3202:
2544:
3197:{\displaystyle {\begin{bmatrix}\mathbf {d} _{x}\\\mathbf {d} _{y}\\\mathbf {d} _{z}\end{bmatrix}}={\begin{bmatrix}1&0&0\\0&\cos(\mathbf {\theta } _{x})&\sin(\mathbf {\theta } _{x})\\0&-\sin(\mathbf {\theta } _{x})&\cos(\mathbf {\theta } _{x})\end{bmatrix}}{\begin{bmatrix}\cos(\mathbf {\theta } _{y})&0&-\sin(\mathbf {\theta } _{y})\\0&1&0\\\sin(\mathbf {\theta } _{y})&0&\cos(\mathbf {\theta } _{y})\end{bmatrix}}{\begin{bmatrix}\cos(\mathbf {\theta } _{z})&\sin(\mathbf {\theta } _{z})&0\\-\sin(\mathbf {\theta } _{z})&\cos(\mathbf {\theta } _{z})&0\\0&0&1\end{bmatrix}}\left({{\begin{bmatrix}\mathbf {a} _{x}\\\mathbf {a} _{y}\\\mathbf {a} _{z}\\\end{bmatrix}}-{\begin{bmatrix}\mathbf {c} _{x}\\\mathbf {c} _{y}\\\mathbf {c} _{z}\\\end{bmatrix}}}\right)}
1801:. They are useful for drawing chessboard floors which, in turn, serve for locating the base of objects on the scene. In the perspective of a geometric solid on the right, after choosing the principal vanishing point —which determines the horizon line— the 45° vanishing point on the left side of the drawing completes the characterization of the (equally distant) point of view. Two lines are drawn from the orthogonal projection of each vertex, one at 45° and one at 90° to the picture plane. After intersecting the ground line, those lines go toward the distance point (for 45°) or the principal point (for 90°). Their new intersection locates the projection of the map. Natural heights are measured above the ground line and then projected in the same way until they meet the vertical from the map.
567:
1195:
3985:
428:
458:
85:
4469:
5312:
420:
3563:
501:
1270:
487:
543:
529:
4205:
1289:
109:
1568:
1440:
515:
1401:) stems from its use in illustrations by the furniture industry. Like cavalier perspective, one face of the projected object is parallel to the viewing plane, and the third axis is projected as going off in an angle (typically 30° or 45° or arctan(2) = 63.4°). Unlike cavalier projection, where the third axis keeps its length, with cabinet projection the length of the receding lines is cut in half.
4926:
1556:
1664:
3980:{\displaystyle {\begin{aligned}\mathbf {d} _{x}&=c_{y}(s_{z}\mathbf {y} +c_{z}\mathbf {x} )-s_{y}\mathbf {z} \\\mathbf {d} _{y}&=s_{x}(c_{y}\mathbf {z} +s_{y}(s_{z}\mathbf {y} +c_{z}\mathbf {x} ))+c_{x}(c_{z}\mathbf {y} -s_{z}\mathbf {x} )\\\mathbf {d} _{z}&=c_{x}(c_{y}\mathbf {z} +s_{y}(s_{z}\mathbf {y} +c_{z}\mathbf {x} ))-s_{x}(c_{z}\mathbf {y} -s_{z}\mathbf {x} )\end{aligned}}}
4190:
1656:
473:
4464:{\displaystyle {\begin{bmatrix}\mathbf {f} _{x}\\\mathbf {f} _{y}\\\mathbf {f} _{w}\end{bmatrix}}={\begin{bmatrix}1&0&{\frac {\mathbf {e} _{x}}{\mathbf {e} _{z}}}\\0&1&{\frac {\mathbf {e} _{y}}{\mathbf {e} _{z}}}\\0&0&{\frac {1}{\mathbf {e} _{z}}}\end{bmatrix}}{\begin{bmatrix}\mathbf {d} _{x}\\\mathbf {d} _{y}\\\mathbf {d} _{z}\end{bmatrix}}}
43:
1174:
1317:, the displayed angles among the axes as well as the foreshortening factors (scale) are arbitrary. The distortion created thereby is usually attenuated by aligning one plane of the imaged object to be parallel with the plane of projection thereby creating a true shape, full-size image of the chosen plane. Special types of oblique projections are:
4704:
1466:. Axonometric instrument drawings are often used to approximate graphical perspective projections, but there is attendant distortion in the approximation. Because pictorial projections innately contain this distortion, in instrument drawings of pictorials great liberties may then be taken for economy of effort and best effect.
1520:), the direction of viewing is such that two of the three axes of space appear equally foreshortened, of which the attendant scale and angles of presentation are determined according to the angle of viewing; the scale of the third direction (vertical) is determined separately. Approximations are common in dimetric drawings.
4012:
5086:
A "weak" perspective projection uses the same principles of an orthographic projection, but requires the scaling factor to be specified, thus ensuring that closer objects appear bigger in the projection, and vice versa. It can be seen as a hybrid between an orthographic and a perspective projection,
4600:
1796:
line. If, as is often the case, the picture plane is vertical, all vertical lines are drawn vertically, and have no finite vanishing point on the picture plane. Various graphical methods can be easily envisaged for projecting geometrical scenes. For example, lines traced from the eye point at 45° to
1308:
the parallel projection rays are not perpendicular to the viewing plane as with orthographic projection, but strike the projection plane at an angle other than ninety degrees. In both orthographic and oblique projection, parallel lines in space appear parallel on the projected image. Because of its
5144:
The weak-perspective model thus approximates perspective projection while using a simpler model, similar to the pure (unscaled) orthographic perspective. It is a reasonable approximation when the depth of the object along the line of sight is small compared to the distance from the camera, and the
391:
of an object's basic shape to create a map of points, that are then connected to one another to create a visual element. The result is a graphic that contains conceptual properties to interpret the figure or image as not actually flat (2D), but rather, as a solid object (3D) being viewed on a 2D
1812:
The perspective projection requires a more involved definition as compared to orthographic projections. A conceptual aid to understanding the mechanics of this projection is to imagine the 2D projection as though the object(s) are being viewed through a camera viewfinder. The camera's position,
435:
Projection is achieved by the use of imaginary "projectors"; the projected, mental image becomes the technician's vision of the desired, finished picture. Methods provide a uniform imaging procedure among people trained in technical graphics (mechanical drawing, computer aided design, etc.). By
1179:
While orthographically projected images represent the three dimensional nature of the object projected, they do not represent the object as it would be recorded photographically or perceived by a viewer observing it directly. In particular, parallel lengths at all points in an orthographically
1797:
the picture plane intersect the latter along a circle whose radius is the distance of the eye point from the plane, thus tracing that circle aids the construction of all the vanishing points of 45° lines; in particular, the intersection of that circle with the horizon line consists of two
959:
1536:), the direction of viewing is such that all of the three axes of space appear unequally foreshortened. The scale along each of the three axes and the angles among them are determined separately as dictated by the angle of viewing. Approximations in Trimetric drawings are common.
1613:(1961), while not strictly utilizing parallel projection, is a well-known example, in which a channel of water seems to travel unaided along a downward path, only to then paradoxically fall once again as it returns to its source. The water thus appears to disobey the
5271:
4921:{\displaystyle {\begin{aligned}\mathbf {b} _{x}&=(\mathbf {d} _{x}\mathbf {s} _{x})/(\mathbf {d} _{z}\mathbf {r} _{x})\mathbf {r} _{z},\\\mathbf {b} _{y}&=(\mathbf {d} _{y}\mathbf {s} _{y})/(\mathbf {d} _{z}\mathbf {r} _{y})\mathbf {r} _{z}.\end{aligned}}}
1595:
In this isometric drawing, the blue sphere is two units higher than the red one. However, this difference in elevation is not apparent if one covers the right half of the picture, as the boxes (which serve as clues suggesting height) are then obscured.
4185:{\displaystyle {\begin{aligned}\mathbf {b} _{x}&={\frac {\mathbf {e} _{z}}{\mathbf {d} _{z}}}\mathbf {d} _{x}+\mathbf {e} _{x},\\\mathbf {b} _{y}&={\frac {\mathbf {e} _{z}}{\mathbf {d} _{z}}}\mathbf {d} _{y}+\mathbf {e} _{y}.\end{aligned}}}
1769:
Graphical projection methods rely on the duality between lines and points, whereby two straight lines determine a point while two points determine a straight line. The orthogonal projection of the eye point onto the picture plane is called the
5589:
This technique, also known as "Inverse Camera", is a
Perspective Projection Calculus with known values to calculate the last point on visible angle, projecting from the invisible point, after all needed transformations finished.
4480:
649:
and is a two-dimensional representation of a three-dimensional object. It is a parallel projection (the lines of projection are parallel both in reality and in the projection plane). It is the projection type of choice for
1169:{\displaystyle {\begin{bmatrix}b_{x}\\b_{y}\end{bmatrix}}={\begin{bmatrix}s_{x}&0&0\\0&0&s_{z}\end{bmatrix}}{\begin{bmatrix}a_{x}\\a_{y}\\a_{z}\end{bmatrix}}+{\begin{bmatrix}c_{x}\\c_{z}\end{bmatrix}}.}
2258:
570:
Parallel projection corresponds to a perspective projection with a hypothetical viewpoint; i.e. one where the camera lies an infinite distance away from the object and has an infinite focal length, or "zoom".
3314:
5190:
4017:
2190:
4693:
1417:. In this case, the horizontal sections are isometrically drawn so that the floor plans are not distorted and the verticals are drawn at an angle. The military projection is given by rotation in the
3355:
1180:
projected image are of the same scale regardless of whether they are far away or near to the virtual viewer. As a result, lengths are not foreshortened as they would be in a perspective projection.
5185:
4709:
4485:
3568:
3528:
3460:
1210:) of an object are produced, with each projection plane parallel to one of the coordinate axes of the object. The views are positioned relative to each other according to either of two schemes:
5426:
1592:, this is not how our eyes or photography normally work. It also can easily result in situations where depth and altitude are difficult to gauge, as is shown in the illustration to the right.
1484:, depending on the exact angle at which the view deviates from the orthogonal. A typical characteristic of orthographic pictorials is that one axis of space is usually displayed as vertical.
1504:
is uniform, therefore the proportionality of all sides and lengths are preserved, and the axes share a common scale. This enables measurements to be read or taken directly from the drawing.
1953:
1659:
Perspective of a geometric solid using two vanishing points. In this case, the map of the solid (orthogonal projection) is drawn below the perspective, as if bending the ground plane.
578:
are parallel to each other. Thus, lines that are parallel in three-dimensional space remain parallel in the two-dimensional projected image. Parallel projection also corresponds to a
936:
872:
2296:
2407:
2004:
1906:
1859:
2513:
2328:
395:
3D objects are largely displayed on two-dimensional mediums (such as paper and computer monitors). As such, graphical projections are a commonly used design element; notably, in
4999:
4964:
2441:
2366:
2094:
1754:. Photographic lenses and the human eye work in the same way, therefore the perspective projection looks the most realistic. Perspective projection is usually categorized into
5073:
5036:
4632:
5170:
5139:
2119:
1750:) appear to intersect in the projected image. For example, if railways are pictured with perspective projection, they appear to converge towards a single point, called the
3419:
2488:
2466:
2056:
2030:
5359:
3555:
3487:
3397:
1500:), the direction of viewing is such that the three axes of space appear equally foreshortened, and there is a common angle of 120° between them. The distortion caused by
1804:
While orthographic projection ignores perspective to allow accurate measurements, perspective projection shows distant objects as smaller to provide additional realism.
1792:
The principal vanishing point is the vanishing point of all horizontal lines perpendicular to the picture plane. The vanishing points of all horizontal lines lie on the
1458:
show an image of an object as viewed from a skew direction in order to reveal all three directions (axes) of space in one picture. Axonometric projections may be either
5586:
Alternatively, one could use clipping techniques, replacing the variables with values of the point that's are out of the FOV-angle and the point inside Camera Matrix.
5565:
5525:
5492:
5459:
5112:
802:
775:
748:
721:
694:
6146:
5300:
4595:{\displaystyle {\begin{aligned}\mathbf {b} _{x}&=\mathbf {f} _{x}/\mathbf {f} _{w}\\\mathbf {b} _{y}&=\mathbf {f} _{y}/\mathbf {f} _{w}\end{aligned}}}
6173:
380:
used to display a three-dimensional (3D) object on a two-dimensional (2D) surface. These projections rely on visual perspective and aspect analysis to
64:
51:
1584:
Objects drawn with parallel projection do not appear larger or smaller as they extend closer to or away from the viewer. While advantageous for
6562:
6535:
6108:
6032:
6007:
5982:
5828:
5801:
5774:
2058:), however negative z values are physically more correct, but the image will be inverted both horizontally and vertically. Which results in:
6578:
6182:
1561:
An example of the limitations of isometric projection. The height difference between the red and blue balls cannot be determined locally.
457:
2195:
6302:
6130:
5741:
3254:
6614:
5892:
5865:
5700:
2127:
4637:
6619:
6166:
355:
6624:
6425:
6226:
5818:
5764:
3319:
5791:
5266:{\displaystyle {\begin{aligned}&P_{x}={\frac {X}{Z_{\text{ave}}}}\\&P_{y}={\frac {Y}{Z_{\text{ave}}}}\end{aligned}}}
1817:
control the behavior of the projection transformation. The following variables are defined to describe this transformation:
4695:
is the viewed angle. (Note: This assumes that you map the points (-1,-1) and (1,1) to the corners of your viewing surface)
6599:
6550:
6540:
6430:
6249:
5145:
field of view is small. With these conditions, it can be assumed that all points on a 3D object are at the same distance
3492:
3424:
6634:
6545:
6410:
6350:
1739:
Perspective projection or perspective transformation is a projection where three-dimensional objects are projected on a
5367:
287:
31:
566:
542:
486:
6338:
6159:
5970:
5078:
Subsequent clipping and scaling operations may be necessary to map the 2D plane onto any particular display media.
1788:
its vanishing point, found at the intersection between the parallel line from the eye point and the picture plane.
1194:
500:
56:
4474:
in conjunction with an argument using similar triangles, leads to division by the homogeneous coordinate, giving
436:
following a method, the technician may produce the envisioned picture on a planar surface such as drawing paper.
1917:
528:
6609:
5615:
1609:
1588:, where measurements must be taken directly from the image, the result is a perceived distortion, since unlike
657:
If the normal of the viewing plane (the camera direction) is parallel to one of the primary axes (which is the
640:
184:
427:
407:. Projections can be calculated through employment of mathematical analysis and formulae, or by using various
1577:
depicts a staircase which seems to ascend (anticlockwise) or descend (clockwise) yet forms a continuous loop.
1313:
is used exclusively for pictorial purposes rather than for formal, working drawings. In an oblique pictorial
6629:
5675:
5650:
5625:
4196:
1642:
949:
is an arbitrary offset. These constants are optional, and can be used to properly align the viewport. Using
878:
814:
634:
548:
448:
154:
149:
130:
2263:
6557:
6507:
6472:
6450:
6445:
5925:
5882:
5664:
2371:
1968:
1956:
1870:
1823:
1614:
1589:
1444:
1434:
1374:
1198:
Symbols used to define whether a multiview projection is either First Angle (left) or Third Angle (right).
579:
514:
2493:
2301:
625:, as in English literature the latter usually refers only to a specific class of pictorials (see below).
6400:
6379:
6323:
5916:
5645:
5002:
4969:
4934:
2535:
2424:
2336:
2064:
1646:
1585:
950:
534:
520:
257:
194:
84:
5172:
from the camera without significant errors in the projection (compared to the full perspective model).
5049:
5012:
4608:
6283:
6269:
6213:
5670:
5635:
5620:
5600:
5043:
1633:
uses tricks of perspective to determine where a player can and cannot move in a puzzle-like fashion.
1533:
1497:
1189:
646:
478:
463:
262:
204:
135:
100:
17:
6100:
5930:
5148:
5117:
6604:
6415:
6343:
6231:
5640:
2099:
1517:
1370:
606:
561:
492:
472:
443:
419:
396:
348:
322:
297:
267:
159:
125:
6064:
3402:
2471:
2449:
2039:
2013:
1222:
onto planes that form a 6-sided box around the object. Although six different sides can be drawn,
6477:
6465:
6312:
6307:
6259:
5943:
5324:
3533:
3465:
3362:
1624:
1410:
1259:
506:
381:
142:
5311:
1766:, depending on the orientation of the projection plane towards the axes of the depicted object.
214:
179:
6049:
1226:
three views of a drawing give enough information to make a 3D object. These views are known as
6527:
6420:
6405:
6221:
6126:
6104:
6028:
6003:
5978:
5974:
5888:
5861:
5824:
5797:
5770:
5685:
5610:
5006:
3212:
2414:
1960:
1747:
1711:
respectively. The parallel lines through P.V. (in red) intercept L.O. in the vanishing points
1675:, and the point of view (P.V.) is right above it. P.P. is its projection on the picture plane
1545:
404:
400:
388:
307:
252:
118:
6512:
6502:
6384:
6372:
6093:
5935:
1629:
1269:
575:
292:
282:
5737:
5543:
5503:
5470:
5437:
5090:
2523:, and can be expressed as follows, expressing the rotation in terms of rotations about the
780:
753:
726:
699:
672:
6333:
6198:
6190:
5878:
5710:
5695:
5630:
2444:
1751:
327:
317:
189:
5908:
3990:
This transformed point can then be projected onto the 2D plane using the formula (here,
1439:
1288:
613:(the rays are not perpendicular to the image plane); but in special cases the result is
6482:
5680:
5660:
5039:
1574:
1501:
651:
591:
341:
272:
108:
6593:
6487:
6361:
5963:
5715:
5605:
5532:
5279:
1814:
1668:
1650:
1366:
1275:
277:
1567:
6492:
6455:
6440:
6435:
6355:
6296:
5528:
3316:), then the matrices drop out (as identities), and this reduces to simply a shift:
3208:
1604:
1369:
and the length on these axes are drawn with a 1:1 scale; it is thus similar to the
808:
represents forward direction - profile view), the following equations can be used:
583:
242:
199:
5947:
1667:
Axonometric projection of a scheme displaying the relevant elements of a vertical
1663:
6460:
6328:
6264:
5536:
2036:
Most conventions use positive z values (the plane being in front of the pinhole
2007:
587:
312:
302:
1743:. This has the effect that distant objects appear smaller than nearer objects.
5705:
5655:
5087:
and described either as a perspective projection with individual point depths
1555:
669:
axis), the mathematical transformation is as follows; To project the 3D point
602:
247:
5690:
1746:
It also means that lines which are parallel in nature (that is, meet at the
1655:
1619:
1448:
595:
219:
5075:
is the distance, from the 3D point being projected, to the entrance pupil.
42:
6002:(2nd ed.). Reading, Mass.: Addison-Wesley Pub. Co. pp. 146–148.
5939:
6318:
1218:
projection. In each, the appearances of views may be thought of as being
439:
There are two graphical projection categories, each with its own method:
408:
209:
804:
using an orthographic projection parallel to the y axis (where positive
6367:
1793:
1671:
perspective. The standing point (P.S.) is located on the ground plane
6497:
6254:
6073:
6066:
3D Pose from 3 Corresponding Points under Weak-Perspective
Projection
1600:
1385:
axis, usually 30 or 45°. The length of the third axis is not scaled.
377:
6151:
2443:
with respect to the initial coordinate system. This is achieved by
1627:
trick an immobile stairway changes its connectivity. The video game
6517:
6203:
1662:
1654:
1438:
1193:
574:
In parallel projection, the lines of sight from the object to the
565:
426:
418:
3219:
convention, which can be interpreted either as "rotate about the
2253:{\displaystyle \mathbf {\theta } _{x,y,z}=\langle 0,0,0\rangle ,}
6241:
3309:{\displaystyle \mathbf {\theta } _{x,y,z}=\langle 0,0,0\rangle }
6155:
2534:
axes (these calculations assume that the axes are ordered as a
601:
Images drawn in parallel projection rely upon the technique of
645:
The orthographic projection is derived from the principles of
36:
1349:. On the drawing, it is represented by only two coordinates,
1337:) a point of the object is represented by three coordinates,
384:
a complex object for viewing capability on a simpler plane.
5571:
Because the camera is in 3D, the same works for the screen
2185:{\displaystyle \mathbf {c} _{x,y,z}=\langle 0,0,0\rangle ,}
1381:, is drawn in diagonal, making an arbitrary angle with the
5909:"Planar Geometric Projections and Viewing Transformations"
5141:, or simply as an orthographic projection plus a scaling.
4688:{\displaystyle \alpha =2\cdot \arctan(1/\mathbf {e} _{z})}
5793:
Drawing distinctions: the varieties of graphic expression
3998:
is used as the projection plane; literature also may use
3251:(reading left-to-right)". If the camera is not rotated (
1774:(P.P. in the scheme on the right, from the Italian term
3350:{\displaystyle \mathbf {d} =\mathbf {a} -\mathbf {c} .}
5282:
4406:
4277:
4214:
3359:
Alternatively, without using matrices (let us replace
3134:
3071:
2916:
2766:
2616:
2553:
2515:
to the result. This transformation is often called a
1679:. L.O. and L.T. are the horizon and the ground lines (
1128:
1071:
1011:
968:
5738:"The Geometry of Perspective Drawing on the Computer"
5546:
5506:
5473:
5440:
5370:
5327:
5188:
5151:
5120:
5093:
5052:
5015:
4972:
4937:
4707:
4640:
4611:
4605:
The distance of the viewer from the display surface,
4483:
4208:
4015:
3566:
3536:
3495:
3468:
3427:
3405:
3365:
3322:
3257:
3207:
This representation corresponds to rotating by three
2547:
2496:
2474:
2452:
2427:
2374:
2339:
2304:
2266:
2198:
2130:
2102:
2067:
2042:
2016:
1971:
1920:
1873:
1826:
962:
881:
817:
783:
756:
729:
702:
675:
6571:
6526:
6393:
6282:
6240:
6212:
6189:
3523:{\displaystyle \sin \left(\theta _{\alpha }\right)}
3455:{\displaystyle \cos \left(\theta _{\alpha }\right)}
6092:
5962:
5740:. University of Utah § Department of Mathematics.
5559:
5519:
5486:
5453:
5420:
5353:
5294:
5265:
5164:
5133:
5106:
5067:
5038:is the distance from the recording surface to the
5030:
4993:
4958:
4920:
4687:
4626:
4594:
4463:
4184:
3979:
3549:
3522:
3481:
3454:
3413:
3391:
3349:
3308:
3196:
2507:
2482:
2460:
2435:
2401:
2360:
2322:
2290:
2252:
2184:
2113:
2088:
2050:
2024:
1998:
1947:
1900:
1853:
1168:
930:
866:
796:
769:
742:
715:
688:
6147:Creating 3D Environments from Digital Photographs
5421:{\displaystyle B_{x}=A_{x}{\frac {B_{z}}{A_{z}}}}
617:(the rays are perpendicular to the image plane).
5965:Mathematical Methods for Physics and Engineering
6025:Image Processing, Analysis & Machine Vision
4634:, directly relates to the field of view, where
6027:(2nd ed.). Chapman and Hall. p. 14.
5763:Mitchell, William; Malcolm McCullough (1994).
4698:The above equations can also be rewritten as:
3239:(reading right-to-left)" or "rotate about the
423:Several types of graphical projection compared
6167:
5847:. Englewood Cliffs: Prentice Hall], chapter 9
1617:. An extreme example is depicted in the film
1472:is further subdivided into three categories:
431:Various projections and how they are produced
349:
8:
3303:
3285:
2317:
2305:
2285:
2267:
2244:
2226:
2176:
2158:
1785:its intersection with the picture plane, and
1599:This visual ambiguity has been exploited in
1421:-plane and a vertical translation an amount
6123:2D/3D Graphics and Splines with Source Code
1603:, as well as "impossible object" drawings.
605:("to measure along axes"), as described in
6237:
6174:
6160:
6152:
5820:Advanced graphics programming using openGL
1948:{\displaystyle \mathbf {\theta } _{x,y,z}}
356:
342:
91:
5929:
5551:
5545:
5511:
5505:
5478:
5472:
5445:
5439:
5410:
5400:
5394:
5388:
5375:
5369:
5345:
5332:
5326:
5281:
5251:
5242:
5233:
5216:
5207:
5198:
5189:
5187:
5156:
5150:
5125:
5119:
5098:
5092:
5059:
5054:
5051:
5022:
5017:
5014:
4979:
4974:
4971:
4944:
4939:
4936:
4905:
4900:
4890:
4885:
4878:
4873:
4864:
4855:
4850:
4843:
4838:
4821:
4816:
4802:
4797:
4787:
4782:
4775:
4770:
4761:
4752:
4747:
4740:
4735:
4718:
4713:
4708:
4706:
4676:
4671:
4665:
4639:
4618:
4613:
4610:
4582:
4577:
4571:
4565:
4560:
4546:
4541:
4530:
4525:
4519:
4513:
4508:
4494:
4489:
4484:
4482:
4447:
4442:
4431:
4426:
4415:
4410:
4401:
4385:
4380:
4374:
4352:
4347:
4340:
4335:
4332:
4310:
4305:
4298:
4293:
4290:
4272:
4255:
4250:
4239:
4234:
4223:
4218:
4209:
4207:
4169:
4164:
4154:
4149:
4140:
4135:
4128:
4123:
4120:
4107:
4102:
4088:
4083:
4073:
4068:
4059:
4054:
4047:
4042:
4039:
4026:
4021:
4016:
4014:
3965:
3959:
3947:
3941:
3928:
3910:
3904:
3892:
3886:
3873:
3861:
3855:
3842:
3825:
3820:
3807:
3801:
3789:
3783:
3770:
3752:
3746:
3734:
3728:
3715:
3703:
3697:
3684:
3667:
3662:
3652:
3646:
3631:
3625:
3613:
3607:
3594:
3577:
3572:
3567:
3565:
3541:
3535:
3510:
3494:
3473:
3467:
3442:
3426:
3406:
3404:
3383:
3370:
3364:
3339:
3331:
3323:
3321:
3264:
3259:
3256:
3175:
3170:
3159:
3154:
3143:
3138:
3129:
3112:
3107:
3096:
3091:
3080:
3075:
3066:
3065:
3022:
3017:
2996:
2991:
2960:
2955:
2934:
2929:
2911:
2894:
2889:
2863:
2858:
2818:
2813:
2784:
2779:
2761:
2744:
2739:
2718:
2713:
2682:
2677:
2656:
2651:
2611:
2594:
2589:
2578:
2573:
2562:
2557:
2548:
2546:
2500:
2495:
2475:
2473:
2453:
2451:
2428:
2426:
2381:
2376:
2373:
2346:
2341:
2338:
2303:
2265:
2205:
2200:
2197:
2137:
2132:
2129:
2103:
2101:
2074:
2069:
2066:
2043:
2041:
2017:
2015:
1978:
1973:
1970:
1927:
1922:
1919:
1880:
1875:
1872:
1833:
1828:
1825:
1149:
1135:
1123:
1106:
1092:
1078:
1066:
1052:
1018:
1006:
989:
975:
963:
961:
922:
909:
899:
886:
880:
858:
845:
835:
822:
816:
788:
782:
761:
755:
734:
728:
707:
701:
680:
674:
5907:Ingrid Carlbom, Joseph Paciorek (1978).
5796:. Cornell University Press. p. 22.
83:
67:of all important aspects of the article.
5728:
2010:'s position relative to aforementioned
1282:with an angle of 45° and a ratio of 2/3
453:
99:
6023:Sonka, M; Hlavac, V; Boyle, R (1995).
5817:McReynolds, Tom; David Blythe (2005).
5321:-coordinate corresponds to a point at
5114:replaced by an average constant depth
2417:defined by the camera, with origin in
931:{\displaystyle b_{y}=s_{z}a_{z}+c_{z}}
867:{\displaystyle b_{x}=s_{x}a_{x}+c_{x}}
88:Classification of some 3D projections
63:Please consider expanding the lead to
2291:{\displaystyle \langle 1,2,0\rangle }
609:. In general, the resulting image is
18:Projection matrix (computer graphics)
7:
6579:List of computer graphics algorithms
5769:. John Wiley and Sons. p. 169.
2402:{\displaystyle \mathbf {d} _{x,y,z}}
1999:{\displaystyle \mathbf {e} _{x,y,z}}
1901:{\displaystyle \mathbf {c} _{x,y,z}}
1854:{\displaystyle \mathbf {a} _{x,y,z}}
1727:, and hence also their intersection
1719:: thus one can draw the projections
5583:in the above diagram and equation.
5531:—the axial distance from the
5361:multiply the point coordinates by:
2508:{\displaystyle -\mathbf {\theta } }
2323:{\displaystyle \langle 1,2\rangle }
1781:Two relevant points of a line are:
4994:{\displaystyle \mathbf {r} _{x,y}}
4959:{\displaystyle \mathbf {s} _{x,y}}
2436:{\displaystyle \mathbf {\theta } }
2361:{\displaystyle \mathbf {b} _{x,y}}
2089:{\displaystyle \mathbf {b} _{x,y}}
1778:, coined during the renaissance).
1540:Limitations of parallel projection
945:is an arbitrary scale factor, and
25:
6125:. Author Solutions Incorporated.
6048:Subhashis Banerjee (2002-02-18).
5843:D. Hearn, & M. Baker (1997).
5744:from the original on Apr 30, 2015
5701:Transform, clipping, and lighting
1357:. On the flat drawing, two axes,
6121:Koehler; Ralph (December 2000).
5310:
5068:{\displaystyle \mathbf {d} _{z}}
5055:
5031:{\displaystyle \mathbf {r} _{z}}
5018:
4975:
4940:
4901:
4886:
4874:
4851:
4839:
4817:
4798:
4783:
4771:
4748:
4736:
4714:
4672:
4627:{\displaystyle \mathbf {e} _{z}}
4614:
4578:
4561:
4542:
4526:
4509:
4490:
4443:
4427:
4411:
4381:
4348:
4336:
4306:
4294:
4251:
4235:
4219:
4165:
4150:
4136:
4124:
4103:
4084:
4069:
4055:
4043:
4022:
3966:
3948:
3911:
3893:
3862:
3821:
3808:
3790:
3753:
3735:
3704:
3663:
3653:
3632:
3614:
3573:
3407:
3340:
3332:
3324:
3171:
3155:
3139:
3108:
3092:
3076:
2590:
2574:
2558:
2490:and then applying a rotation by
2476:
2454:
2377:
2342:
2133:
2104:
2070:
2044:
2018:
1974:
1876:
1829:
1566:
1554:
1287:
1268:
541:
527:
513:
499:
485:
471:
456:
107:
41:
5001:is the recording surface size (
55:may be too short to adequately
6095:3D Game Programming All in One
5165:{\displaystyle Z_{\text{ave}}}
5134:{\displaystyle Z_{\text{ave}}}
4896:
4869:
4861:
4834:
4793:
4766:
4758:
4731:
4682:
4659:
3970:
3934:
3918:
3915:
3879:
3848:
3812:
3776:
3760:
3757:
3721:
3690:
3636:
3600:
3028:
3013:
3002:
2987:
2966:
2951:
2940:
2925:
2900:
2885:
2869:
2854:
2824:
2809:
2790:
2775:
2750:
2735:
2724:
2709:
2688:
2673:
2662:
2647:
2298:is projected to the 2D vector
1959:of the camera (represented by
586:(the distance from a camera's
65:provide an accessible overview
1:
6536:3D computer graphics software
6050:"The Weak-Perspective Camera"
2114:{\displaystyle \mathbf {a} .}
1908:– the 3D position of a point
1861:– the 3D position of a point
1615:law of conservation of energy
1206:, up to six pictures (called
6351:Hidden-surface determination
5845:Computer Graphics, C Version
3414:{\displaystyle \mathbf {x} }
2483:{\displaystyle \mathbf {a} }
2461:{\displaystyle \mathbf {c} }
2051:{\displaystyle \mathbf {c} }
2025:{\displaystyle \mathbf {c} }
621:should not be confused with
5998:Goldstein, Herbert (1980).
5354:{\displaystyle A_{x},A_{z}}
5082:Weak perspective projection
3550:{\displaystyle s_{\alpha }}
3482:{\displaystyle c_{\alpha }}
3392:{\displaystyle a_{x}-c_{x}}
288:Projection (linear algebra)
32:Projection (disambiguation)
6651:
6099:. Thomson Course. p.
6091:Kenneth C. Finney (2004).
6063:Alter, T. D. (July 1992).
5971:Cambridge University Press
5887:, Springer, p. xxix,
5860:. Boston: Addison-Wesley.
5575:-coordinate, substituting
5317:To determine which screen
3421:and so on, and abbreviate
1640:
1543:
1432:
1377:, as the third axis, here
1257:
1187:
638:
632:
559:
29:
5823:. Elsevier. p. 502.
4195:Or, in matrix form using
2409:as the position of point
2368:we first define a vector
1772:principal vanishing point
1321:Cavalier projection (45°)
6615:Euclidean solid geometry
6072:(Technical report). MIT
5790:Maynard, Patric (2005).
5616:Cross section (geometry)
5567:is the subject distance.
1912:representing the camera.
1865:that is to be projected.
1373:, although it is not an
953:, the equations become:
641:Geometric transformation
411:and optical techniques.
6563:Vector graphics editors
6558:Raster graphics editors
5676:Perspective (graphical)
5651:Homogeneous coordinates
5626:Curvilinear perspective
4197:homogeneous coordinates
2096:– the 2D projection of
1764:three-point perspective
1643:Perspective (graphical)
1456:Axonometric projections
635:Orthographic projection
629:Orthographic projection
549:Three-point perspective
387:3D projections use the
155:Curvilinear perspective
131:Orthographic projection
6620:Functions and mappings
6446:Checkerboard rendering
5884:The geometry of an art
5665:Cylindrical projection
5561:
5521:
5488:
5455:
5422:
5355:
5296:
5276:assuming focal length
5267:
5166:
5135:
5108:
5069:
5032:
4995:
4960:
4922:
4689:
4628:
4596:
4465:
4186:
3981:
3551:
3524:
3483:
3456:
3415:
3393:
3351:
3310:
3198:
2509:
2484:
2462:
2437:
2403:
2362:
2333:Otherwise, to compute
2324:
2292:
2254:
2186:
2115:
2090:
2052:
2026:
2000:
1949:
1902:
1855:
1736:
1660:
1637:Perspective projection
1590:perspective projection
1586:architectural drawings
1470:Axonometric projection
1452:
1435:Axonometric projection
1429:Axonometric projection
1375:axonometric projection
1199:
1170:
932:
868:
798:
771:
744:
717:
690:
623:axonometric projection
580:perspective projection
571:
449:perspective projection
432:
424:
150:Perspective projection
89:
6625:Graphical projections
6401:Affine transformation
6380:Surface triangulation
6324:Anisotropic filtering
5940:10.1145/356744.356750
5917:ACM Computing Surveys
5646:Exploded-view drawing
5562:
5560:{\displaystyle A_{z}}
5522:
5520:{\displaystyle B_{z}}
5489:
5487:{\displaystyle A_{x}}
5456:
5454:{\displaystyle B_{x}}
5423:
5356:
5297:
5268:
5167:
5136:
5109:
5107:{\displaystyle Z_{i}}
5070:
5033:
4996:
4966:is the display size,
4961:
4923:
4690:
4629:
4597:
4466:
4187:
3982:
3552:
3525:
3484:
3457:
3416:
3394:
3352:
3311:
3199:
2510:
2485:
2463:
2438:
2404:
2363:
2325:
2293:
2255:
2187:
2116:
2091:
2053:
2027:
2001:
1950:
1903:
1856:
1666:
1658:
1647:Transformation matrix
1442:
1204:multiview projections
1197:
1171:
951:matrix multiplication
933:
869:
799:
797:{\displaystyle b_{y}}
772:
770:{\displaystyle b_{x}}
745:
743:{\displaystyle a_{z}}
718:
716:{\displaystyle a_{y}}
691:
689:{\displaystyle a_{x}}
569:
535:Two-point perspective
521:One-point perspective
430:
422:
258:Computer-aided design
195:Exploded view drawing
87:
6600:3D computer graphics
5856:James Foley (1997).
5766:Digital design media
5736:Treibergs, Andrejs.
5671:Multiview projection
5636:Descriptive geometry
5621:Cross-sectional view
5601:3D computer graphics
5544:
5504:
5471:
5438:
5368:
5325:
5280:
5186:
5149:
5118:
5091:
5050:
5013:
4970:
4935:
4705:
4638:
4609:
4481:
4206:
4013:
3564:
3534:
3493:
3466:
3425:
3403:
3363:
3320:
3255:
2545:
2494:
2472:
2450:
2425:
2372:
2337:
2302:
2264:
2196:
2128:
2100:
2065:
2040:
2014:
1969:
1918:
1871:
1824:
1808:Mathematical formula
1534:Trimetric projection
1530:trimetric pictorials
1524:Trimetric projection
1498:Isometric projection
1494:isometric pictorials
1488:Isometric projection
1482:trimetric projection
1474:isometric projection
1371:dimetric projections
1331:cavalier perspective
1296:military perspective
1294:Stone arch drawn in
1190:Multiview projection
1184:Multiview projection
960:
879:
815:
781:
754:
727:
700:
673:
647:descriptive geometry
479:Isometric projection
464:Multiview projection
374:graphical projection
263:Descriptive geometry
136:Isometric projection
101:Graphical projection
30:For other uses, see
6635:Projective geometry
6416:Collision detection
6344:Global illumination
6000:Classical Mechanics
5961:Riley, K F (2006).
5641:Engineering drawing
1518:Dimetric projection
1514:dimetric pictorials
1508:Dimetric projection
1478:dimetric projection
1415:military projection
1405:Military projection
1399:cabinet perspective
1365:on the figure, are
1327:cavalier projection
1306:oblique projections
562:Parallel projection
556:Parallel projection
493:Military projection
444:parallel projection
397:engineering drawing
323:Video game graphics
298:Projective geometry
268:Engineering drawing
160:Reverse perspective
126:Parallel projection
95:Part of a series on
6466:Scanline rendering
6260:Parallax scrolling
6250:Isometric graphics
5557:
5517:
5484:
5451:
5418:
5351:
5292:
5263:
5261:
5162:
5131:
5104:
5065:
5028:
4991:
4956:
4918:
4916:
4685:
4624:
4592:
4590:
4461:
4455:
4395:
4263:
4182:
4180:
3977:
3975:
3547:
3520:
3479:
3452:
3411:
3389:
3347:
3306:
3243:axes (axes of the
3223:axes (axes of the
3194:
3183:
3120:
3055:
2905:
2755:
2602:
2505:
2480:
2458:
2433:
2413:with respect to a
2399:
2358:
2320:
2288:
2250:
2182:
2111:
2086:
2048:
2022:
1996:
1945:
1898:
1851:
1737:
1687:). The bold lines
1661:
1625:forced perspective
1532:(for methods, see
1516:(for methods, see
1496:(for methods, see
1453:
1411:oblique projection
1395:cabinet projection
1389:Cabinet projection
1311:oblique projection
1280:cabinet projection
1260:Oblique projection
1254:Oblique projection
1200:
1166:
1157:
1114:
1060:
997:
928:
864:
794:
767:
750:onto the 2D point
740:
713:
686:
572:
507:Cabinet projection
433:
425:
143:Oblique projection
90:
6587:
6586:
6528:Graphics software
6421:Planar projection
6406:Back-face culling
6278:
6277:
6222:Alpha compositing
6183:Computer graphics
6110:978-1-59200-136-1
6034:978-0-412-45570-4
6009:978-0-201-02918-5
5984:978-0-521-67971-8
5858:Computer Graphics
5830:978-1-55860-659-3
5803:978-0-8014-7280-0
5776:978-0-471-28666-0
5686:Technical drawing
5611:Computer graphics
5416:
5257:
5254:
5222:
5219:
5159:
5128:
5007:Photographic film
4391:
4358:
4316:
4146:
4065:
3213:Tait–Bryan angles
2538:system of axes):
2415:coordinate system
1961:Tait–Bryan angles
1813:orientation, and
1748:point at infinity
1681:linea d'orizzonte
1546:Impossible object
1445:axonometric views
941:where the vector
582:with an infinite
405:computer graphics
389:primary qualities
366:
365:
308:Technical drawing
253:Computer graphics
82:
81:
16:(Redirected from
6642:
6513:Volume rendering
6385:Wire-frame model
6238:
6176:
6169:
6162:
6153:
6136:
6117:
6098:
6078:
6077:
6071:
6060:
6054:
6053:
6045:
6039:
6038:
6020:
6014:
6013:
5995:
5989:
5988:
5968:
5958:
5952:
5951:
5933:
5913:
5904:
5898:
5897:
5875:
5869:
5854:
5848:
5841:
5835:
5834:
5814:
5808:
5807:
5787:
5781:
5780:
5760:
5754:
5753:
5751:
5749:
5733:
5566:
5564:
5563:
5558:
5556:
5555:
5526:
5524:
5523:
5518:
5516:
5515:
5493:
5491:
5490:
5485:
5483:
5482:
5460:
5458:
5457:
5452:
5450:
5449:
5427:
5425:
5424:
5419:
5417:
5415:
5414:
5405:
5404:
5395:
5393:
5392:
5380:
5379:
5360:
5358:
5357:
5352:
5350:
5349:
5337:
5336:
5314:
5301:
5299:
5298:
5295:{\textstyle f=1}
5293:
5272:
5270:
5269:
5264:
5262:
5258:
5256:
5255:
5252:
5243:
5238:
5237:
5227:
5223:
5221:
5220:
5217:
5208:
5203:
5202:
5192:
5171:
5169:
5168:
5163:
5161:
5160:
5157:
5140:
5138:
5137:
5132:
5130:
5129:
5126:
5113:
5111:
5110:
5105:
5103:
5102:
5074:
5072:
5071:
5066:
5064:
5063:
5058:
5037:
5035:
5034:
5029:
5027:
5026:
5021:
5000:
4998:
4997:
4992:
4990:
4989:
4978:
4965:
4963:
4962:
4957:
4955:
4954:
4943:
4927:
4925:
4924:
4919:
4917:
4910:
4909:
4904:
4895:
4894:
4889:
4883:
4882:
4877:
4868:
4860:
4859:
4854:
4848:
4847:
4842:
4826:
4825:
4820:
4807:
4806:
4801:
4792:
4791:
4786:
4780:
4779:
4774:
4765:
4757:
4756:
4751:
4745:
4744:
4739:
4723:
4722:
4717:
4694:
4692:
4691:
4686:
4681:
4680:
4675:
4669:
4633:
4631:
4630:
4625:
4623:
4622:
4617:
4601:
4599:
4598:
4593:
4591:
4587:
4586:
4581:
4575:
4570:
4569:
4564:
4551:
4550:
4545:
4535:
4534:
4529:
4523:
4518:
4517:
4512:
4499:
4498:
4493:
4470:
4468:
4467:
4462:
4460:
4459:
4452:
4451:
4446:
4436:
4435:
4430:
4420:
4419:
4414:
4400:
4399:
4392:
4390:
4389:
4384:
4375:
4359:
4357:
4356:
4351:
4345:
4344:
4339:
4333:
4317:
4315:
4314:
4309:
4303:
4302:
4297:
4291:
4268:
4267:
4260:
4259:
4254:
4244:
4243:
4238:
4228:
4227:
4222:
4191:
4189:
4188:
4183:
4181:
4174:
4173:
4168:
4159:
4158:
4153:
4147:
4145:
4144:
4139:
4133:
4132:
4127:
4121:
4112:
4111:
4106:
4093:
4092:
4087:
4078:
4077:
4072:
4066:
4064:
4063:
4058:
4052:
4051:
4046:
4040:
4031:
4030:
4025:
3986:
3984:
3983:
3978:
3976:
3969:
3964:
3963:
3951:
3946:
3945:
3933:
3932:
3914:
3909:
3908:
3896:
3891:
3890:
3878:
3877:
3865:
3860:
3859:
3847:
3846:
3830:
3829:
3824:
3811:
3806:
3805:
3793:
3788:
3787:
3775:
3774:
3756:
3751:
3750:
3738:
3733:
3732:
3720:
3719:
3707:
3702:
3701:
3689:
3688:
3672:
3671:
3666:
3656:
3651:
3650:
3635:
3630:
3629:
3617:
3612:
3611:
3599:
3598:
3582:
3581:
3576:
3556:
3554:
3553:
3548:
3546:
3545:
3529:
3527:
3526:
3521:
3519:
3515:
3514:
3488:
3486:
3485:
3480:
3478:
3477:
3461:
3459:
3458:
3453:
3451:
3447:
3446:
3420:
3418:
3417:
3412:
3410:
3398:
3396:
3395:
3390:
3388:
3387:
3375:
3374:
3356:
3354:
3353:
3348:
3343:
3335:
3327:
3315:
3313:
3312:
3307:
3281:
3280:
3263:
3211:(more properly,
3203:
3201:
3200:
3195:
3193:
3189:
3188:
3187:
3180:
3179:
3174:
3164:
3163:
3158:
3148:
3147:
3142:
3125:
3124:
3117:
3116:
3111:
3101:
3100:
3095:
3085:
3084:
3079:
3060:
3059:
3027:
3026:
3021:
3001:
3000:
2995:
2965:
2964:
2959:
2939:
2938:
2933:
2910:
2909:
2899:
2898:
2893:
2868:
2867:
2862:
2823:
2822:
2817:
2789:
2788:
2783:
2760:
2759:
2749:
2748:
2743:
2723:
2722:
2717:
2687:
2686:
2681:
2661:
2660:
2655:
2607:
2606:
2599:
2598:
2593:
2583:
2582:
2577:
2567:
2566:
2561:
2521:
2520:
2519:camera transform
2514:
2512:
2511:
2506:
2504:
2489:
2487:
2486:
2481:
2479:
2467:
2465:
2464:
2459:
2457:
2442:
2440:
2439:
2434:
2432:
2408:
2406:
2405:
2400:
2398:
2397:
2380:
2367:
2365:
2364:
2359:
2357:
2356:
2345:
2329:
2327:
2326:
2321:
2297:
2295:
2294:
2289:
2259:
2257:
2256:
2251:
2222:
2221:
2204:
2191:
2189:
2188:
2183:
2154:
2153:
2136:
2120:
2118:
2117:
2112:
2107:
2095:
2093:
2092:
2087:
2085:
2084:
2073:
2057:
2055:
2054:
2049:
2047:
2031:
2029:
2028:
2023:
2021:
2005:
2003:
2002:
1997:
1995:
1994:
1977:
1954:
1952:
1951:
1946:
1944:
1943:
1926:
1907:
1905:
1904:
1899:
1897:
1896:
1879:
1860:
1858:
1857:
1852:
1850:
1849:
1832:
1776:punto principale
1699:, and intercept
1570:
1558:
1291:
1272:
1175:
1173:
1172:
1167:
1162:
1161:
1154:
1153:
1140:
1139:
1119:
1118:
1111:
1110:
1097:
1096:
1083:
1082:
1065:
1064:
1057:
1056:
1023:
1022:
1002:
1001:
994:
993:
980:
979:
937:
935:
934:
929:
927:
926:
914:
913:
904:
903:
891:
890:
873:
871:
870:
865:
863:
862:
850:
849:
840:
839:
827:
826:
803:
801:
800:
795:
793:
792:
776:
774:
773:
768:
766:
765:
749:
747:
746:
741:
739:
738:
722:
720:
719:
714:
712:
711:
695:
693:
692:
687:
685:
684:
652:working drawings
607:Pohlke's theorem
576:projection plane
545:
531:
517:
503:
489:
475:
460:
378:design technique
358:
351:
344:
293:Projection plane
283:Plans (drawings)
111:
92:
77:
74:
68:
45:
37:
27:Design technique
21:
6650:
6649:
6645:
6644:
6643:
6641:
6640:
6639:
6610:Display devices
6590:
6589:
6588:
6583:
6567:
6522:
6389:
6334:Fluid animation
6274:
6236:
6208:
6199:Diffusion curve
6191:Vector graphics
6185:
6180:
6143:
6133:
6120:
6111:
6090:
6087:
6085:Further reading
6082:
6081:
6069:
6062:
6061:
6057:
6047:
6046:
6042:
6035:
6022:
6021:
6017:
6010:
5997:
5996:
5992:
5985:
5960:
5959:
5955:
5931:10.1.1.532.4774
5911:
5906:
5905:
5901:
5895:
5879:Kirsti Andersen
5877:
5876:
5872:
5855:
5851:
5842:
5838:
5831:
5816:
5815:
5811:
5804:
5789:
5788:
5784:
5777:
5762:
5761:
5757:
5747:
5745:
5735:
5734:
5730:
5725:
5720:
5711:Viewing frustum
5696:Texture mapping
5631:Cutaway drawing
5596:
5547:
5542:
5541:
5507:
5502:
5501:
5474:
5469:
5468:
5441:
5436:
5435:
5406:
5396:
5384:
5371:
5366:
5365:
5341:
5328:
5323:
5322:
5308:
5278:
5277:
5260:
5259:
5247:
5229:
5225:
5224:
5212:
5194:
5184:
5183:
5152:
5147:
5146:
5121:
5116:
5115:
5094:
5089:
5088:
5084:
5053:
5048:
5047:
5016:
5011:
5010:
4973:
4968:
4967:
4938:
4933:
4932:
4915:
4914:
4899:
4884:
4872:
4849:
4837:
4827:
4815:
4812:
4811:
4796:
4781:
4769:
4746:
4734:
4724:
4712:
4703:
4702:
4670:
4636:
4635:
4612:
4607:
4606:
4589:
4588:
4576:
4559:
4552:
4540:
4537:
4536:
4524:
4507:
4500:
4488:
4479:
4478:
4454:
4453:
4441:
4438:
4437:
4425:
4422:
4421:
4409:
4402:
4394:
4393:
4379:
4372:
4367:
4361:
4360:
4346:
4334:
4330:
4325:
4319:
4318:
4304:
4292:
4288:
4283:
4273:
4262:
4261:
4249:
4246:
4245:
4233:
4230:
4229:
4217:
4210:
4204:
4203:
4179:
4178:
4163:
4148:
4134:
4122:
4113:
4101:
4098:
4097:
4082:
4067:
4053:
4041:
4032:
4020:
4011:
4010:
3974:
3973:
3955:
3937:
3924:
3900:
3882:
3869:
3851:
3838:
3831:
3819:
3816:
3815:
3797:
3779:
3766:
3742:
3724:
3711:
3693:
3680:
3673:
3661:
3658:
3657:
3642:
3621:
3603:
3590:
3583:
3571:
3562:
3561:
3537:
3532:
3531:
3506:
3502:
3491:
3490:
3469:
3464:
3463:
3438:
3434:
3423:
3422:
3401:
3400:
3379:
3366:
3361:
3360:
3318:
3317:
3258:
3253:
3252:
3247:) in the order
3227:) in the order
3182:
3181:
3169:
3166:
3165:
3153:
3150:
3149:
3137:
3130:
3119:
3118:
3106:
3103:
3102:
3090:
3087:
3086:
3074:
3067:
3061:
3054:
3053:
3048:
3043:
3037:
3036:
3031:
3016:
3005:
2990:
2975:
2974:
2969:
2954:
2943:
2928:
2912:
2904:
2903:
2888:
2877:
2872:
2857:
2845:
2844:
2839:
2834:
2828:
2827:
2812:
2798:
2793:
2778:
2762:
2754:
2753:
2738:
2727:
2712:
2698:
2692:
2691:
2676:
2665:
2650:
2639:
2633:
2632:
2627:
2622:
2612:
2601:
2600:
2588:
2585:
2584:
2572:
2569:
2568:
2556:
2549:
2543:
2542:
2518:
2517:
2492:
2491:
2470:
2469:
2448:
2447:
2423:
2422:
2421:and rotated by
2375:
2370:
2369:
2340:
2335:
2334:
2300:
2299:
2262:
2261:
2199:
2194:
2193:
2131:
2126:
2125:
2098:
2097:
2068:
2063:
2062:
2038:
2037:
2012:
2011:
2008:display surface
1972:
1967:
1966:
1921:
1916:
1915:
1874:
1869:
1868:
1827:
1822:
1821:
1810:
1799:distance points
1752:vanishing point
1653:
1639:
1582:
1581:
1580:
1579:
1578:
1571:
1563:
1562:
1559:
1548:
1542:
1526:
1510:
1490:
1437:
1431:
1407:
1391:
1335:high view point
1323:
1302:
1301:
1300:
1299:
1298:
1292:
1284:
1283:
1273:
1262:
1256:
1250:are also used.
1192:
1186:
1156:
1155:
1145:
1142:
1141:
1131:
1124:
1113:
1112:
1102:
1099:
1098:
1088:
1085:
1084:
1074:
1067:
1059:
1058:
1048:
1046:
1041:
1035:
1034:
1029:
1024:
1014:
1007:
996:
995:
985:
982:
981:
971:
964:
958:
957:
918:
905:
895:
882:
877:
876:
854:
841:
831:
818:
813:
812:
784:
779:
778:
757:
752:
751:
730:
725:
724:
703:
698:
697:
676:
671:
670:
643:
637:
631:
564:
558:
551:
546:
537:
532:
523:
518:
509:
504:
495:
490:
481:
476:
467:
461:
417:
362:
333:
332:
328:Viewing frustum
318:Vanishing point
233:
225:
224:
215:Worm's-eye view
190:Cutaway drawing
180:Bird's-eye view
175:
167:
166:
121:
78:
72:
69:
62:
50:This article's
46:
35:
28:
23:
22:
15:
12:
11:
5:
6648:
6646:
6638:
6637:
6632:
6630:Linear algebra
6627:
6622:
6617:
6612:
6607:
6602:
6592:
6591:
6585:
6584:
6582:
6581:
6575:
6573:
6569:
6568:
6566:
6565:
6560:
6555:
6554:
6553:
6548:
6543:
6532:
6530:
6524:
6523:
6521:
6520:
6515:
6510:
6505:
6500:
6495:
6490:
6485:
6483:Shadow mapping
6480:
6475:
6470:
6469:
6468:
6463:
6458:
6453:
6448:
6443:
6438:
6428:
6423:
6418:
6413:
6408:
6403:
6397:
6395:
6391:
6390:
6388:
6387:
6382:
6377:
6376:
6375:
6365:
6358:
6353:
6348:
6347:
6346:
6336:
6331:
6326:
6321:
6316:
6310:
6305:
6299:
6294:
6288:
6286:
6280:
6279:
6276:
6275:
6273:
6272:
6267:
6262:
6257:
6252:
6246:
6244:
6235:
6234:
6229:
6224:
6218:
6216:
6210:
6209:
6207:
6206:
6201:
6195:
6193:
6187:
6186:
6181:
6179:
6178:
6171:
6164:
6156:
6150:
6149:
6142:
6141:External links
6139:
6138:
6137:
6132:978-0759611870
6131:
6118:
6115:3D projection.
6109:
6086:
6083:
6080:
6079:
6055:
6040:
6033:
6015:
6008:
5990:
5983:
5953:
5924:(4): 465–502.
5899:
5893:
5870:
5849:
5836:
5829:
5809:
5802:
5782:
5775:
5755:
5727:
5726:
5724:
5721:
5719:
5718:
5713:
5708:
5703:
5698:
5693:
5688:
5683:
5681:Plan (drawing)
5678:
5673:
5668:
5661:Map projection
5658:
5653:
5648:
5643:
5638:
5633:
5628:
5623:
5618:
5613:
5608:
5603:
5597:
5595:
5592:
5569:
5568:
5554:
5550:
5539:
5514:
5510:
5499:
5481:
5477:
5466:
5461:is the screen
5448:
5444:
5429:
5428:
5413:
5409:
5403:
5399:
5391:
5387:
5383:
5378:
5374:
5348:
5344:
5340:
5335:
5331:
5307:
5304:
5291:
5288:
5285:
5274:
5273:
5250:
5246:
5241:
5236:
5232:
5228:
5226:
5215:
5211:
5206:
5201:
5197:
5193:
5191:
5155:
5124:
5101:
5097:
5083:
5080:
5062:
5057:
5040:entrance pupil
5025:
5020:
4988:
4985:
4982:
4977:
4953:
4950:
4947:
4942:
4929:
4928:
4913:
4908:
4903:
4898:
4893:
4888:
4881:
4876:
4871:
4867:
4863:
4858:
4853:
4846:
4841:
4836:
4833:
4830:
4828:
4824:
4819:
4814:
4813:
4810:
4805:
4800:
4795:
4790:
4785:
4778:
4773:
4768:
4764:
4760:
4755:
4750:
4743:
4738:
4733:
4730:
4727:
4725:
4721:
4716:
4711:
4710:
4684:
4679:
4674:
4668:
4664:
4661:
4658:
4655:
4652:
4649:
4646:
4643:
4621:
4616:
4603:
4602:
4585:
4580:
4574:
4568:
4563:
4558:
4555:
4553:
4549:
4544:
4539:
4538:
4533:
4528:
4522:
4516:
4511:
4506:
4503:
4501:
4497:
4492:
4487:
4486:
4472:
4471:
4458:
4450:
4445:
4440:
4439:
4434:
4429:
4424:
4423:
4418:
4413:
4408:
4407:
4405:
4398:
4388:
4383:
4378:
4373:
4371:
4368:
4366:
4363:
4362:
4355:
4350:
4343:
4338:
4331:
4329:
4326:
4324:
4321:
4320:
4313:
4308:
4301:
4296:
4289:
4287:
4284:
4282:
4279:
4278:
4276:
4271:
4266:
4258:
4253:
4248:
4247:
4242:
4237:
4232:
4231:
4226:
4221:
4216:
4215:
4213:
4193:
4192:
4177:
4172:
4167:
4162:
4157:
4152:
4143:
4138:
4131:
4126:
4119:
4116:
4114:
4110:
4105:
4100:
4099:
4096:
4091:
4086:
4081:
4076:
4071:
4062:
4057:
4050:
4045:
4038:
4035:
4033:
4029:
4024:
4019:
4018:
3988:
3987:
3972:
3968:
3962:
3958:
3954:
3950:
3944:
3940:
3936:
3931:
3927:
3923:
3920:
3917:
3913:
3907:
3903:
3899:
3895:
3889:
3885:
3881:
3876:
3872:
3868:
3864:
3858:
3854:
3850:
3845:
3841:
3837:
3834:
3832:
3828:
3823:
3818:
3817:
3814:
3810:
3804:
3800:
3796:
3792:
3786:
3782:
3778:
3773:
3769:
3765:
3762:
3759:
3755:
3749:
3745:
3741:
3737:
3731:
3727:
3723:
3718:
3714:
3710:
3706:
3700:
3696:
3692:
3687:
3683:
3679:
3676:
3674:
3670:
3665:
3660:
3659:
3655:
3649:
3645:
3641:
3638:
3634:
3628:
3624:
3620:
3616:
3610:
3606:
3602:
3597:
3593:
3589:
3586:
3584:
3580:
3575:
3570:
3569:
3544:
3540:
3518:
3513:
3509:
3505:
3501:
3498:
3476:
3472:
3450:
3445:
3441:
3437:
3433:
3430:
3409:
3386:
3382:
3378:
3373:
3369:
3346:
3342:
3338:
3334:
3330:
3326:
3305:
3302:
3299:
3296:
3293:
3290:
3287:
3284:
3279:
3276:
3273:
3270:
3267:
3262:
3205:
3204:
3192:
3186:
3178:
3173:
3168:
3167:
3162:
3157:
3152:
3151:
3146:
3141:
3136:
3135:
3133:
3128:
3123:
3115:
3110:
3105:
3104:
3099:
3094:
3089:
3088:
3083:
3078:
3073:
3072:
3070:
3064:
3058:
3052:
3049:
3047:
3044:
3042:
3039:
3038:
3035:
3032:
3030:
3025:
3020:
3015:
3012:
3009:
3006:
3004:
2999:
2994:
2989:
2986:
2983:
2980:
2977:
2976:
2973:
2970:
2968:
2963:
2958:
2953:
2950:
2947:
2944:
2942:
2937:
2932:
2927:
2924:
2921:
2918:
2917:
2915:
2908:
2902:
2897:
2892:
2887:
2884:
2881:
2878:
2876:
2873:
2871:
2866:
2861:
2856:
2853:
2850:
2847:
2846:
2843:
2840:
2838:
2835:
2833:
2830:
2829:
2826:
2821:
2816:
2811:
2808:
2805:
2802:
2799:
2797:
2794:
2792:
2787:
2782:
2777:
2774:
2771:
2768:
2767:
2765:
2758:
2752:
2747:
2742:
2737:
2734:
2731:
2728:
2726:
2721:
2716:
2711:
2708:
2705:
2702:
2699:
2697:
2694:
2693:
2690:
2685:
2680:
2675:
2672:
2669:
2666:
2664:
2659:
2654:
2649:
2646:
2643:
2640:
2638:
2635:
2634:
2631:
2628:
2626:
2623:
2621:
2618:
2617:
2615:
2610:
2605:
2597:
2592:
2587:
2586:
2581:
2576:
2571:
2570:
2565:
2560:
2555:
2554:
2552:
2503:
2499:
2478:
2456:
2431:
2396:
2393:
2390:
2387:
2384:
2379:
2355:
2352:
2349:
2344:
2319:
2316:
2313:
2310:
2307:
2287:
2284:
2281:
2278:
2275:
2272:
2269:
2260:the 3D vector
2249:
2246:
2243:
2240:
2237:
2234:
2231:
2228:
2225:
2220:
2217:
2214:
2211:
2208:
2203:
2181:
2178:
2175:
2172:
2169:
2166:
2163:
2160:
2157:
2152:
2149:
2146:
2143:
2140:
2135:
2122:
2121:
2110:
2106:
2083:
2080:
2077:
2072:
2046:
2034:
2033:
2020:
1993:
1990:
1987:
1984:
1981:
1976:
1964:
1942:
1939:
1936:
1933:
1930:
1925:
1913:
1895:
1892:
1889:
1886:
1883:
1878:
1866:
1848:
1845:
1842:
1839:
1836:
1831:
1809:
1806:
1790:
1789:
1786:
1685:linea di terra
1638:
1635:
1575:Penrose stairs
1572:
1565:
1564:
1560:
1553:
1552:
1551:
1550:
1549:
1541:
1538:
1525:
1522:
1509:
1506:
1502:foreshortening
1489:
1486:
1433:Main article:
1430:
1427:
1406:
1403:
1390:
1387:
1322:
1319:
1293:
1286:
1285:
1274:
1267:
1266:
1265:
1264:
1263:
1258:Main article:
1255:
1252:
1188:Main article:
1185:
1182:
1177:
1176:
1165:
1160:
1152:
1148:
1144:
1143:
1138:
1134:
1130:
1129:
1127:
1122:
1117:
1109:
1105:
1101:
1100:
1095:
1091:
1087:
1086:
1081:
1077:
1073:
1072:
1070:
1063:
1055:
1051:
1047:
1045:
1042:
1040:
1037:
1036:
1033:
1030:
1028:
1025:
1021:
1017:
1013:
1012:
1010:
1005:
1000:
992:
988:
984:
983:
978:
974:
970:
969:
967:
939:
938:
925:
921:
917:
912:
908:
902:
898:
894:
889:
885:
874:
861:
857:
853:
848:
844:
838:
834:
830:
825:
821:
791:
787:
764:
760:
737:
733:
710:
706:
683:
679:
633:Main article:
630:
627:
560:Main article:
557:
554:
553:
552:
547:
540:
538:
533:
526:
524:
519:
512:
510:
505:
498:
496:
491:
484:
482:
477:
470:
468:
462:
455:
452:
451:
446:
416:
413:
364:
363:
361:
360:
353:
346:
338:
335:
334:
331:
330:
325:
320:
315:
310:
305:
300:
295:
290:
285:
280:
275:
273:Map projection
270:
265:
260:
255:
250:
245:
240:
234:
231:
230:
227:
226:
223:
222:
217:
212:
207:
202:
197:
192:
187:
182:
176:
173:
172:
169:
168:
165:
164:
163:
162:
157:
147:
146:
145:
140:
139:
138:
122:
117:
116:
113:
112:
104:
103:
97:
96:
80:
79:
59:the key points
49:
47:
40:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
6647:
6636:
6633:
6631:
6628:
6626:
6623:
6621:
6618:
6616:
6613:
6611:
6608:
6606:
6603:
6601:
6598:
6597:
6595:
6580:
6577:
6576:
6574:
6570:
6564:
6561:
6559:
6556:
6552:
6549:
6547:
6544:
6542:
6539:
6538:
6537:
6534:
6533:
6531:
6529:
6525:
6519:
6516:
6514:
6511:
6509:
6506:
6504:
6501:
6499:
6496:
6494:
6491:
6489:
6488:Shadow volume
6486:
6484:
6481:
6479:
6476:
6474:
6471:
6467:
6464:
6462:
6459:
6457:
6454:
6452:
6449:
6447:
6444:
6442:
6439:
6437:
6434:
6433:
6432:
6429:
6427:
6424:
6422:
6419:
6417:
6414:
6412:
6409:
6407:
6404:
6402:
6399:
6398:
6396:
6392:
6386:
6383:
6381:
6378:
6374:
6371:
6370:
6369:
6366:
6363:
6362:Triangle mesh
6359:
6357:
6354:
6352:
6349:
6345:
6342:
6341:
6340:
6337:
6335:
6332:
6330:
6327:
6325:
6322:
6320:
6317:
6314:
6311:
6309:
6306:
6304:
6300:
6298:
6295:
6293:
6292:3D projection
6290:
6289:
6287:
6285:
6281:
6271:
6268:
6266:
6263:
6261:
6258:
6256:
6253:
6251:
6248:
6247:
6245:
6243:
6239:
6233:
6232:Text-to-image
6230:
6228:
6225:
6223:
6220:
6219:
6217:
6215:
6211:
6205:
6202:
6200:
6197:
6196:
6194:
6192:
6188:
6184:
6177:
6172:
6170:
6165:
6163:
6158:
6157:
6154:
6148:
6145:
6144:
6140:
6134:
6128:
6124:
6119:
6116:
6112:
6106:
6102:
6097:
6096:
6089:
6088:
6084:
6075:
6068:
6067:
6059:
6056:
6051:
6044:
6041:
6036:
6030:
6026:
6019:
6016:
6011:
6005:
6001:
5994:
5991:
5986:
5980:
5976:
5972:
5967:
5966:
5957:
5954:
5949:
5945:
5941:
5937:
5932:
5927:
5923:
5919:
5918:
5910:
5903:
5900:
5896:
5894:9780387259611
5890:
5886:
5885:
5880:
5874:
5871:
5867:
5866:0-201-84840-6
5863:
5859:
5853:
5850:
5846:
5840:
5837:
5832:
5826:
5822:
5821:
5813:
5810:
5805:
5799:
5795:
5794:
5786:
5783:
5778:
5772:
5768:
5767:
5759:
5756:
5743:
5739:
5732:
5729:
5722:
5717:
5716:Virtual globe
5714:
5712:
5709:
5707:
5704:
5702:
5699:
5697:
5694:
5692:
5689:
5687:
5684:
5682:
5679:
5677:
5674:
5672:
5669:
5666:
5662:
5659:
5657:
5654:
5652:
5649:
5647:
5644:
5642:
5639:
5637:
5634:
5632:
5629:
5627:
5624:
5622:
5619:
5617:
5614:
5612:
5609:
5607:
5606:Camera matrix
5604:
5602:
5599:
5598:
5593:
5591:
5587:
5584:
5582:
5578:
5574:
5552:
5548:
5540:
5538:
5534:
5533:camera center
5530:
5512:
5508:
5500:
5497:
5494:is the model
5479:
5475:
5467:
5464:
5446:
5442:
5434:
5433:
5432:
5411:
5407:
5401:
5397:
5389:
5385:
5381:
5376:
5372:
5364:
5363:
5362:
5346:
5342:
5338:
5333:
5329:
5320:
5315:
5313:
5305:
5303:
5289:
5286:
5283:
5248:
5244:
5239:
5234:
5230:
5213:
5209:
5204:
5199:
5195:
5182:
5181:
5180:
5179:
5178:
5173:
5153:
5142:
5122:
5099:
5095:
5081:
5079:
5076:
5060:
5045:
5044:camera center
5041:
5023:
5008:
5004:
4986:
4983:
4980:
4951:
4948:
4945:
4911:
4906:
4891:
4879:
4865:
4856:
4844:
4831:
4829:
4822:
4808:
4803:
4788:
4776:
4762:
4753:
4741:
4728:
4726:
4719:
4701:
4700:
4699:
4696:
4677:
4666:
4662:
4656:
4653:
4650:
4647:
4644:
4641:
4619:
4583:
4572:
4566:
4556:
4554:
4547:
4531:
4520:
4514:
4504:
4502:
4495:
4477:
4476:
4475:
4456:
4448:
4432:
4416:
4403:
4396:
4386:
4376:
4369:
4364:
4353:
4341:
4327:
4322:
4311:
4299:
4285:
4280:
4274:
4269:
4264:
4256:
4240:
4224:
4211:
4202:
4201:
4200:
4199:, the system
4198:
4175:
4170:
4160:
4155:
4141:
4129:
4117:
4115:
4108:
4094:
4089:
4079:
4074:
4060:
4048:
4036:
4034:
4027:
4009:
4008:
4007:
4005:
4001:
3997:
3993:
3960:
3956:
3952:
3942:
3938:
3929:
3925:
3921:
3905:
3901:
3897:
3887:
3883:
3874:
3870:
3866:
3856:
3852:
3843:
3839:
3835:
3833:
3826:
3802:
3798:
3794:
3784:
3780:
3771:
3767:
3763:
3747:
3743:
3739:
3729:
3725:
3716:
3712:
3708:
3698:
3694:
3685:
3681:
3677:
3675:
3668:
3647:
3643:
3639:
3626:
3622:
3618:
3608:
3604:
3595:
3591:
3587:
3585:
3578:
3560:
3559:
3558:
3542:
3538:
3516:
3511:
3507:
3503:
3499:
3496:
3474:
3470:
3448:
3443:
3439:
3435:
3431:
3428:
3384:
3380:
3376:
3371:
3367:
3357:
3344:
3336:
3328:
3300:
3297:
3294:
3291:
3288:
3282:
3277:
3274:
3271:
3268:
3265:
3260:
3250:
3246:
3242:
3238:
3234:
3230:
3226:
3222:
3218:
3215:), using the
3214:
3210:
3190:
3184:
3176:
3160:
3144:
3131:
3126:
3121:
3113:
3097:
3081:
3068:
3062:
3056:
3050:
3045:
3040:
3033:
3023:
3018:
3010:
3007:
2997:
2992:
2984:
2981:
2978:
2971:
2961:
2956:
2948:
2945:
2935:
2930:
2922:
2919:
2913:
2906:
2895:
2890:
2882:
2879:
2874:
2864:
2859:
2851:
2848:
2841:
2836:
2831:
2819:
2814:
2806:
2803:
2800:
2795:
2785:
2780:
2772:
2769:
2763:
2756:
2745:
2740:
2732:
2729:
2719:
2714:
2706:
2703:
2700:
2695:
2683:
2678:
2670:
2667:
2657:
2652:
2644:
2641:
2636:
2629:
2624:
2619:
2613:
2608:
2603:
2595:
2579:
2563:
2550:
2541:
2540:
2539:
2537:
2533:
2529:
2526:
2522:
2501:
2497:
2446:
2429:
2420:
2416:
2412:
2394:
2391:
2388:
2385:
2382:
2353:
2350:
2347:
2331:
2314:
2311:
2308:
2282:
2279:
2276:
2273:
2270:
2247:
2241:
2238:
2235:
2232:
2229:
2223:
2218:
2215:
2212:
2209:
2206:
2201:
2179:
2173:
2170:
2167:
2164:
2161:
2155:
2150:
2147:
2144:
2141:
2138:
2108:
2081:
2078:
2075:
2061:
2060:
2059:
2009:
1991:
1988:
1985:
1982:
1979:
1965:
1962:
1958:
1940:
1937:
1934:
1931:
1928:
1923:
1914:
1911:
1893:
1890:
1887:
1884:
1881:
1867:
1864:
1846:
1843:
1840:
1837:
1834:
1820:
1819:
1818:
1816:
1815:field of view
1807:
1805:
1802:
1800:
1795:
1787:
1784:
1783:
1782:
1779:
1777:
1773:
1767:
1765:
1761:
1757:
1753:
1749:
1744:
1742:
1741:picture plane
1734:
1730:
1726:
1722:
1718:
1714:
1710:
1706:
1702:
1698:
1694:
1690:
1686:
1682:
1678:
1674:
1670:
1669:picture plane
1665:
1657:
1652:
1651:Camera matrix
1648:
1644:
1636:
1634:
1632:
1631:
1626:
1623:, where by a
1622:
1621:
1616:
1612:
1611:
1606:
1602:
1597:
1593:
1591:
1587:
1576:
1569:
1557:
1547:
1539:
1537:
1535:
1531:
1523:
1521:
1519:
1515:
1507:
1505:
1503:
1499:
1495:
1487:
1485:
1483:
1479:
1475:
1471:
1467:
1465:
1461:
1457:
1450:
1446:
1441:
1436:
1428:
1426:
1424:
1420:
1416:
1412:
1409:A variant of
1404:
1402:
1400:
1396:
1388:
1386:
1384:
1380:
1376:
1372:
1368:
1367:perpendicular
1364:
1360:
1356:
1352:
1348:
1344:
1340:
1336:
1332:
1328:
1320:
1318:
1316:
1312:
1307:
1297:
1290:
1281:
1277:
1276:Potting bench
1271:
1261:
1253:
1251:
1249:
1245:
1241:
1237:
1233:
1229:
1225:
1221:
1217:
1213:
1209:
1208:primary views
1205:
1196:
1191:
1183:
1181:
1163:
1158:
1150:
1146:
1136:
1132:
1125:
1120:
1115:
1107:
1103:
1093:
1089:
1079:
1075:
1068:
1061:
1053:
1049:
1043:
1038:
1031:
1026:
1019:
1015:
1008:
1003:
998:
990:
986:
976:
972:
965:
956:
955:
954:
952:
948:
944:
923:
919:
915:
910:
906:
900:
896:
892:
887:
883:
875:
859:
855:
851:
846:
842:
836:
832:
828:
823:
819:
811:
810:
809:
807:
789:
785:
762:
758:
735:
731:
708:
704:
681:
677:
668:
664:
660:
655:
653:
648:
642:
636:
628:
626:
624:
620:
616:
612:
608:
604:
599:
597:
593:
589:
585:
581:
577:
568:
563:
555:
550:
544:
539:
536:
530:
525:
522:
516:
511:
508:
502:
497:
494:
488:
483:
480:
474:
469:
465:
459:
454:
450:
447:
445:
442:
441:
440:
437:
429:
421:
414:
412:
410:
406:
402:
398:
393:
390:
385:
383:
379:
375:
371:
370:3D projection
359:
354:
352:
347:
345:
340:
339:
337:
336:
329:
326:
324:
321:
319:
316:
314:
311:
309:
306:
304:
301:
299:
296:
294:
291:
289:
286:
284:
281:
279:
278:Picture plane
276:
274:
271:
269:
266:
264:
261:
259:
256:
254:
251:
249:
246:
244:
241:
239:
238:3D projection
236:
235:
229:
228:
221:
218:
216:
213:
211:
208:
206:
203:
201:
198:
196:
193:
191:
188:
186:
185:Cross section
183:
181:
178:
177:
171:
170:
161:
158:
156:
153:
152:
151:
148:
144:
141:
137:
134:
133:
132:
129:
128:
127:
124:
123:
120:
115:
114:
110:
106:
105:
102:
98:
94:
93:
86:
76:
66:
60:
58:
53:
48:
44:
39:
38:
33:
19:
6493:Shear matrix
6456:Path tracing
6441:Cone tracing
6436:Beam tracing
6356:Polygon mesh
6297:3D rendering
6291:
6122:
6114:
6094:
6065:
6058:
6043:
6024:
6018:
5999:
5993:
5964:
5956:
5921:
5915:
5902:
5883:
5873:
5868:], chapter 6
5857:
5852:
5844:
5839:
5819:
5812:
5792:
5785:
5765:
5758:
5746:. Retrieved
5731:
5588:
5585:
5580:
5576:
5572:
5570:
5529:focal length
5495:
5462:
5430:
5318:
5316:
5309:
5275:
5176:
5175:
5174:
5143:
5085:
5077:
4930:
4697:
4604:
4473:
4194:
4003:
3999:
3995:
3991:
3989:
3358:
3248:
3244:
3240:
3236:
3232:
3228:
3224:
3220:
3216:
3209:Euler angles
3206:
2531:
2527:
2524:
2516:
2418:
2410:
2332:
2123:
2035:
1909:
1862:
1811:
1803:
1798:
1791:
1780:
1775:
1771:
1768:
1763:
1759:
1755:
1745:
1740:
1738:
1732:
1728:
1724:
1720:
1716:
1712:
1708:
1704:
1700:
1696:
1692:
1688:
1684:
1680:
1676:
1672:
1628:
1618:
1608:
1605:M. C. Escher
1598:
1594:
1583:
1529:
1527:
1513:
1511:
1493:
1491:
1481:
1477:
1473:
1469:
1468:
1463:
1460:orthographic
1459:
1455:
1454:
1422:
1418:
1414:
1408:
1398:
1394:
1392:
1382:
1378:
1362:
1358:
1354:
1350:
1346:
1342:
1338:
1334:
1330:
1326:
1324:
1314:
1310:
1309:simplicity,
1305:
1303:
1295:
1279:
1247:
1243:
1239:
1238:. The terms
1235:
1231:
1227:
1223:
1219:
1215:
1211:
1207:
1203:
1201:
1178:
946:
942:
940:
805:
666:
662:
658:
656:
644:
622:
618:
615:orthographic
614:
610:
600:
584:focal length
573:
438:
434:
394:
386:
373:
369:
367:
243:Anamorphosis
237:
200:Fisheye lens
70:
54:
52:lead section
6508:Translation
6461:Ray casting
6451:Ray tracing
6329:Cel shading
6303:Image-based
6284:3D graphics
6265:Ray casting
6214:2D graphics
5973:. pp.
5663:(including
5537:image plane
2536:left-handed
2445:subtracting
1957:orientation
1397:(sometimes
1329:(sometimes
1216:third-angle
1212:first-angle
592:focal point
466:(elevation)
313:True length
303:Stereoscopy
6605:3D imaging
6594:Categories
6572:Algorithms
6426:Reflection
5723:References
5706:Video card
5656:Homography
5498:coordinate
5465:coordinate
1641:See also:
1544:See also:
1447:, here of
1443:The three
1413:is called
1228:front view
639:See also:
619:Axonometry
603:axonometry
248:Axonometry
205:Multiviews
6551:rendering
6541:animation
6431:Rendering
5926:CiteSeerX
5691:Tesseract
4931:In which
4657:
4651:⋅
4642:α
3953:−
3922:−
3795:−
3640:−
3543:α
3512:α
3508:θ
3500:
3475:α
3444:α
3440:θ
3432:
3377:−
3337:−
3304:⟩
3286:⟨
3261:θ
3241:intrinsic
3221:extrinsic
3127:−
3019:θ
3011:
2993:θ
2985:
2979:−
2957:θ
2949:
2931:θ
2923:
2891:θ
2883:
2860:θ
2852:
2815:θ
2807:
2801:−
2781:θ
2773:
2741:θ
2733:
2715:θ
2707:
2701:−
2679:θ
2671:
2653:θ
2645:
2502:θ
2498:−
2430:θ
2318:⟩
2306:⟨
2286:⟩
2268:⟨
2245:⟩
2227:⟨
2202:θ
2177:⟩
2159:⟨
1924:θ
1760:two-point
1756:one-point
1620:Inception
1610:Waterfall
1449:cabinetry
1393:The term
1278:drawn in
1240:elevation
1220:projected
409:geometric
392:display.
220:Zoom lens
73:July 2019
57:summarize
6546:modeling
6473:Rotation
6411:Clipping
6394:Concepts
6373:Deferred
6339:Lighting
6319:Aliasing
6313:Unbiased
6308:Spectral
5881:(2007),
5748:24 April
5742:Archived
5594:See also
5177:Equation
1236:end view
1232:top view
415:Overview
401:drafting
210:Panorama
6478:Scaling
6368:Shading
5977:, 942.
5535:to the
5527:is the
5431:where
5306:Diagram
5046:), and
3249:x, y, z
1794:horizon
1695:lie on
1464:oblique
1315:drawing
1248:section
1224:usually
611:oblique
594:), or "
382:project
376:) is a
6498:Shader
6270:Skybox
6255:Mode 7
6227:Layers
6129:
6107:
6074:AI Lab
6031:
6006:
5981:
5948:708008
5946:
5928:
5891:
5864:
5827:
5800:
5773:
4654:arctan
3245:camera
2006:– the
1955:– The
1649:, and
1601:op art
1480:, and
1234:, and
403:, and
232:Topics
119:Planar
6518:Voxel
6503:Texel
6204:Pixel
6070:(PDF)
5944:S2CID
5912:(PDF)
3399:with
3225:scene
2468:from
2124:When
1202:With
665:, or
174:Views
6242:2.5D
6127:ISBN
6105:ISBN
6029:ISBN
6004:ISBN
5979:ISBN
5889:ISBN
5862:ISBN
5825:ISBN
5798:ISBN
5771:ISBN
5750:2015
5579:for
3489:and
2530:and
2192:and
1762:and
1723:and
1715:and
1707:and
1691:and
1683:and
1573:The
1361:and
1353:and
1345:and
1246:and
1244:plan
596:zoom
590:and
588:lens
372:(or
5975:931
5936:doi
5253:ave
5218:ave
5158:ave
5127:ave
5009:),
5005:or
5003:CCD
4006:):
3557:):
3530:to
3497:sin
3462:to
3429:cos
3217:xyz
3008:cos
2982:sin
2946:sin
2920:cos
2880:cos
2849:sin
2804:sin
2770:cos
2730:cos
2704:sin
2668:sin
2642:cos
1731:on
1703:at
1630:Fez
1607:'s
1528:In
1512:In
1492:In
1462:or
1333:or
1325:In
1304:In
1214:or
598:".
6596::
6113:.
6103:.
6101:93
5969:.
5942:.
5934:.
5922:10
5920:.
5914:.
5302:.
3235:,
3231:,
2528:y,
2525:x,
2330:.
1963:).
1758:,
1729:R′
1725:q′
1721:s′
1717:Fq
1713:Fs
1709:Tq
1705:Ts
1645:,
1476:,
1425:.
1419:xy
1383:x″
1355:y″
1351:x″
1341:,
1242:,
1230:,
777:,
723:,
696:,
661:,
654:.
399:,
368:A
6364:)
6360:(
6315:)
6301:(
6175:e
6168:t
6161:v
6135:.
6076:.
6052:.
6037:.
6012:.
5987:.
5950:.
5938::
5833:.
5806:.
5779:.
5752:.
5667:)
5581:x
5577:y
5573:y
5553:z
5549:A
5513:z
5509:B
5496:x
5480:x
5476:A
5463:x
5447:x
5443:B
5412:z
5408:A
5402:z
5398:B
5390:x
5386:A
5382:=
5377:x
5373:B
5347:z
5343:A
5339:,
5334:x
5330:A
5319:x
5290:1
5287:=
5284:f
5249:Z
5245:Y
5240:=
5235:y
5231:P
5214:Z
5210:X
5205:=
5200:x
5196:P
5154:Z
5123:Z
5100:i
5096:Z
5061:z
5056:d
5042:(
5024:z
5019:r
4987:y
4984:,
4981:x
4976:r
4952:y
4949:,
4946:x
4941:s
4912:.
4907:z
4902:r
4897:)
4892:y
4887:r
4880:z
4875:d
4870:(
4866:/
4862:)
4857:y
4852:s
4845:y
4840:d
4835:(
4832:=
4823:y
4818:b
4809:,
4804:z
4799:r
4794:)
4789:x
4784:r
4777:z
4772:d
4767:(
4763:/
4759:)
4754:x
4749:s
4742:x
4737:d
4732:(
4729:=
4720:x
4715:b
4683:)
4678:z
4673:e
4667:/
4663:1
4660:(
4648:2
4645:=
4620:z
4615:e
4584:w
4579:f
4573:/
4567:y
4562:f
4557:=
4548:y
4543:b
4532:w
4527:f
4521:/
4515:x
4510:f
4505:=
4496:x
4491:b
4457:]
4449:z
4444:d
4433:y
4428:d
4417:x
4412:d
4404:[
4397:]
4387:z
4382:e
4377:1
4370:0
4365:0
4354:z
4349:e
4342:y
4337:e
4328:1
4323:0
4312:z
4307:e
4300:x
4295:e
4286:0
4281:1
4275:[
4270:=
4265:]
4257:w
4252:f
4241:y
4236:f
4225:x
4220:f
4212:[
4176:.
4171:y
4166:e
4161:+
4156:y
4151:d
4142:z
4137:d
4130:z
4125:e
4118:=
4109:y
4104:b
4095:,
4090:x
4085:e
4080:+
4075:x
4070:d
4061:z
4056:d
4049:z
4044:e
4037:=
4028:x
4023:b
4004:z
4002:/
4000:x
3996:y
3994:/
3992:x
3971:)
3967:x
3961:z
3957:s
3949:y
3943:z
3939:c
3935:(
3930:x
3926:s
3919:)
3916:)
3912:x
3906:z
3902:c
3898:+
3894:y
3888:z
3884:s
3880:(
3875:y
3871:s
3867:+
3863:z
3857:y
3853:c
3849:(
3844:x
3840:c
3836:=
3827:z
3822:d
3813:)
3809:x
3803:z
3799:s
3791:y
3785:z
3781:c
3777:(
3772:x
3768:c
3764:+
3761:)
3758:)
3754:x
3748:z
3744:c
3740:+
3736:y
3730:z
3726:s
3722:(
3717:y
3713:s
3709:+
3705:z
3699:y
3695:c
3691:(
3686:x
3682:s
3678:=
3669:y
3664:d
3654:z
3648:y
3644:s
3637:)
3633:x
3627:z
3623:c
3619:+
3615:y
3609:z
3605:s
3601:(
3596:y
3592:c
3588:=
3579:x
3574:d
3539:s
3517:)
3504:(
3471:c
3449:)
3436:(
3408:x
3385:x
3381:c
3372:x
3368:a
3345:.
3341:c
3333:a
3329:=
3325:d
3301:0
3298:,
3295:0
3292:,
3289:0
3283:=
3278:z
3275:,
3272:y
3269:,
3266:x
3237:x
3233:y
3229:z
3191:)
3185:]
3177:z
3172:c
3161:y
3156:c
3145:x
3140:c
3132:[
3122:]
3114:z
3109:a
3098:y
3093:a
3082:x
3077:a
3069:[
3063:(
3057:]
3051:1
3046:0
3041:0
3034:0
3029:)
3024:z
3014:(
3003:)
2998:z
2988:(
2972:0
2967:)
2962:z
2952:(
2941:)
2936:z
2926:(
2914:[
2907:]
2901:)
2896:y
2886:(
2875:0
2870:)
2865:y
2855:(
2842:0
2837:1
2832:0
2825:)
2820:y
2810:(
2796:0
2791:)
2786:y
2776:(
2764:[
2757:]
2751:)
2746:x
2736:(
2725:)
2720:x
2710:(
2696:0
2689:)
2684:x
2674:(
2663:)
2658:x
2648:(
2637:0
2630:0
2625:0
2620:1
2614:[
2609:=
2604:]
2596:z
2591:d
2580:y
2575:d
2564:x
2559:d
2551:[
2532:z
2477:a
2455:c
2419:C
2411:A
2395:z
2392:,
2389:y
2386:,
2383:x
2378:d
2354:y
2351:,
2348:x
2343:b
2315:2
2312:,
2309:1
2283:0
2280:,
2277:2
2274:,
2271:1
2248:,
2242:0
2239:,
2236:0
2233:,
2230:0
2224:=
2219:z
2216:,
2213:y
2210:,
2207:x
2180:,
2174:0
2171:,
2168:0
2165:,
2162:0
2156:=
2151:z
2148:,
2145:y
2142:,
2139:x
2134:c
2109:.
2105:a
2082:y
2079:,
2076:x
2071:b
2045:c
2032:.
2019:c
1992:z
1989:,
1986:y
1983:,
1980:x
1975:e
1941:z
1938:,
1935:y
1932:,
1929:x
1910:C
1894:z
1891:,
1888:y
1885:,
1882:x
1877:c
1863:A
1847:z
1844:,
1841:y
1838:,
1835:x
1830:a
1735:.
1733:R
1701:α
1697:π
1693:q
1689:s
1677:α
1673:π
1451:.
1423:z
1379:y
1363:z
1359:x
1347:z
1343:y
1339:x
1164:.
1159:]
1151:z
1147:c
1137:x
1133:c
1126:[
1121:+
1116:]
1108:z
1104:a
1094:y
1090:a
1080:x
1076:a
1069:[
1062:]
1054:z
1050:s
1044:0
1039:0
1032:0
1027:0
1020:x
1016:s
1009:[
1004:=
999:]
991:y
987:b
977:x
973:b
966:[
947:c
943:s
924:z
920:c
916:+
911:z
907:a
901:z
897:s
893:=
888:y
884:b
860:x
856:c
852:+
847:x
843:a
837:x
833:s
829:=
824:x
820:b
806:y
790:y
786:b
763:x
759:b
736:z
732:a
709:y
705:a
682:x
678:a
667:z
663:y
659:x
357:e
350:t
343:v
75:)
71:(
61:.
34:.
20:)
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
