3280:
98:
71:
1533:
2367:
3292:
1130:
1523:
2768:
22:
3090:
471:
3265:
is an ellipse, one can map four points on orthogonal diameters and the surrounding square of tangents and in the image parallelogram fill-in an ellipse by hand. A better, but more time consuming method consists of drawing the images of two perpendicular diameters of the circle, which are conjugate diameters of the image ellipse, determining the axes of the ellipse with
3264:
A parallel projection of a circle is in general an ellipse. An important special case occurs, if the circle's plane is parallel to the image plane–the image of the circle is then a congruent circle. In the diagram, the circle contained in the front face is undistorted. If the image of a circle
3311:
axonometry. But, as the engineer projection and the standard isometry are scaled orthographic projections, the contour of a sphere is a circle in these cases, as well. As the diagram shows, an ellipse as the contour of a sphere might be confusing, so, if a sphere is part of an object to be mapped,
434:
perspective and does not represent what the eye actually sees: in particular parallel lines remain parallel and distant objects are not reduced in size. It can be considered a conical perspective conique whose center has been pushed out to infinity, i.e. very far from the object observed.
1518:
Only for suitable choices of angles and foreshortenings does one get undistorted images. The next diagram shows the images of the unit cube for various angles and foreshortenings and gives some hints for how to make these personal choices.
1725:
1441:
2567:
In the literature the terms "cavalier perspective" and "cabinet perspective" are not uniformly defined. The above definition is the most general one. Often, further restrictions are applied. For example:
2524:
2955:
2829:
3080:
1514:
2456:
786:
2672:
2603:
3209:
3151:
2995:
2902:
2046:
1375:
1348:
1296:
1269:
1217:
1190:
1107:
1075:
1012:
949:
889:
815:
499:
1048:
985:
922:
3254:
2636:
859:
543:
1321:
1163:
2753:
2705:
1605:
1242:
727:
700:
673:
628:
601:
574:
1578:
1558:
641:
Select projections of the coordinate axes, such that all three coordinate axes are not collapsed to a single point or line. Usually the z-axis is vertical.
4197:
3868:
3838:
1113:
In order to obtain undistorted results, select the projections of the axes and foreshortenings carefully (see below). In order to produce an
4167:
1388:
1740:
Commonly used projections and perspectives with angles between the transformed coordinate axes (α, β, γ), angles from the horizon (α
1731:
axonometry. The image plane is parallel to the y-z-plane and any planar figure parallel to the y-z-plane appears in its true shape.
2468:
3547:
3392:
2909:
4319:
2789:
4309:
4252:
3858:
3411:
3373:
3350:
3331:
3307:
In a general axonometry of a sphere the image contour is an ellipse. The contour of a sphere is a circle only in an
3014:
1451:
47:
637:
is the basis for the following procedure to construct a scaled parallel projection of a three-dimensional object:
3863:
2390:
344:
4432:
4427:
3571:
3279:
732:
3853:
2644:
2575:
3540:
3156:
3098:
2970:
2848:
380:
of the coordinate axes play a crucial role. The result of an axonometric procedure is a uniformly-scaled
369:
276:
3782:
2022:
1118:
1117:, only the projections of the coordinate axes are freely selected; the foreshortenings are fixed (see
3606:
1353:
1326:
1274:
1247:
1195:
1168:
1085:
1053:
990:
927:
867:
793:
477:
3520:
3631:
3626:
3591:
3556:
3291:
173:
35:
There may be logic or math errors, complicated by the fact that this article was translated from a
1020:
957:
894:
3214:
2759:
Such axonometries are often used for city maps, in order to keep horizontal figures undistorted.
1114:
419:
393:
143:
138:
119:
1720:{\displaystyle \alpha =135^{\circ },\beta =90^{\circ },\ v_{y}=v_{z}=1,\;v_{x}=1/{\sqrt {2}}\ .}
4202:
3754:
3641:
3533:
3266:
2608:
820:
504:
454:
42:
3818:
1303:
1145:
861:
is determined in three sub-steps (the result is independent of the order of these sub-steps):
4096:
3909:
3833:
3651:
3312:
one should choose an orthogonal axonometry or an engineer projection or a standard isometry.
2725:
2677:
1224:
415:
246:
183:
2786:
all foreshortenings are equal. The angles can be chosen arbitrarily, but a common choice is
4376:
4267:
4091:
4041:
3949:
3934:
3878:
3843:
3739:
3636:
3611:
1540:
In order to keep the drawing simple, one should choose simple foreshortenings, for example
1526:
Various axonometric images of a unit cube. (The image plane is parallel to the y-z-plane.)
705:
678:
651:
606:
579:
552:
361:
251:
193:
124:
89:
8:
4356:
4111:
4046:
3883:
3744:
3694:
3689:
3525:
1563:
1543:
634:
381:
337:
311:
286:
256:
148:
114:
74:
4396:
4056:
4051:
4005:
3995:
3929:
3621:
3596:
3586:
385:
377:
203:
168:
131:
4262:
4391:
4341:
4314:
4242:
4121:
4101:
3944:
3749:
3646:
3407:
3388:
3369:
3365:
3346:
3327:
1602:
The parameters in the diagram at right (e.g. of the house drawn on graph paper) are:
1528:
The left and the far right images look more like prolonged cuboids instead of a cube.
430:. Sometimes also called rapid perspective or artificial perspective, it differs from
407:
296:
241:
107:
396:(the rays are perpendicular to the image plane), which in this context is called an
4401:
4386:
4381:
4361:
4212:
4187:
4151:
4146:
4081:
4015:
3919:
3823:
3813:
3787:
3734:
3661:
3601:
3576:
281:
271:
3828:
3270:
1837:
4406:
4346:
4257:
4182:
4126:
4076:
3719:
3616:
316:
306:
178:
67:
The process of projecting a three-dimensional object onto a two-dimensional plane
3385:
Engineering
Graphics: Theoretical Foundations of Engineering Geometry for Design
2997:. Hence the image has a good impression and the contour of a sphere is a circle.
4371:
4336:
4277:
4232:
4131:
4116:
4010:
3985:
3939:
3893:
3888:
3724:
3656:
2551:
1124:
645:
442:
is used both for the graphical procedure described below, as well as the image
330:
261:
36:
4421:
4331:
4217:
4141:
4106:
4086:
3990:
3954:
3808:
3792:
3777:
3581:
398:
389:
368:
of a three-dimensional object. The term "axonometry" means "to measure along
266:
226:
4366:
4326:
4247:
4227:
4192:
4177:
4071:
4066:
4036:
3914:
411:
365:
231:
188:
4351:
4299:
4237:
4207:
4136:
4061:
4031:
3969:
3924:
301:
291:
97:
70:
3008:
In order to prevent scaling, one can choose the unhandy foreshortenings
1532:
4222:
4000:
3964:
3959:
3709:
2530:
2061:
1536:
Axonometry (cavalier perspective) of a house on checked pattern paper.
4304:
4272:
3873:
3848:
3729:
3714:
2366:
373:
208:
2543:
a uniformly scaled orthographic projection with scaling factor 1.06,
1129:
3699:
2776:
1522:
198:
4172:
3684:
1589:
If the three foreshortenings are equal, the projection is called
2967:
the image is a scaled orthographic projection with scale factor
2767:
384:
of the object. In general, the resulting parallel projection is
3089:
1595:
If all foreshortenings are different, the projection is called
1436:{\displaystyle 0^{\circ }<\alpha +\beta <360^{\circ }\ .}
427:
423:
2546:
the contour of a sphere is a circle (in general, an ellipse) .
3679:
470:
2557:
2519:{\displaystyle \alpha =132^{\circ },\ \beta =97^{\circ }\ .}
1125:
The choice of the images of the axes and the foreshortenings
3001:
2234:
2213:
1583:
If two foreshortenings are equal, the projection is called
431:
3555:
3704:
3086:
and the image is an (unscaled) orthographic projection.
392:
to the image plane); but in special cases the result is
2950:{\displaystyle \alpha =\beta =\gamma =120^{\circ }\ .}
2711:
2025:
3217:
3159:
3101:
3017:
3004:) provide a suitable raster (see diagram) as support.
2973:
2912:
2851:
2792:
2728:
2680:
2647:
2611:
2578:
2471:
2393:
1608:
1566:
1546:
1454:
1391:
1356:
1329:
1306:
1277:
1250:
1227:
1198:
1171:
1148:
1088:
1056:
1023:
993:
960:
930:
897:
870:
823:
796:
735:
708:
681:
654:
609:
582:
555:
507:
480:
422:
objects whose goal is to preserve the impression of
3499:
3475:
3439:
2824:{\displaystyle \alpha =\beta =\gamma =120^{\circ }}
3463:
3451:
3427:
3362:Geometrische Grundlagen der Architekturdarstellung
3248:
3203:
3145:
3074:
2989:
2949:
2896:
2823:
2747:
2699:
2666:
2630:
2597:
2518:
2450:
2040:
1719:
1572:
1552:
1508:
1435:
1369:
1342:
1315:
1290:
1263:
1236:
1211:
1184:
1157:
1101:
1069:
1042:
1006:
979:
943:
916:
883:
853:
809:
780:
721:
694:
667:
622:
595:
568:
537:
493:
3487:
3153:, dimetric engineering and cavalier projections:
2771:standard isometry: cube, cuboid, house and sphere
4419:
458:, which in English literature usually refers to
3075:{\displaystyle v_{x}=v_{y}=v_{z}={\sqrt {2/3}}}
1509:{\displaystyle 0<\;v_{x},\;v_{y},\;v_{z}\ .}
3541:
338:
31:needs attention from an expert in mathematics
3000:Some computer graphic systems (for example,
2317:
2153:
1987:
1953:
1950:
1947:
1905:
1896:
1893:
1890:
2451:{\displaystyle v_{x}=0.5,\ v_{y}=v_{z}=1\ }
3548:
3534:
2641:cavalier perspective: additionally choose
2085:
1682:
1489:
1475:
1461:
465:
345:
331:
2722:military projection: additionally choose
2572:cabinet perspective: additionally choose
2558:Cavalier perspective, cabinet perspective
3302:
3259:
3088:
2766:
2365:
2104:
1531:
1521:
1128:
469:
69:
3382:
3359:
2964:the coordinates can be taken unchanged,
2960:The advantage of a standard isometry:
2762:
2536:Advantages of an engineer projection:
2529:These angles are marked on many German
1734:
781:{\displaystyle v_{x},v_{y},v_{z}>0.}
414:, axonometric perspective is a form of
4420:
2374:
360:is a graphical procedure belonging to
50:may be able to help recruit an expert.
3529:
3505:
3481:
3445:
3401:
3383:Brailov, Aleksandr Yurievich (2016).
3340:
3322:Graf, Ulrich; Barner, Martin (1961).
2291:
2272:
2266:
2197:
2126:
2006:
1998:
1995:
1923:
3493:
3469:
3457:
3433:
3321:
2667:{\displaystyle \alpha =135^{\circ }}
2598:{\displaystyle \alpha =135^{\circ }}
15:
3204:{\displaystyle v_{x}=0.5,v_{y,z}=1}
3146:{\displaystyle v_{z}=0.5,v_{x,y}=1}
2990:{\displaystyle {\sqrt {1.5}}=1.225}
2897:{\displaystyle v_{x}=v_{y}=v_{z}=1}
2712:Birds eye view, military projection
2370:Parameters of special axonometries.
2041:{\textstyle {\sqrt {\frac {2}{3}}}}
13:
3326:. Heidelberg: Quelle & Meyer.
2717:image plane parallel to x-y-plane.
2563:image plane parallel to y-z-plane.
14:
4444:
3514:
1838:Orthogonal, orthographic, planar
1082:Mark the final position as point
644:Select for these projections the
3290:
3278:
2328:
2280:
2258:
2159:
1902:
1899:
1863:
96:
20:
3093:various axonometries of a tower
1370:{\displaystyle {\overline {y}}}
1343:{\displaystyle {\overline {x}}}
1291:{\displaystyle {\overline {y}}}
1264:{\displaystyle {\overline {z}}}
1212:{\displaystyle {\overline {x}}}
1185:{\displaystyle {\overline {z}}}
1102:{\displaystyle {\overline {P}}}
1070:{\displaystyle {\overline {z}}}
1007:{\displaystyle {\overline {y}}}
944:{\displaystyle {\overline {x}}}
884:{\displaystyle {\overline {O}}}
810:{\displaystyle {\overline {P}}}
494:{\displaystyle {\overline {P}}}
3095:dimetric military projection:
2017:Standard, shortened isometric
848:
830:
532:
514:
1:
3572:Biological data visualization
3315:
3285:Cavalier perspective: circles
2173:Standard, isometric cavalier
501:is the projection of a point
3345:. Leipzig: Fachbuch-Verlag.
3341:Fucke, Kirch Nickel (1998).
2775:(Not to be confused with an
1758:= 90°) and scaling factors (
1362:
1335:
1283:
1256:
1204:
1177:
1094:
1062:
1043:{\displaystyle v_{z}\cdot z}
999:
980:{\displaystyle v_{y}\cdot y}
936:
917:{\displaystyle v_{x}\cdot x}
876:
802:
486:
452:should not be confused with
7:
3297:Military projection: sphere
3249:{\displaystyle v_{x,y,z}=1}
2165:Cabinet, dimetric cavalier
277:Projection (linear algebra)
33:. The specific problem is:
10:
4449:
3612:Mathematical visualization
3360:Leopold, Cornelie (2005).
1119:de:orthogonale Axonometrie
549:. The foreshortenings are
545:onto the projection plane
372:", and indicates that the
77:of a semicircular archway.
4290:
4160:
4024:
3978:
3902:
3801:
3770:
3763:
3670:
3607:Information visualization
3592:Educational visualization
3564:
2631:{\displaystyle v_{x}=0.5}
2458:(dimetric axonometry) and
2320:
2309:
2301:
2283:
2275:
2269:
2194:
2184:
2181:
2178:
2175:
2156:
2150:
2147:
2139:
2131:
2055:
1913:
1887:
1879:
1871:
1855:
854:{\displaystyle P=(x,y,z)}
538:{\displaystyle P=(x,y,z)}
3783:Charles-René de Fourcroy
3632:Scientific visualization
3559:of technical information
3211:, isometric axonometry:
2779:between metric spaces.)
2264:Aerial, bird's eye view
1316:{\displaystyle \gamma :}
1158:{\displaystyle \alpha :}
1133:Parameters and notations
2748:{\displaystyle v_{z}=1}
2700:{\displaystyle v_{x}=1}
2540:simple foreshortenings,
1237:{\displaystyle \beta :}
1115:orthographic projection
466:Principle of axonometry
144:Curvilinear perspective
120:Orthographic projection
48:WikiProject Mathematics
4203:Christopher R. Johnson
3755:Technical illustration
3642:Software visualization
3404:Darstellende Geometrie
3402:Stärk, Roland (1978).
3343:Darstellende Geometrie
3324:Darstellende Geometrie
3256:
3250:
3205:
3147:
3076:
2991:
2951:
2904:(all axes undistorted)
2898:
2825:
2772:
2749:
2701:
2668:
2632:
2599:
2550:For more details: see
2520:
2465:between the axes are:
2452:
2371:
2342:Shortened planometric
2042:
2004:Normal, 1:1 isometric
1939:Oblique, clinographic
1721:
1574:
1554:
1537:
1529:
1510:
1437:
1385:can be chosen so that
1371:
1344:
1317:
1292:
1265:
1238:
1213:
1186:
1159:
1134:
1103:
1071:
1044:
1008:
981:
945:
918:
885:
864:starting at the point
855:
811:
782:
723:
696:
669:
631:
624:
597:
570:
539:
495:
455:axonometric projection
139:Perspective projection
78:
4433:Graphical projections
4097:Lawrence J. Rosenblum
3910:Edward Walter Maunder
3834:Charles Joseph Minard
3652:User interface design
3627:Product visualization
3521:Orthogonal axonometry
3303:Spheres in axonometry
3260:Circles in axonometry
3251:
3206:
3148:
3092:
3077:
2992:
2952:
2899:
2826:
2770:
2750:
2702:
2669:
2633:
2600:
2521:
2453:
2369:
2192:Standard 1:2 cabinet
2053:Pixel, 1:2 isometric
2043:
1722:
1575:
1555:
1535:
1525:
1511:
1438:
1372:
1345:
1318:
1293:
1266:
1239:
1214:
1187:
1160:
1132:
1104:
1072:
1045:
1009:
982:
946:
919:
891:, move by the amount
886:
856:
812:
783:
724:
722:{\displaystyle v_{z}}
697:
695:{\displaystyle v_{y}}
670:
668:{\displaystyle v_{x}}
625:
623:{\displaystyle v_{z}}
598:
596:{\displaystyle v_{y}}
571:
569:{\displaystyle v_{x}}
540:
496:
473:
460:orthogonal axonometry
247:Computer-aided design
184:Exploded view drawing
73:
4428:Descriptive geometry
4377:Scientific modelling
4352:Information graphics
4092:Clifford A. Pickover
4042:William S. Cleveland
3950:Henry Norris Russell
3935:Howard G. Funkhouser
3879:Florence Nightingale
3844:Francis Amasa Walker
3740:Statistical graphics
3662:Volume visualization
3637:Social visualization
3215:
3157:
3099:
3015:
2971:
2910:
2849:
2790:
2784:isometric axonometry
2763:Isometric axonometry
2726:
2678:
2645:
2609:
2576:
2469:
2391:
2023:
1735:Special axonometries
1606:
1564:
1544:
1452:
1389:
1354:
1327:
1304:
1275:
1248:
1225:
1196:
1169:
1146:
1086:
1054:
1050:in the direction of
1021:
991:
987:in the direction of
958:
928:
924:in the direction of
895:
868:
821:
794:
733:
706:
679:
652:
607:
580:
553:
505:
478:
362:descriptive geometry
252:Descriptive geometry
125:Isometric projection
90:Graphical projection
4357:Information science
4320:in computer science
4112:Sheelagh Carpendale
4047:George G. Robertson
3884:Karl Wilhelm Pohlke
3819:André-Michel Guerry
3695:Graph of a function
3690:Engineering drawing
3271:drawing the ellipse
3267:Rytz's construction
2375:Engineer projection
2334:Normal planometric
1766:
1573:{\displaystyle 0.5}
1553:{\displaystyle 1.0}
1017:move by the amount
954:move by the amount
446:by this procedure.
382:parallel projection
312:Video game graphics
287:Projective geometry
257:Engineering drawing
149:Reverse perspective
115:Parallel projection
84:Part of a series on
75:Cavalier projection
4397:Volume cartography
4161:Early 21st century
4057:Catherine Plaisant
4052:Bruce H. McCormick
4006:Mary Eleanor Spear
3996:Arthur H. Robinson
3930:Arthur Lyon Bowley
3903:Early 20th century
3750:Technical drawings
3622:Molecular graphics
3597:Flow visualization
3587:Data visualization
3257:
3246:
3201:
3143:
3072:
2987:
2947:
2894:
2821:
2773:
2745:
2697:
2664:
2628:
2595:
2516:
2448:
2372:
2038:
1739:
1717:
1570:
1550:
1538:
1530:
1506:
1433:
1367:
1340:
1313:
1288:
1261:
1234:
1209:
1182:
1155:
1135:
1099:
1067:
1040:
1004:
977:
941:
914:
881:
851:
807:
778:
719:
692:
665:
632:
620:
593:
566:
535:
491:
418:representation of
388:(the rays are not
132:Oblique projection
79:
4415:
4414:
4392:Visual perception
4342:Graphic organizer
4315:Computer graphics
4286:
4285:
4268:Martin Wattenberg
4243:Hanspeter Pfister
4198:Martin Krzywinski
4122:Jock D. Mackinlay
4102:Thomas A. DeFanti
4025:Late 20th century
3945:Ejnar Hertzsprung
3647:Technical drawing
3394:978-3-319-29717-0
3366:Kohlhammer Verlag
3070:
2979:
2943:
2836:standard isometry
2512:
2493:
2447:
2415:
2364:
2363:
2036:
2035:
1770:Name or property
1713:
1709:
1649:
1502:
1429:
1365:
1338:
1286:
1259:
1207:
1180:
1097:
1065:
1002:
939:
879:
805:
489:
420:three-dimensional
408:technical drawing
364:that generates a
355:
354:
297:Technical drawing
242:Computer graphics
65:
64:
4440:
4402:Volume rendering
4387:Visual analytics
4382:Spatial analysis
4362:Misleading graph
4213:David McCandless
4188:Gordon Kindlmann
4152:Alfred Inselberg
4147:Leland Wilkinson
4082:Michael Friendly
4016:Howard T. Fisher
3979:Mid 20th century
3920:W. E. B. Du Bois
3824:William Playfair
3814:Adolphe Quetelet
3788:Joseph Priestley
3771:Pre-19th century
3768:
3767:
3735:Skeletal formula
3602:Geovisualization
3577:Chemical imaging
3550:
3543:
3536:
3527:
3526:
3509:
3503:
3497:
3491:
3485:
3479:
3473:
3467:
3461:
3455:
3449:
3443:
3437:
3431:
3417:
3398:
3379:
3356:
3337:
3294:
3282:
3255:
3253:
3252:
3247:
3239:
3238:
3210:
3208:
3207:
3202:
3194:
3193:
3169:
3168:
3152:
3150:
3149:
3144:
3136:
3135:
3111:
3110:
3081:
3079:
3078:
3073:
3071:
3066:
3058:
3053:
3052:
3040:
3039:
3027:
3026:
2996:
2994:
2993:
2988:
2980:
2975:
2956:
2954:
2953:
2948:
2941:
2940:
2939:
2903:
2901:
2900:
2895:
2887:
2886:
2874:
2873:
2861:
2860:
2830:
2828:
2827:
2822:
2820:
2819:
2754:
2752:
2751:
2746:
2738:
2737:
2706:
2704:
2703:
2698:
2690:
2689:
2673:
2671:
2670:
2665:
2663:
2662:
2637:
2635:
2634:
2629:
2621:
2620:
2604:
2602:
2601:
2596:
2594:
2593:
2525:
2523:
2522:
2517:
2510:
2509:
2508:
2491:
2487:
2486:
2457:
2455:
2454:
2449:
2445:
2438:
2437:
2425:
2424:
2413:
2403:
2402:
2359:
2357:
2356:
2353:
2350:
2120:
2118:
2117:
2114:
2111:
2101:
2099:
2098:
2095:
2092:
2047:
2045:
2044:
2039:
2037:
2028:
2027:
1767:
1738:
1726:
1724:
1723:
1718:
1711:
1710:
1705:
1703:
1692:
1691:
1672:
1671:
1659:
1658:
1647:
1643:
1642:
1624:
1623:
1579:
1577:
1576:
1571:
1559:
1557:
1556:
1551:
1515:
1513:
1512:
1507:
1500:
1499:
1498:
1485:
1484:
1471:
1470:
1442:
1440:
1439:
1434:
1427:
1426:
1425:
1401:
1400:
1376:
1374:
1373:
1368:
1366:
1358:
1349:
1347:
1346:
1341:
1339:
1331:
1322:
1320:
1319:
1314:
1297:
1295:
1294:
1289:
1287:
1279:
1270:
1268:
1267:
1262:
1260:
1252:
1243:
1241:
1240:
1235:
1218:
1216:
1215:
1210:
1208:
1200:
1191:
1189:
1188:
1183:
1181:
1173:
1164:
1162:
1161:
1156:
1108:
1106:
1105:
1100:
1098:
1090:
1076:
1074:
1073:
1068:
1066:
1058:
1049:
1047:
1046:
1041:
1033:
1032:
1013:
1011:
1010:
1005:
1003:
995:
986:
984:
983:
978:
970:
969:
950:
948:
947:
942:
940:
932:
923:
921:
920:
915:
907:
906:
890:
888:
887:
882:
880:
872:
860:
858:
857:
852:
816:
814:
813:
808:
806:
798:
787:
785:
784:
779:
771:
770:
758:
757:
745:
744:
728:
726:
725:
720:
718:
717:
701:
699:
698:
693:
691:
690:
674:
672:
671:
666:
664:
663:
635:Pohlke's theorem
629:
627:
626:
621:
619:
618:
602:
600:
599:
594:
592:
591:
575:
573:
572:
567:
565:
564:
544:
542:
541:
536:
500:
498:
497:
492:
490:
482:
347:
340:
333:
282:Projection plane
272:Plans (drawings)
100:
81:
80:
60:
57:
51:
24:
23:
16:
4448:
4447:
4443:
4442:
4441:
4439:
4438:
4437:
4418:
4417:
4416:
4411:
4407:Information art
4347:Imaging science
4292:
4282:
4263:Fernanda Viégas
4258:Moritz Stefaner
4183:Jessica Hullman
4156:
4127:Alan MacEachren
4077:Ben Shneiderman
4020:
3974:
3898:
3797:
3759:
3672:
3666:
3617:Medical imaging
3560:
3554:
3517:
3512:
3504:
3500:
3492:
3488:
3480:
3476:
3468:
3464:
3456:
3452:
3444:
3440:
3432:
3428:
3414:
3395:
3376:
3353:
3334:
3318:
3305:
3298:
3295:
3286:
3283:
3262:
3222:
3218:
3216:
3213:
3212:
3183:
3179:
3164:
3160:
3158:
3155:
3154:
3125:
3121:
3106:
3102:
3100:
3097:
3096:
3094:
3062:
3057:
3048:
3044:
3035:
3031:
3022:
3018:
3016:
3013:
3012:
2974:
2972:
2969:
2968:
2935:
2931:
2911:
2908:
2907:
2882:
2878:
2869:
2865:
2856:
2852:
2850:
2847:
2846:
2815:
2811:
2791:
2788:
2787:
2765:
2733:
2729:
2727:
2724:
2723:
2714:
2685:
2681:
2679:
2676:
2675:
2658:
2654:
2646:
2643:
2642:
2616:
2612:
2610:
2607:
2606:
2589:
2585:
2577:
2574:
2573:
2560:
2504:
2500:
2482:
2478:
2470:
2467:
2466:
2433:
2429:
2420:
2416:
2398:
2394:
2392:
2389:
2388:
2385:foreshortenings
2377:
2354:
2351:
2348:
2347:
2345:
2326:
2315:
2307:
2240:
2219:
2145:
2115:
2112:
2109:
2108:
2106:
2096:
2093:
2090:
2089:
2087:
2026:
2024:
2021:
2020:
1985:
1962:
1885:
1877:
1827:
1819:
1811:
1804:
1796:
1763:
1757:
1751:
1745:
1737:
1704:
1699:
1687:
1683:
1667:
1663:
1654:
1650:
1638:
1634:
1619:
1615:
1607:
1604:
1603:
1594:
1588:
1565:
1562:
1561:
1545:
1542:
1541:
1527:
1494:
1490:
1480:
1476:
1466:
1462:
1453:
1450:
1449:
1446:foreshortenings
1443:
1421:
1417:
1396:
1392:
1390:
1387:
1386:
1357:
1355:
1352:
1351:
1330:
1328:
1325:
1324:
1305:
1302:
1301:
1278:
1276:
1273:
1272:
1251:
1249:
1246:
1245:
1226:
1223:
1222:
1199:
1197:
1194:
1193:
1172:
1170:
1167:
1166:
1147:
1144:
1143:
1127:
1089:
1087:
1084:
1083:
1057:
1055:
1052:
1051:
1028:
1024:
1022:
1019:
1018:
994:
992:
989:
988:
965:
961:
959:
956:
955:
931:
929:
926:
925:
902:
898:
896:
893:
892:
871:
869:
866:
865:
822:
819:
818:
797:
795:
792:
791:
790:The projection
766:
762:
753:
749:
740:
736:
734:
731:
730:
713:
709:
707:
704:
703:
686:
682:
680:
677:
676:
659:
655:
653:
650:
649:
646:foreshortenings
614:
610:
608:
605:
604:
587:
583:
581:
578:
577:
560:
556:
554:
551:
550:
506:
503:
502:
481:
479:
476:
475:
468:
416:two-dimensional
351:
322:
321:
317:Viewing frustum
307:Vanishing point
222:
214:
213:
204:Worm's-eye view
179:Cutaway drawing
169:Bird's-eye view
164:
156:
155:
110:
68:
61:
55:
52:
46:
37:German original
25:
21:
12:
11:
5:
4446:
4436:
4435:
4430:
4413:
4412:
4410:
4409:
4404:
4399:
4394:
4389:
4384:
4379:
4374:
4372:Patent drawing
4369:
4364:
4359:
4354:
4349:
4344:
4339:
4337:Graphic design
4334:
4329:
4324:
4323:
4322:
4312:
4307:
4302:
4296:
4294:
4288:
4287:
4284:
4283:
4281:
4280:
4278:Hadley Wickham
4275:
4270:
4265:
4260:
4255:
4250:
4245:
4240:
4235:
4233:Tamara Munzner
4230:
4225:
4220:
4215:
4210:
4205:
4200:
4195:
4190:
4185:
4180:
4175:
4170:
4164:
4162:
4158:
4157:
4155:
4154:
4149:
4144:
4139:
4134:
4132:David Goodsell
4129:
4124:
4119:
4117:Cynthia Brewer
4114:
4109:
4104:
4099:
4094:
4089:
4084:
4079:
4074:
4069:
4064:
4059:
4054:
4049:
4044:
4039:
4034:
4028:
4026:
4022:
4021:
4019:
4018:
4013:
4011:Edgar Anderson
4008:
4003:
3998:
3993:
3988:
3986:Jacques Bertin
3982:
3980:
3976:
3975:
3973:
3972:
3967:
3962:
3957:
3952:
3947:
3942:
3940:John B. Peddle
3937:
3932:
3927:
3922:
3917:
3912:
3906:
3904:
3900:
3899:
3897:
3896:
3894:Francis Galton
3891:
3889:Toussaint Loua
3886:
3881:
3876:
3871:
3869:Georg von Mayr
3866:
3861:
3859:Matthew Sankey
3856:
3851:
3846:
3841:
3836:
3831:
3826:
3821:
3816:
3811:
3805:
3803:
3799:
3798:
3796:
3795:
3790:
3785:
3780:
3774:
3772:
3765:
3761:
3760:
3758:
3757:
3752:
3747:
3742:
3737:
3732:
3727:
3725:Sankey diagram
3722:
3717:
3712:
3707:
3702:
3697:
3692:
3687:
3682:
3676:
3674:
3668:
3667:
3665:
3664:
3659:
3657:Visual culture
3654:
3649:
3644:
3639:
3634:
3629:
3624:
3619:
3614:
3609:
3604:
3599:
3594:
3589:
3584:
3579:
3574:
3568:
3566:
3562:
3561:
3553:
3552:
3545:
3538:
3530:
3524:
3523:
3516:
3515:External links
3513:
3511:
3510:
3508:, p. 159.
3498:
3486:
3484:, p. 168.
3474:
3472:, p. 155.
3462:
3460:, p. 145.
3450:
3448:, p. 156.
3438:
3436:, p. 144.
3425:
3424:
3423:
3419:
3418:
3412:
3399:
3393:
3380:
3374:
3357:
3351:
3338:
3332:
3317:
3314:
3304:
3301:
3300:
3299:
3296:
3289:
3287:
3284:
3277:
3261:
3258:
3245:
3242:
3237:
3234:
3231:
3228:
3225:
3221:
3200:
3197:
3192:
3189:
3186:
3182:
3178:
3175:
3172:
3167:
3163:
3142:
3139:
3134:
3131:
3128:
3124:
3120:
3117:
3114:
3109:
3105:
3084:
3083:
3082:(instead of 1)
3069:
3065:
3061:
3056:
3051:
3047:
3043:
3038:
3034:
3030:
3025:
3021:
3006:
3005:
2998:
2986:
2983:
2978:
2965:
2958:
2957:
2946:
2938:
2934:
2930:
2927:
2924:
2921:
2918:
2915:
2905:
2893:
2890:
2885:
2881:
2877:
2872:
2868:
2864:
2859:
2855:
2818:
2814:
2810:
2807:
2804:
2801:
2798:
2795:
2764:
2761:
2757:
2756:
2744:
2741:
2736:
2732:
2719:
2718:
2713:
2710:
2709:
2708:
2696:
2693:
2688:
2684:
2674:(oblique) and
2661:
2657:
2653:
2650:
2639:
2627:
2624:
2619:
2615:
2605:(oblique) and
2592:
2588:
2584:
2581:
2565:
2564:
2559:
2556:
2552:de:Axonometrie
2548:
2547:
2544:
2541:
2527:
2526:
2515:
2507:
2503:
2499:
2496:
2490:
2485:
2481:
2477:
2474:
2459:
2444:
2441:
2436:
2432:
2428:
2423:
2419:
2412:
2409:
2406:
2401:
2397:
2379:In this case
2376:
2373:
2362:
2361:
2343:
2339:
2338:
2335:
2331:
2330:
2327:
2322:
2319:
2316:
2311:
2308:
2303:
2300:
2296:
2295:
2290:
2286:
2285:
2282:
2279:
2274:
2271:
2268:
2265:
2261:
2260:
2257:
2254:
2251:
2248:
2244:
2243:
2238:
2233:
2230:
2227:
2223:
2222:
2217:
2212:
2209:
2206:
2202:
2201:
2196:
2193:
2189:
2188:
2183:
2180:
2177:
2174:
2170:
2169:
2166:
2162:
2161:
2158:
2155:
2152:
2149:
2146:
2141:
2138:
2134:
2133:
2130:
2125:
2122:
2103:
2084:
2081:
2078:
2075:
2071:
2070:
2067:
2060:
2057:
2054:
2050:
2049:
2034:
2031:
2018:
2014:
2013:
2010:
2005:
2001:
2000:
1997:
1994:
1990:
1989:
1986:
1981:
1978:
1975:
1972:
1969:
1965:
1964:
1958:
1955:
1952:
1949:
1946:
1943:
1940:
1936:
1935:
1932:
1928:
1927:
1922:
1918:
1917:
1912:
1908:
1907:
1904:
1901:
1898:
1895:
1892:
1889:
1886:
1881:
1878:
1873:
1870:
1866:
1865:
1862:
1859:
1854:
1851:
1848:
1845:
1842:
1839:
1835:
1834:
1829:
1825:
1821:
1817:
1813:
1809:
1805:
1800:
1797:
1792:
1789:
1783:
1777:
1771:
1761:
1753:
1747:
1741:
1736:
1733:
1727:Hence it is a
1716:
1708:
1702:
1698:
1695:
1690:
1686:
1681:
1678:
1675:
1670:
1666:
1662:
1657:
1653:
1646:
1641:
1637:
1633:
1630:
1627:
1622:
1618:
1614:
1611:
1569:
1549:
1505:
1497:
1493:
1488:
1483:
1479:
1474:
1469:
1465:
1460:
1457:
1432:
1424:
1420:
1416:
1413:
1410:
1407:
1404:
1399:
1395:
1379:
1378:
1364:
1361:
1337:
1334:
1323:angle between
1312:
1309:
1299:
1285:
1282:
1258:
1255:
1244:angle between
1233:
1230:
1220:
1206:
1203:
1179:
1176:
1165:angle between
1154:
1151:
1126:
1123:
1111:
1110:
1096:
1093:
1080:
1079:
1078:
1064:
1061:
1039:
1036:
1031:
1027:
1015:
1001:
998:
976:
973:
968:
964:
952:
938:
935:
913:
910:
905:
901:
878:
875:
850:
847:
844:
841:
838:
835:
832:
829:
826:
804:
801:
788:
777:
774:
769:
765:
761:
756:
752:
748:
743:
739:
716:
712:
689:
685:
662:
658:
642:
617:
613:
590:
586:
563:
559:
534:
531:
528:
525:
522:
519:
516:
513:
510:
488:
485:
467:
464:
353:
352:
350:
349:
342:
335:
327:
324:
323:
320:
319:
314:
309:
304:
299:
294:
289:
284:
279:
274:
269:
264:
262:Map projection
259:
254:
249:
244:
239:
234:
229:
223:
220:
219:
216:
215:
212:
211:
206:
201:
196:
191:
186:
181:
176:
171:
165:
162:
161:
158:
157:
154:
153:
152:
151:
146:
136:
135:
134:
129:
128:
127:
111:
106:
105:
102:
101:
93:
92:
86:
85:
66:
63:
62:
28:
26:
19:
9:
6:
4:
3:
2:
4445:
4434:
4431:
4429:
4426:
4425:
4423:
4408:
4405:
4403:
4400:
4398:
4395:
4393:
4390:
4388:
4385:
4383:
4380:
4378:
4375:
4373:
4370:
4368:
4365:
4363:
4360:
4358:
4355:
4353:
4350:
4348:
4345:
4343:
4340:
4338:
4335:
4333:
4332:Graph drawing
4330:
4328:
4325:
4321:
4318:
4317:
4316:
4313:
4311:
4308:
4306:
4303:
4301:
4298:
4297:
4295:
4289:
4279:
4276:
4274:
4271:
4269:
4266:
4264:
4261:
4259:
4256:
4254:
4253:Claudio Silva
4251:
4249:
4246:
4244:
4241:
4239:
4236:
4234:
4231:
4229:
4226:
4224:
4221:
4219:
4218:Mauro Martino
4216:
4214:
4211:
4209:
4206:
4204:
4201:
4199:
4196:
4194:
4191:
4189:
4186:
4184:
4181:
4179:
4176:
4174:
4171:
4169:
4166:
4165:
4163:
4159:
4153:
4150:
4148:
4145:
4143:
4142:Michael Maltz
4140:
4138:
4135:
4133:
4130:
4128:
4125:
4123:
4120:
4118:
4115:
4113:
4110:
4108:
4107:George Furnas
4105:
4103:
4100:
4098:
4095:
4093:
4090:
4088:
4087:Howard Wainer
4085:
4083:
4080:
4078:
4075:
4073:
4070:
4068:
4065:
4063:
4060:
4058:
4055:
4053:
4050:
4048:
4045:
4043:
4040:
4038:
4035:
4033:
4030:
4029:
4027:
4023:
4017:
4014:
4012:
4009:
4007:
4004:
4002:
3999:
3997:
3994:
3992:
3991:Rudolf Modley
3989:
3987:
3984:
3983:
3981:
3977:
3971:
3968:
3966:
3963:
3961:
3958:
3956:
3955:Max O. Lorenz
3953:
3951:
3948:
3946:
3943:
3941:
3938:
3936:
3933:
3931:
3928:
3926:
3923:
3921:
3918:
3916:
3913:
3911:
3908:
3907:
3905:
3901:
3895:
3892:
3890:
3887:
3885:
3882:
3880:
3877:
3875:
3872:
3870:
3867:
3865:
3864:Charles Booth
3862:
3860:
3857:
3855:
3852:
3850:
3847:
3845:
3842:
3840:
3839:Luigi Perozzo
3837:
3835:
3832:
3830:
3829:August Kekulé
3827:
3825:
3822:
3820:
3817:
3815:
3812:
3810:
3809:Charles Dupin
3807:
3806:
3804:
3800:
3794:
3793:Gaspard Monge
3791:
3789:
3786:
3784:
3781:
3779:
3778:Edmond Halley
3776:
3775:
3773:
3769:
3766:
3762:
3756:
3753:
3751:
3748:
3746:
3743:
3741:
3738:
3736:
3733:
3731:
3728:
3726:
3723:
3721:
3718:
3716:
3713:
3711:
3708:
3706:
3703:
3701:
3698:
3696:
3693:
3691:
3688:
3686:
3683:
3681:
3678:
3677:
3675:
3669:
3663:
3660:
3658:
3655:
3653:
3650:
3648:
3645:
3643:
3640:
3638:
3635:
3633:
3630:
3628:
3625:
3623:
3620:
3618:
3615:
3613:
3610:
3608:
3605:
3603:
3600:
3598:
3595:
3593:
3590:
3588:
3585:
3583:
3582:Crime mapping
3580:
3578:
3575:
3573:
3570:
3569:
3567:
3563:
3558:
3557:Visualization
3551:
3546:
3544:
3539:
3537:
3532:
3531:
3528:
3522:
3519:
3518:
3507:
3502:
3496:, p. 95.
3495:
3490:
3483:
3478:
3471:
3466:
3459:
3454:
3447:
3442:
3435:
3430:
3426:
3421:
3420:
3415:
3413:3-506-37443-5
3409:
3406:. Schöningh.
3405:
3400:
3396:
3390:
3386:
3381:
3377:
3375:3-17-018489-X
3371:
3367:
3364:. Stuttgart:
3363:
3358:
3354:
3352:3-446-00778-4
3348:
3344:
3339:
3335:
3333:3-494-00488-9
3329:
3325:
3320:
3319:
3313:
3310:
3293:
3288:
3281:
3276:
3275:
3274:
3272:
3268:
3243:
3240:
3235:
3232:
3229:
3226:
3223:
3219:
3198:
3195:
3190:
3187:
3184:
3180:
3176:
3173:
3170:
3165:
3161:
3140:
3137:
3132:
3129:
3126:
3122:
3118:
3115:
3112:
3107:
3103:
3091:
3087:
3067:
3063:
3059:
3054:
3049:
3045:
3041:
3036:
3032:
3028:
3023:
3019:
3011:
3010:
3009:
3003:
2999:
2984:
2981:
2976:
2966:
2963:
2962:
2961:
2944:
2936:
2932:
2928:
2925:
2922:
2919:
2916:
2913:
2906:
2891:
2888:
2883:
2879:
2875:
2870:
2866:
2862:
2857:
2853:
2845:
2844:
2843:
2842:one chooses:
2841:
2837:
2832:
2816:
2812:
2808:
2805:
2802:
2799:
2796:
2793:
2785:
2780:
2778:
2769:
2760:
2742:
2739:
2734:
2730:
2721:
2720:
2716:
2715:
2694:
2691:
2686:
2682:
2659:
2655:
2651:
2648:
2640:
2625:
2622:
2617:
2613:
2590:
2586:
2582:
2579:
2571:
2570:
2569:
2562:
2561:
2555:
2553:
2545:
2542:
2539:
2538:
2537:
2534:
2532:
2513:
2505:
2501:
2497:
2494:
2488:
2483:
2479:
2475:
2472:
2464:
2460:
2442:
2439:
2434:
2430:
2426:
2421:
2417:
2410:
2407:
2404:
2399:
2395:
2386:
2382:
2381:
2380:
2368:
2344:
2341:
2340:
2336:
2333:
2332:
2325:
2314:
2306:
2298:
2297:
2294:
2288:
2287:
2278:
2263:
2262:
2255:
2252:
2249:
2247:30° cavalier
2246:
2245:
2241:
2231:
2228:
2225:
2224:
2220:
2210:
2207:
2204:
2203:
2200:
2191:
2190:
2187:
2172:
2171:
2167:
2164:
2163:
2144:
2136:
2135:
2129:
2123:
2082:
2079:
2076:
2073:
2072:
2068:
2065:
2058:
2052:
2051:
2032:
2029:
2019:
2016:
2015:
2011:
2009:
2003:
2002:
1992:
1991:
1984:
1979:
1976:
1973:
1970:
1967:
1966:
1961:
1956:
1944:
1941:
1938:
1937:
1933:
1930:
1929:
1926:
1920:
1919:
1916:
1910:
1909:
1884:
1876:
1868:
1867:
1860:
1858:
1852:
1849:
1846:
1843:
1840:
1836:
1833:
1830:
1828:
1822:
1820:
1814:
1812:
1806:
1803:
1798:
1795:
1790:
1788:
1784:
1782:
1778:
1776:
1772:
1769:
1768:
1764:
1756:
1750:
1744:
1732:
1730:
1714:
1706:
1700:
1696:
1693:
1688:
1684:
1679:
1676:
1673:
1668:
1664:
1660:
1655:
1651:
1644:
1639:
1635:
1631:
1628:
1625:
1620:
1616:
1612:
1609:
1600:
1598:
1592:
1586:
1581:
1567:
1547:
1534:
1524:
1520:
1516:
1503:
1495:
1491:
1486:
1481:
1477:
1472:
1467:
1463:
1458:
1455:
1447:
1430:
1422:
1418:
1414:
1411:
1408:
1405:
1402:
1397:
1393:
1384:
1359:
1332:
1310:
1307:
1300:
1280:
1253:
1231:
1228:
1221:
1201:
1174:
1152:
1149:
1142:
1141:
1140:
1139:
1131:
1122:
1120:
1116:
1091:
1081:
1059:
1037:
1034:
1029:
1025:
1016:
996:
974:
971:
966:
962:
953:
933:
911:
908:
903:
899:
873:
863:
862:
845:
842:
839:
836:
833:
827:
824:
799:
789:
775:
772:
767:
763:
759:
754:
750:
746:
741:
737:
714:
710:
687:
683:
660:
656:
647:
643:
640:
639:
638:
636:
615:
611:
588:
584:
561:
557:
548:
529:
526:
523:
520:
517:
511:
508:
483:
472:
463:
461:
457:
456:
451:
447:
445:
441:
436:
433:
429:
425:
421:
417:
413:
409:
404:
402:
400:
395:
391:
390:perpendicular
387:
383:
379:
375:
371:
367:
363:
359:
348:
343:
341:
336:
334:
329:
328:
326:
325:
318:
315:
313:
310:
308:
305:
303:
300:
298:
295:
293:
290:
288:
285:
283:
280:
278:
275:
273:
270:
268:
267:Picture plane
265:
263:
260:
258:
255:
253:
250:
248:
245:
243:
240:
238:
235:
233:
230:
228:
227:3D projection
225:
224:
218:
217:
210:
207:
205:
202:
200:
197:
195:
192:
190:
187:
185:
182:
180:
177:
175:
174:Cross section
172:
170:
167:
166:
160:
159:
150:
147:
145:
142:
141:
140:
137:
133:
130:
126:
123:
122:
121:
118:
117:
116:
113:
112:
109:
104:
103:
99:
95:
94:
91:
88:
87:
83:
82:
76:
72:
59:
49:
44:
40:
38:
32:
29:This article
27:
18:
17:
4367:Neuroimaging
4327:CPK coloring
4310:Color coding
4248:Hans Rosling
4228:Miriah Meyer
4193:Aaron Koblin
4178:Jeffrey Heer
4072:Edward Tufte
4067:Pat Hanrahan
4037:Nigel Holmes
3915:Otto Neurath
3854:Oliver Byrne
3802:19th century
3501:
3489:
3477:
3465:
3453:
3441:
3429:
3403:
3387:. Springer.
3384:
3361:
3342:
3323:
3308:
3306:
3263:
3085:
3007:
2959:
2839:
2835:
2833:
2783:
2781:
2774:
2758:
2755:(isometric).
2707:(isometric).
2566:
2549:
2535:
2528:
2462:
2384:
2378:
2323:
2312:
2304:
2299:Planometric
2292:
2276:
2236:
2226:60° cabinet
2215:
2205:30° cabinet
2198:
2185:
2142:
2127:
2074:Engineering
2063:
2007:
1993:Equiangular
1982:
1959:
1924:
1914:
1888:360° − α − β
1882:
1874:
1856:
1831:
1823:
1815:
1807:
1801:
1793:
1786:
1780:
1774:
1759:
1754:
1748:
1742:
1728:
1601:
1596:
1590:
1584:
1582:
1539:
1517:
1445:
1382:
1380:
1137:
1136:
1112:
633:
546:
459:
453:
449:
448:
443:
439:
437:
412:architecture
405:
397:
394:orthographic
366:planar image
357:
356:
236:
232:Anamorphosis
189:Fisheye lens
53:
45:for details.
34:
30:
4300:Cartography
4238:Ade Olufeko
4208:Manuel Lima
4137:Kwan-Liu Ma
4062:Stuart Card
4032:Borden Dent
3970:Erwin Raisz
3925:Henry Gantt
2638:(dimetric),
2531:set squares
1752:, without γ
1271:-axis and
1077:and finally
817:of a point
302:True length
292:Stereoscopy
4422:Categories
4223:John Maeda
4001:John Tukey
3965:Harry Beck
3960:Fritz Kahn
3710:Photograph
3506:Stärk 1978
3482:Stärk 1978
3446:Stärk 1978
3316:References
3309:orthogonal
2168:< 100%
1974:360° − 2·α
1968:Symmetric
1921:Isometric
1869:Trimetric
1350:-axis and
1192:-axis and
474:The point
450:Axonometry
440:axonometry
401:axonometry
399:orthogonal
374:dimensions
358:Axonometry
237:Axonometry
194:Multiviews
4305:Chartjunk
4273:Bang Wong
4168:Polo Chau
3874:John Snow
3849:John Venn
3730:Schematic
3715:Pictogram
3494:Graf 1961
3470:Graf 1961
3458:Graf 1961
3434:Graf 1961
2937:∘
2926:γ
2920:β
2914:α
2817:∘
2806:γ
2800:β
2794:α
2660:∘
2649:α
2591:∘
2580:α
2506:∘
2495:β
2484:∘
2473:α
2289:Military
2137:Cavalier
1945:< 90°
1911:Dimetric
1640:∘
1629:β
1621:∘
1610:α
1597:trimetric
1591:isometric
1423:∘
1412:β
1406:α
1398:∘
1363:¯
1336:¯
1308:γ
1284:¯
1257:¯
1229:β
1205:¯
1178:¯
1150:α
1138:Notation:
1095:¯
1063:¯
1035:⋅
1000:¯
972:⋅
937:¯
909:⋅
877:¯
803:¯
487:¯
438:The term
209:Zoom lens
43:talk page
4291:Related
3700:Ideogram
2840:isometry
2838:or just
2834:For the
2777:isometry
2310:180° − α
2151:270° − α
1977:< 90°
1942:< 90°
1729:dimetric
1585:dimetric
729:, where
444:produced
199:Panorama
56:May 2017
41:See the
4173:Ben Fry
3685:Diagram
2782:For an
2358:
2346:
2321:90° − α
2302:90° + α
2235:arccot(
2214:arctan(
2140:90° + α
2119:
2107:
2105:arcsin(
2100:
2088:
2086:arccos(
2062:arctan(
1931:Normal
1880:90° + β
1872:90° + α
432:conical
410:and in
386:oblique
378:scaling
4293:topics
3764:People
3671:Image
3565:Fields
3410:
3391:
3372:
3349:
3330:
2942:
2511:
2492:
2463:angles
2446:
2414:
2360:≈ 67%
2232:116.6°
2229:153.4°
2211:153.4°
2208:116.6°
2083:131.4°
2077:131.4°
2059:126.9°
2056:116.6°
2048:≈ 81%
1712:
1648:
1501:
1428:
1383:angles
1377:-axis.
1014:, then
951:, then
428:relief
424:volume
221:Topics
108:Planar
3745:Table
3680:Chart
3673:types
3422:Notes
2985:1.225
2387:are:
2337:100%
2284:100%
2132:100%
2080:97.2°
2012:100%
1957:tan(α
1934:100%
1853:270°
1785:γ = ∠
1779:β = ∠
1773:α = ∠
1298:-axis
1219:-axis
163:Views
3720:Plot
3408:ISBN
3389:ISBN
3370:ISBN
3347:ISBN
3328:ISBN
3269:and
3002:xfig
2461:the
2383:the
2329:any
2273:45°
2267:135°
2259:any
2256:30°
2253:150°
2250:120°
2182:45°
2179:135°
2176:135°
2160:any
2069:50%
1999:30°
1996:120°
1988:any
1906:any
1894:any
1864:any
1847:270°
1775:x̄z̄
1459:<
1444:The
1415:<
1403:<
1381:The
773:>
702:and
603:and
376:and
370:axes
3705:Map
3174:0.5
3116:0.5
2977:1.5
2933:120
2813:120
2656:135
2626:0.5
2587:135
2480:132
2408:0.5
2318:any
2281:any
2270:90°
2195:50%
2157:0°
2154:any
2148:90°
2124:50%
1954:any
1951:any
1948:any
1903:any
1900:any
1897:any
1891:any
1841:90°
1787:x̄ȳ
1781:ȳz̄
1746:, β
1617:135
1568:0.5
1560:or
1548:1.0
1419:360
1121:).
426:or
406:In
4424::
3368:.
3273:.
2831:.
2554:.
2533:.
2502:97
2242:)
2221:)
2121:)
2066:)
1963:)
1861:0%
1850:0°
1844:0°
1765:)
1636:90
1599:.
1580:.
1448::
776:0.
675:,
648:,
576:,
462:.
403:.
3549:e
3542:t
3535:v
3416:.
3397:.
3378:.
3355:.
3336:.
3244:1
3241:=
3236:z
3233:,
3230:y
3227:,
3224:x
3220:v
3199:1
3196:=
3191:z
3188:,
3185:y
3181:v
3177:,
3171:=
3166:x
3162:v
3141:1
3138:=
3133:y
3130:,
3127:x
3123:v
3119:,
3113:=
3108:z
3104:v
3068:3
3064:/
3060:2
3055:=
3050:z
3046:v
3042:=
3037:y
3033:v
3029:=
3024:x
3020:v
2982:=
2945:.
2929:=
2923:=
2917:=
2892:1
2889:=
2884:z
2880:v
2876:=
2871:y
2867:v
2863:=
2858:x
2854:v
2809:=
2803:=
2797:=
2743:1
2740:=
2735:z
2731:v
2695:1
2692:=
2687:x
2683:v
2652:=
2623:=
2618:x
2614:v
2583:=
2514:.
2498:=
2489:,
2476:=
2443:1
2440:=
2435:z
2431:v
2427:=
2422:y
2418:v
2411:,
2405:=
2400:x
2396:v
2355:3
2352:/
2349:2
2324:h
2313:h
2305:h
2293:v
2277:v
2239:x
2237:v
2218:x
2216:v
2199:v
2186:v
2143:h
2128:v
2116:8
2113:/
2110:1
2102:)
2097:4
2094:/
2091:3
2064:v
2033:3
2030:2
2008:v
1983:h
1980:α
1971:α
1960:h
1925:v
1915:v
1883:h
1875:h
1857:v
1832:v
1826:z
1824:v
1818:y
1816:v
1810:x
1808:v
1802:h
1799:β
1794:h
1791:α
1762:i
1760:v
1755:h
1749:h
1743:h
1715:.
1707:2
1701:/
1697:1
1694:=
1689:x
1685:v
1680:,
1677:1
1674:=
1669:z
1665:v
1661:=
1656:y
1652:v
1645:,
1632:=
1626:,
1613:=
1593:.
1587:.
1504:.
1496:z
1492:v
1487:,
1482:y
1478:v
1473:,
1468:x
1464:v
1456:0
1431:.
1409:+
1394:0
1360:y
1333:x
1311::
1281:y
1254:z
1232::
1202:x
1175:z
1153::
1109:.
1092:P
1060:z
1038:z
1030:z
1026:v
997:y
975:y
967:y
963:v
934:x
912:x
904:x
900:v
874:O
849:)
846:z
843:,
840:y
837:,
834:x
831:(
828:=
825:P
800:P
768:z
764:v
760:,
755:y
751:v
747:,
742:x
738:v
715:z
711:v
688:y
684:v
661:x
657:v
630:.
616:z
612:v
589:y
585:v
562:x
558:v
547:Π
533:)
530:z
527:,
524:y
521:,
518:x
515:(
512:=
509:P
484:P
346:e
339:t
332:v
58:)
54:(
39:.
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