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10 axonometric projections 10 1 axonometric views g f h c e b d a c g b f s d h a e r f b isometric drawing y ...

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                                                                                                        10  
                                                                    Axonometric Projections 
                            10.1  AXONOMETRIC VIEWS 
                                                        G
                                                               F,H
                                              C
                                                                      E
                                                      B,D
                                                            A
                             C,G             B,F
                                                              S
                            D,H              A,E
                                              R                      F
                                                          B                                   Isometric Drawing
                                                                        Y
                            D,C              A,B
                                                                             E Isometric View
                                                                 A,G                      R = 45.00°
                                                     C                                    S = 35.26°
                                                                           X              X = 30.00°
                            H,G              E,F                                          Y = 30.00°
                                                                        H
                                                             D                                                   
                            10-1  
                            An isometric (and axonometric view) of a cube 
                       
                      Axonometric projections are parallel projections onto an oblique plane. Axonometric 
                      projections  have  the  advantage  that  they  give  a  pictorial  view  of  the  object,  yet 
                      dimensions are measurable.  
                      Manually, axonometric views can be constructed from orthographic views. This is best 
                      illustrated by an example. The construction in Figure 10-1 shows a cube in plan and 
                      elevation, from which an axonometric view of the cube is constructed in a direction 
                      parallel to one of its diagonals.   
                      Notice that in this view each of the sides of the cube has been foreshortened equally (to 
                                                                    √2
                      0.8165 of the actual length, or more precisely,  /√3) and that the indicated angles X and Y 
                      are each 30°. Such a projection is also called an isometric projection, meaning equal 
                      measure.  Isometric views can be drawn directly, as shown in Figure 10-2 where the 
                      view has been rotated until the vertical edge of the cube appears vertical.   
                                                     ordinary scale
                                                                                   width
                                                            isometric  scale             height
                                                     is = 30.00°
                                                              os = 45.00°
                                                                                               width
                                                                                               height  = 1.73
                                                                                                           
                      10-2  
                      Isometric scale for the cube in 10-1 
                      The 30° isometric projection has a height to width ratio of 1:√3. Two other common 
                      isometric views are shown in Figures 10-3 and 10-4. There are popular projections, 
                      which, however, are not true axonometric projections. 
                       
                       
                      The projection shown on the right is a                        height
                      27°    isometric  projection   (actually,                     width  = 0.50
                      26°34'12")  also  known  as  a  1:2 
                      projection as this is the height to width 
                      ratio of the top rhombic face.  
                                                           10-3  
                                                   1:2 projection 
                                                                        X = 27°                   Y = 27°
                                                                                                           
                      294   
                              
                              
                             The  one  on  the  left  based  is  a  45° 
                             isometric view, also known as a military 
                             projection.  It has a unit height to width                          height
                                                                                                  width  = 1.00
                             ratio. 
                                                                    10-4  
                                                         Military projection 
                              
                                                                                       X = 45.00°            Y = 45.00°
                                                                                                                         
                             10.1.1  Axonometric scales 
                             By adjusting the angles X and Y, views of the cube can be created according to a variety 
                             of axial scales. Notice that in some drawings two directions are equally scaled and one 
                             differently (called a diametric projection) and in other drawings all three directions are 
                             scaled  differently  (called  a  trimetric  projection).  These  non-isometric  axonometric 
                             projections tend to be more realistic in their depiction. In fact, Chinese scroll paintings 
                             tend to use diametric projections.  See Figure 10-6 for an example.  
                             Equally as is shown in Figure 10-1, every axonometric projection corresponds to a line 
                             of sight whose bearing is indicated by angle R and altitude (true angle of inclination) by 
                             angle  S.    Correspondingly,  we  can  specify  the  axonometric  scale  by  specifying  the 
                             angles for the line of sight.  
                             Table 10-1 gives the angles for the line of sight for the axonometric scales shown in 
                             Figure 10-5. 
                              
                                    1             1                                                3/4         3/4
                                                                  1            1
                                                                                                           1
                                             3/4
                                                                         1/2
                                 36°50'           36°50'      41°25'           41°25'     13°38'                     13°38'  
                             10-5  
                             Various axonometric scales 
                             Sides along the same axial direction have the same scale.  Unmarked sides have unit value 
                                                                                                                       295 
                                
                                          1               3/4                                      1/2
                                                                                    1                                          1             1/3
                                                      1                                         1                                          1
                                    16°20'                   36°50'    7°11'                           41°25'   3°11'                              43°24'
                                                                                                                                                           
                                                                              7/8                3/4                    7/8              2/3
                                                         1
                                         1
                                                                                           1                                        1
                                                 3/4
                                                             62°44'
                                     13°38'                                 17°                    24°46'      12°28'                        23°16'  
                                
                               10-5 (continued) 
                               Various axonometric scales 
                                
                               Table 10-1  Line of sight for the axonometric scales shown in Figure 10-5 
                                                                                    Direction of the            Angle of                    True fore-
                               Type of        Scale ratios                          sight angles                drawing axes                shortening 
                               drawing                                                                                                      ratio 
                                                                                    R              S            X             Y 
                               Isometric      X = 1         Y =1         Z = 1      45º            35º16'       30º           30º           0.8165 
                                                                              3
                               Dimetric       X = 1         Y =1         Z =  /     45º            48º30'       36º50'        36º50'        0.8835 
                                                                               4
                                                                              1
                               Dimetric       X = 1         Y =1         Z =  /     45º            61º52'       41º25'        41º25'        0.9428 
                                                                               2
                                                  3             3
                               Dimetric       X =  /        Y =  /       Z = 1      45º            14º2'        13º38'        13º38'        0.9701 
                                                    4             4
                                                                3
                               Dimetric       X = 1         Y =  /       Z = 1      32º2'          27º56'       16º20'        36º50'        0.8835 
                                                                  4
                                                                1
                               Dimetric       X = 1         Y =  /       Z = 1      20º42'         19º28'       7º11'         41º25'        0.9428 
                                                                  2
                                                                1
                               Dimetric       X = 1         Y =  /       Z = 1      13º38'         13º16'       3º11'         43º24'        0.9733 
                                                                  3
                                                                3             3
                               Dimetric       X = 1         Y =  /       Z =  /     19º28'         43º19'       13º38'        62º44'        0.9701 
                                                                  4            4
                                                  7             3
                               Trimetric      X =  /        Y =  /       Z = 1      39º8'          22º3'        17º0'         24º46'        0.9269 
                                                    8             4
                                                  7             2
                               Trimetric      X =  /        Y =  /       Z = 1      35º38'         17º57'       12º28'        23º16'        0.9513 
                                                    8             3
                                
                               296   
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...Axonometric projections views g f h c e b d a s r isometric drawing y view x an and of cube are parallel onto oblique plane have the advantage that they give pictorial object yet dimensions measurable manually can be constructed from orthographic this is best illustrated by example construction in figure shows plan elevation which direction to one its diagonals notice each sides has been foreshortened equally actual length or more precisely indicated angles such projection also called meaning equal measure drawn directly as shown where rotated until vertical edge appears ordinary scale width height os for ratio two other common figures there popular however not true on right actually known top rhombic face left based military it unit scales adjusting created according variety axial some drawings directions scaled differently diametric all three trimetric these non tend realistic their depiction fact chinese scroll paintings use see every corresponds line sight whose bearing angle altit...

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