:
216:
206:
202:
198:
192:
191:
186:This article
184:
175:
174:
165:
162:
154:
151:December 2009
143:
140:
136:
133:
129:
126:
122:
119:
115:
112: –
111:
107:
106:Find sources:
100:
96:
90:
89:
84:This article
82:
78:
73:
72:
67:
65:
58:
57:
52:
51:
46:
41:
32:
31:
19:
7944:anime series
7902:Motion comic
7771:visual music
7717:Pose to pose
7692:Inbetweening
7672:Chuckimation
7614:Shadowmation
7567:Animatronics
7468:eye tracking
7448:Morph target
7400:Multi-sketch
7366:
7151:Short series
7065:Art pipeline
7043:Story artist
6989:World War II
6858:South Africa
6692:Neuroimaging
6652:CPK coloring
6635:Color coding
6573:Hans Rosling
6553:Miriah Meyer
6518:Aaron Koblin
6503:Jeffrey Heer
6397:Edward Tufte
6392:Pat Hanrahan
6362:Nigel Holmes
6240:Otto Neurath
6179:Oliver Byrne
6127:19th century
5754:Shear matrix
5717:Path tracing
5702:Cone tracing
5697:Beam tracing
5617:Polygon mesh
5558:3D rendering
5474:
5400:. Retrieved
5396:
5387:
5367:
5365:(May 2013).
5344:12 September
5342:. Retrieved
5338:(PowerPoint)
5328:
5319:
5310:
5297:
5199:
5184:
5170:
5132:
5128:
5114:
5069:
5067:
5048:
5016:
4973:Super Scaler
4867:arcade games
4848:
4840:
4833:co-processor
4814:
4788:
4765:
4749:
4738:
4729:
4709:
4704:
4692:
4678:
4646:
4642:
4639:exclusive or
4621:
4612:
4594:
4583:
4576:line segment
4563:, such as a
4536:
4528:frame buffer
4509:
4403:
4112:
4108:
4106:
3958:
3956:
3638:
3461:
3457:
3442:
3438:
3421:
3401:
3394:
3390:
3374:
3372:
3356:
3350:
3335:
3068:
2928:
2924:
2909:
2905:
2900:
2890:
2886:
2882:
2875:
2871:
2867:
2865:
2857:scale factor
2844:
2837:
2833:
2827:
2812:
2803:
2793:
2786:
2779:
2772:
2760:
2748:Please help
2743:verification
2740:
2472:
2456:
2451:
2447:
2443:
2439:
2435:
2431:
2427:
2421:right-handed
2418:
2412:
2295:
2174:
2014:
1912:
1906:
1888:
1875:
1869:
1787:
1780:
1765:
1749:
1744:
1741:
1734:
1727:
1719:
1711:
1709:
1601:
1595:
1583:
1509:
1444:
1100:
939:
935:
931:
926:
920:
916:
911:
907:
902:
898:
894:
889:
885:
880:
876:
871:
867:
863:
845:
834:
830:
826:
822:
818:
811:
807:
800:
796:
792:
784:
780:
769:
759:
754:
750:
745:
741:
737:
733:
729:
725:
721:
714:
713:of a subset
706:
704:
699:
695:
691:
686:
682:
677:
673:
669:
667:
558:
543:rigid motion
536:
530:
503:
472:
378:
359:
328:
288:
253:
252:
237:
219:
210:
187:
157:
148:
138:
131:
124:
117:
105:
93:Please help
88:verification
85:
61:
54:
48:
47:Please help
44:
7870:model sheet
7727:Rubber hose
7650:model sheet
7428:Cel shading
7270:Stop motion
7255:Rotoscoping
7227:Traditional
7156:Stop-motion
7102:Outsourcing
6863:South Korea
6843:Philippines
6838:North Korea
6625:Cartography
6563:Ade Olufeko
6533:Manuel Lima
6462:Kwan-Liu Ma
6387:Stuart Card
6357:Borden Dent
6295:Erwin Raisz
6250:Henry Gantt
5769:Translation
5722:Ray casting
5712:Ray tracing
5590:Cel shading
5564:Image-based
5545:3D graphics
5526:Ray casting
5475:2D graphics
5397:blender.org
5191:Adobe Flash
5080:as well as
5051:video games
4930:Hudson Soft
4882:Atari, Inc.
4877:, include:
4849:Classic 2D
4831:drawing. A
4701:transparent
4697:translucent
4632:translucent
4628:transparent
4622:Painting a
4609:screentones
4584:virtual pen
3391:enlargement
2877:anisotropic
1802:determinant
1768:of rotation
1586:commutative
842:Translation
726:translation
413:translation
347:resolutions
335:engineering
324:photography
311:advertising
303:cartography
8001:Categories
7875:walk cycle
7742:Syncro-Vox
7655:walk cycle
7559:Mechanical
7485:Procedural
7385:PowerPoint
7338:Puppetoons
7333:Pixilation
7298:silhouette
7287:strata-cut
7278:Claymation
7219:Techniques
7208:Television
6979:Silent Era
6911:Bangladesh
6906:Azerbaijan
6793:Bangladesh
6782:By country
6548:John Maeda
6326:John Tukey
6290:Harry Beck
6285:Fritz Kahn
6035:Photograph
5833:Algorithms
5687:Reflection
5402:2019-04-24
5289:References
5007:YM7101 VDP
4801:See also:
4776:characters
4760:resolution
4689:refraction
4685:reflection
4667:composited
4512:raster map
4501:Techniques
3412:projection
2891:stretching
2806:April 2008
2776:newspapers
850:but not a
717:under the
595:such that
474:duplicates
370:PostScript
299:typography
197:improve it
121:newspapers
50:improve it
7885:off-model
7855:Key frame
7712:Pixel art
7707:Pinscreen
7665:off-model
7609:Scanimate
7527:Machinima
7326:Brickfilm
7314:go motion
7240:Flip book
6774:Animation
6630:Chartjunk
6598:Bang Wong
6493:Polo Chau
6199:John Snow
6174:John Venn
6055:Schematic
6040:Pictogram
5812:rendering
5802:animation
5692:Rendering
5283:Pixel art
5153:Photoshop
5102:CorelDRAW
5094:Macintosh
5055:solitaire
5029:, or the
4908:Commodore
4861:to early
4789:See also
4772:polylines
2849:homothety
2839:isotropic
2689:−
2658:∘
2614:−
2594:−
2575:∘
2519:−
2495:∘
2377:θ
2374:
2366:θ
2363:
2357:−
2350:θ
2347:
2339:θ
2336:
2316:θ
2313:−
2279:θ
2276:
2264:θ
2261:
2221:θ
2218:
2209:−
2206:θ
2203:
2125:θ
2122:
2114:θ
2111:
2101:θ
2098:
2092:−
2087:θ
2084:
1991:θ
1988:
1980:θ
1977:
1967:θ
1964:
1958:−
1953:θ
1950:
1930:θ
1833:−
1804: 1:
1687:θ
1684:
1676:θ
1673:
1663:θ
1660:
1654:−
1649:θ
1646:
1484:−
1468:−
647:δ
609:δ
580:δ
482: and
444:paradigms
433:rendering
405:equations
401:functions
213:July 2019
201:verifying
56:talk page
7971:Category
7880:lip sync
7760:Variants
7747:Zoetrope
7697:Morphing
7660:lip sync
7640:Blocking
7532:Aniforms
7509:Puppetry
7490:Skeletal
7357:timeline
7348:Computer
7203:Internet
7085:regional
7021:Animator
7014:Industry
6878:Thailand
6848:Portugal
6828:Malaysia
6616:Related
6025:Ideogram
5807:modeling
5734:Rotation
5672:Clipping
5655:Concepts
5634:Deferred
5600:Lighting
5580:Aliasing
5574:Unbiased
5569:Spectral
5253:Graphics
5238:Bit blit
5212:See also
5141:MacPaint
5110:Inkscape
5063:mahjongg
5013:Software
4837:blitting
4825:blitting
4797:Hardware
4784:aliasing
4752:rendered
4732:and the
4617:cartoons
4565:triangle
3479:matrix:
3396:dilation
3338:diameter
2248:′
2190:′
2058:′
2046:′
1878:forms a
1752:geometry
1612:rotation
1592:Rotation
766:isometry
719:function
565:operator
506:May 2022
417:rotation
411:such as
343:rendered
339:business
291:printing
7986:Outline
7353:history
7304:Graphic
7250:Masking
7141:Package
6966:Ukraine
6936:Hungary
6898:History
6888:Vietnam
6853:Romania
6813:Estonia
6808:Czechia
6498:Ben Fry
6010:Diagram
5739:Scaling
5629:Shading
5202:Blender
5163:, etc.
5145:MacDraw
5090:MacDraw
5065:, etc.
4990:TMS9918
4938:HuC6270
4934:Cynthia
4842:Blitter
4715:⁄
4681:shadows
4636:bitwise
4574:draw a
3406:with a
2879:scaling
2868:scaling
2861:similar
2851:) is a
2841:scaling
2790:scholar
2722:Scaling
1792:, with
1756:physics
787:). The
724:is the
553:of the
488:Please
421:scaling
393:typeset
295:drawing
283:sprites
256:is the
195:Please
135:scholar
7981:Portal
7542:Live2D
7458:facial
7423:T-pose
7321:Object
7294:Cutout
7173:Series
7122:Films
6961:Russia
6931:France
6921:Canada
6916:Brazil
6873:Taiwan
6833:Mexico
6798:Bhutan
6776:topics
6618:topics
6089:People
5996:Image
5890:Fields
5759:Shader
5531:Skybox
5516:Mode 7
5488:Layers
5375:
5322:, 2003
5320:w3.org
4995:Yamaha
4925:VIC-II
4899:Capcom
4873:, and
4863:16-bit
4829:sprite
4821:pixels
4809:, and
4693:layers
4657:Layers
4569:circle
4530:for a
4520:bitmap
4516:pixels
3436:vector
3346:volume
2903:vector
2792:
2785:
2778:
2771:
2763:
1764:angle
1758:, and
1608:matrix
929:vector
924:, 1).
860:matrix
563:is an
551:origin
547:vector
440:pixels
436:method
429:object
419:, and
337:, and
137:
130:
123:
116:
108:
7797:Anime
7438:Crowd
7380:Flash
7309:Model
7198:Flash
7146:Short
7116:Works
6956:Korea
6951:Japan
6941:India
6926:China
6868:Spain
6823:Japan
6818:India
6803:China
6070:Table
6005:Chart
5998:types
5779:Voxel
5764:Texel
5465:Pixel
5173:RETAS
5137:Apple
5059:chess
5044:mouse
5023:macOS
5017:Many
5003:V9958
4999:V9938
4960:S-PPU
4952:Ricoh
4890:ANTIC
4859:8-bit
4705:depth
4699:, or
4624:pixel
4551:image
2895:shape
2797:JSTOR
2783:books
2459:below
1880:group
1800:with
1606:is a
799:) by
760:In a
711:image
423:. In
315:image
142:JSTOR
128:books
7737:Sand
7375:2.5D
7053:List
7026:List
6946:Iran
6045:Plot
5503:2.5D
5373:ISBN
5346:2008
5218:2.5D
5178:and
5155:and
5149:GIMP
5106:xfig
5100:and
5005:and
4979:and
4965:Sega
4958:and
4936:and
4923:and
4853:and
4844:chip
4768:text
4630:and
3342:area
2769:news
2457:See
1870:The
1794:real
1600:, a
694:) =
557:. A
535:, a
403:and
397:font
293:and
114:news
7860:Cel
7433:CGI
7395:CSS
7390:SVG
6030:Map
5233:CGI
5204:or
5139:'s
5108:or
4997:'s
4969:VDP
4967:'s
4956:PPU
4954:'s
4945:'s
4943:NEC
4932:'s
4921:VIC
4919:'s
4912:OCS
4910:'s
4901:'s
4886:TIA
4884:'s
4778:or
4770:or
4741:map
4645:or
4619:).
4580:arc
4121:, p
4117:, p
4111:= (
3470:, p
3466:, p
3460:= (
3451:, v
3447:, v
3441:= (
3422:In
3393:or
3387:= k
3383:= v
3379:= v
3365:= v
3361:= v
2937:, p
2933:, p
2927:= (
2918:, v
2914:, v
2908:= (
2889:or
2828:In
2752:by
2654:270
2571:180
2371:cos
2360:sin
2344:sin
2333:cos
2273:cos
2258:sin
2215:sin
2200:cos
2119:cos
2108:sin
2095:sin
2081:cos
1985:cos
1974:sin
1961:sin
1947:cos
1887:SO(
1872:set
1844:det
1681:cos
1670:sin
1657:sin
1643:cos
1614:in
1596:In
897:= (
866:= (
827:/ T
814:):
791:of
776:of
740:by
732:by
728:of
705:If
668:If
531:In
446:of
199:by
97:by
8003::
7415:3D
7367:2D
7355:,
7285:,
5395:.
5354:^
5318:,
5197:.
5061:,
5057:,
5025:,
5001:,
4988:'
4975:,
4971:,
4892:,
4888:,
4869:,
4865:,
4846:.
4805:,
4793:.
4736:.
4687:,
4683:,
4578:,
4534:.
2946::
2881:,
2847:,
2843:,
2832:,
2491:90
2465:.
2023::
1893:.
1754:,
1712:xy
1618:.
942::
915:,
906:,
884:,
875:,
854:,
837:).
829:≅
825:)
757:.
753:+
702:.
698:+
450:.
415:,
357:.
333:,
309:,
305:,
301:,
59:.
7773:)
7769:(
7359:)
7351:(
7300:)
7296:(
7098:)
7094:(
6766:e
6759:t
6752:v
5874:e
5867:t
5860:v
5625:)
5621:(
5576:)
5562:(
5436:e
5429:t
5422:v
5405:.
5381:.
5348:.
4717:2
4713:1
4485:.
4480:]
4474:1
4465:z
4461:p
4457:s
4448:y
4444:p
4440:s
4431:x
4427:p
4423:s
4417:[
4387:]
4379:s
4376:1
4365:z
4361:p
4351:y
4347:p
4337:x
4333:p
4326:[
4321:=
4316:]
4310:1
4301:z
4297:p
4287:y
4283:p
4273:x
4269:p
4262:[
4255:]
4247:s
4244:1
4237:0
4232:0
4227:0
4220:0
4215:1
4210:0
4205:0
4198:0
4193:0
4188:1
4183:0
4176:0
4171:0
4166:0
4161:1
4155:[
4150:=
4147:p
4142:v
4138:S
4123:z
4119:y
4115:x
4113:p
4109:p
4092:.
4087:]
4079:s
4076:1
4069:0
4064:0
4059:0
4052:0
4047:1
4042:0
4037:0
4030:0
4025:0
4020:1
4015:0
4008:0
4003:0
3998:0
3993:1
3987:[
3982:=
3977:v
3973:S
3959:s
3942:.
3937:]
3931:1
3922:z
3918:p
3912:z
3908:v
3898:y
3894:p
3888:y
3884:v
3874:x
3870:p
3864:x
3860:v
3853:[
3848:=
3843:]
3837:1
3828:z
3824:p
3814:y
3810:p
3800:x
3796:p
3789:[
3782:]
3776:1
3771:0
3766:0
3761:0
3754:0
3747:z
3743:v
3737:0
3732:0
3725:0
3720:0
3713:y
3709:v
3703:0
3696:0
3691:0
3686:0
3679:x
3675:v
3668:[
3663:=
3660:p
3655:v
3651:S
3624:.
3619:]
3613:1
3608:0
3603:0
3598:0
3591:0
3584:z
3580:v
3574:0
3569:0
3562:0
3557:0
3550:y
3546:v
3540:0
3533:0
3528:0
3523:0
3516:x
3512:v
3505:[
3500:=
3495:v
3491:S
3472:z
3468:y
3464:x
3462:p
3458:p
3453:z
3449:y
3445:x
3443:v
3439:v
3385:z
3381:y
3377:x
3375:v
3367:z
3363:y
3359:x
3357:v
3321:.
3316:]
3308:z
3304:p
3298:z
3294:v
3284:y
3280:p
3274:y
3270:v
3260:x
3256:p
3250:x
3246:v
3239:[
3234:=
3229:]
3221:z
3217:p
3207:y
3203:p
3193:x
3189:p
3182:[
3175:]
3167:z
3163:v
3157:0
3152:0
3145:0
3138:y
3134:v
3128:0
3121:0
3116:0
3109:x
3105:v
3098:[
3093:=
3090:p
3085:v
3081:S
3054:.
3049:]
3041:z
3037:v
3031:0
3026:0
3019:0
3012:y
3008:v
3002:0
2995:0
2990:0
2983:x
2979:v
2972:[
2967:=
2962:v
2958:S
2939:z
2935:y
2931:x
2929:p
2925:p
2920:z
2916:y
2912:x
2910:v
2906:v
2874:(
2836:(
2819:)
2813:(
2808:)
2804:(
2794:·
2787:·
2780:·
2773:·
2746:.
2703:]
2697:0
2692:1
2682:1
2677:0
2671:[
2666:=
2663:)
2650:(
2647:R
2623:]
2617:1
2609:0
2602:0
2597:1
2588:[
2583:=
2580:)
2567:(
2564:R
2540:]
2534:0
2529:1
2522:1
2514:0
2508:[
2503:=
2500:)
2487:(
2484:R
2452:y
2448:θ
2444:y
2440:x
2436:θ
2432:y
2428:x
2413:θ
2398:.
2383:]
2327:[
2322:=
2319:)
2310:(
2307:R
2292:.
2270:y
2267:+
2255:x
2252:=
2245:y
2234:,
2212:y
2197:x
2194:=
2187:x
2171:.
2157:]
2151:y
2144:x
2138:[
2131:]
2075:[
2070:=
2065:]
2055:y
2043:x
2036:[
2011:.
1997:]
1941:[
1936:=
1933:)
1927:(
1924:R
1907:θ
1891:)
1889:n
1876:n
1866:.
1853:1
1850:=
1847:R
1841:,
1836:1
1829:R
1825:=
1820:T
1816:R
1766:θ
1745:v
1742:R
1735:v
1728:R
1720:θ
1714:-
1693:]
1637:[
1632:=
1629:R
1568:.
1562:v
1558:+
1554:u
1549:T
1545:=
1539:v
1534:T
1527:u
1522:T
1494:.
1488:v
1480:T
1476:=
1471:1
1462:v
1457:T
1429:v
1425:+
1421:p
1417:=
1412:]
1406:1
1397:z
1393:v
1389:+
1384:z
1380:p
1370:y
1366:v
1362:+
1357:y
1353:p
1343:x
1339:v
1335:+
1330:x
1326:p
1319:[
1314:=
1309:]
1303:1
1294:z
1290:p
1280:y
1276:p
1266:x
1262:p
1255:[
1248:]
1242:1
1237:0
1232:0
1227:0
1218:z
1214:v
1208:1
1203:0
1198:0
1189:y
1185:v
1179:0
1174:1
1169:0
1160:x
1156:v
1150:0
1145:0
1140:1
1134:[
1129:=
1125:p
1118:v
1113:T
1084:]
1078:1
1073:0
1068:0
1063:0
1054:z
1050:v
1044:1
1039:0
1034:0
1025:y
1021:v
1015:0
1010:1
1005:0
996:x
992:v
986:0
981:0
976:1
970:[
965:=
959:v
954:T
936:p
932:v
921:z
917:w
912:y
908:w
903:x
899:w
895:w
890:z
886:w
881:y
877:w
872:x
868:w
864:w
835:n
833:(
831:O
823:n
821:(
819:E
812:n
810:(
808:O
801:T
797:n
795:(
793:E
785:n
783:(
781:E
770:T
755:v
751:A
746:v
742:T
738:A
734:T
730:A
722:T
715:A
707:T
700:v
696:p
692:p
690:(
687:v
683:T
678:v
674:T
670:v
654:.
651:)
643:+
639:v
635:(
632:f
629:=
626:)
622:v
618:(
615:f
604:T
575:T
508:)
504:(
486:.
244:)
238:(
226:)
220:(
215:)
211:(
193:.
164:)
158:(
153:)
149:(
139:·
132:·
125:·
118:·
91:.
66:)
62:(
20:)
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
