Abstract:
Methods and apparatus are provided for receiving a print file having an actual page size, and a nominal imposition template specifying a nominal page size, and generating an imposition flat for printing. If the actual page size matches the nominal page size, the nominal imposition template is applied to the print file without change. If, however, the actual page size differs from the nominal page size, the nominal imposition template is automatically modified based on the actual page size, and then the modified imposition template is applied to the print file to create the imposition flat.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
       [0001]    This application is continuation of U.S. patent application Ser. No. 10/966,612, filed Oct. 15, 2004, the entirety of which is incorporated herein by this reference thereto. 
     
    
     BACKGROUND OF THE INVENTION 
       [0002]    1. Field of the Invention 
         [0003]    This invention relates to methods and apparatus for printing. More particularly, this invention relates to methods and apparatus for formatting multi-page documents for printing. 
         [0004]    2. Description of the Related Art 
         [0005]    A print shop, such as a commercial printer or corporate printing department, typically prints multiple pages of a multi-page document on one or more press sheets, which may then be assembled, folded, cut and bound to form a final document. The specific operations performed on the printed press sheets (e.g., how the press sheets will be folded and cut, and the type of binding that will be used) are commonly called finishing operations. Prior to printing, a process called imposition typically is performed to determine the layout of the individual document pages on the press sheets. The imposition layout, often called the imposition flat, is determined based on the size of the press sheets, the desired finished size of the document and the various finishing operations that will be performed on the printed sheets. 
         [0006]    An exemplary imposition flat for a two-page document is illustrated in  FIG. 1 . Exemplary imposition flat  10  includes press sheet  12  and pages  14   a  and  14   b  of the desired document. Press sheet  12  may be a 20″×15″ sheet of paper, and pages  14   a  and  14   b  each may have a finished size of 8.5″×11″. Imposition flat  10  also may include various alignment and identification marks, such as bleed marks  16 , trim marks  18  and sheet registration marks  20 . The specific locations on press sheet  12  of pages  14   a  and  14   b , bleed marks  16 , trim marks  18  and sheet registration marks  20  typically are determined based on the size of press sheet  12 , the finished size of pages  14   a  and  14   b , and specific finishing operations to be performed on the printed sheets. 
         [0007]    An imposition flat, such as exemplary imposition flat  10 , may be created manually by a person familiar with the operation of the equipment that will be used to print and finish the print job. More commonly, however, imposition flats are generated using imposition software programs, such as Fiery® DocBuilder Pro™ software by Electronics for Imaging, Foster City, Calif., U.S.A. An imposition software program may operate on a personal computer, laptop computer, computer workstation, print server, or other similar computer device. After a user provides the imposition software with page data for the desired output pages, and specifies the sheet size, finished output size and desired finishing operations, the imposition software generates an imposition flat, such as imposition flat  10 . 
         [0008]    For commonly recurring page layouts and finishing operations, many imposition software programs allow a user to create imposition templates, which are electronic representations of imposition page layouts, but without actual page data. The imposition templates subsequently may be applied to a print file containing the actual page data to create an imposition flat. In particular, a user typically submits a print file to the imposition software, selects a desired imposition template from a database of predefined templates, and the imposition software then generates the imposition flat that may be used to print the document. 
         [0009]    An exemplary imposition template is illustrated in  FIG. 2 . Exemplary imposition template  20  specifies the size of press sheet  22  and the finished size of pages  24 . In addition, imposition template  20  may include bleed marks  28   a , trim marks  28   b  and sheet registration marks  28   c  (collectively referred to herein as “mark objects”  28 ), binding edges  30 , and the locations of such objects on sheet  22 . The locations of pages  24 , mark objects  28  and binding edges  30  typically are specified in terms of two-dimensional coordinates, such as (x,y) coordinates. Once imposition template  20  has been created, the locations of pages  24 , mark objects  28  and binding edges  30  typically are fixed. 
         [0010]    In numerous instances, a print shop receives a new print job that has a finished page size that does not correspond exactly to the finished page size specified in a preexisting imposition template. For example, a print shop may have preexisting imposition template  20  designed for letter size (8.5″×11″) pages, but may receive a new print job having custom page sizes (e.g., 8″×12″). Alternatively, a print shop may have a preexisting imposition template that matches the finished page size of the new print job, but the template specifies a press sheet size that may only be used on one piece of equipment in the print shop. If the specified piece of equipment suddenly goes down for repair, the print shop may not have other print equipment that may be immediately used to complete the new print job. For example, although the print shop may have other print equipment that uses an alternative sheet size that may accommodate the print job, the preexisting templates for that sheet size may not match the print job&#39;s finished page size. 
         [0011]    In both instances, the print shop typically must create an entirely new imposition template for the new print job. To do so, the print shop may start from scratch, and use an imposition software program to create the template. This may be a very time-consuming process, however, and may cause a delay in printing the print job. In particular, if the print job is a rush job, the time required to generate the custom imposition template may cause the print shop to miss a required deadline for completing the job. Also, if the operator is inexperienced in template creation, the newly created imposition template may include numerous errors that further delay job completion and increase the total job cost. 
         [0012]    Alternatively, rather than creating a new imposition template from scratch, the print operator may attempt to manually edit a preexisting template to accommodate the new print job. For example, the imposition software program may permit a user to import a preexisting imposition template, and then manually modify the locations of one or more of pages  24 , bleed marks  28  or trim marks  30  based on the new page size. If the preexisting imposition template includes a large number of pages per sheet, however, (e.g., 16 pages), this may require a substantial amount of time, and may be prone to operator error, resulting in delay and added cost. 
         [0013]    Further, it may be undesirable to continually create new imposition templates for every new print job. Indeed, the proliferation of imposition templates often creates an unwieldy data management problem for many print shops. In particular, if a print shop employs numerous print operators, it is not uncommon for each print operator to create their own personal set of imposition templates, named according to the operator&#39;s individual naming convention. In a large print shop that employs a large number of print operators, the print shop may have a database of a very large number of imposition templates. As a result, when a print operator attempts to locate a specific imposition template for a particular print job, the operator may waste a considerable amount of time searching the database to locate the correct template. 
         [0014]    In view of the foregoing, it would be desirable to provide methods and apparatus to allow a preexisting imposition template to be used with a document having a finished page size different from the finished page size specified in the preexisting template. 
         [0015]    It further would be desirable to provide methods and apparatus to automatically modify a preexisting imposition template for use with a document having a finished page size different from the finished page size specified in the preexisting template. 
         [0016]    It additionally would be desirable to provide methods and apparatus to reduce the number of imposition templates that must be created and maintained for printing print jobs having varying finished page sizes. 
       SUMMARY 
       [0017]    In view of the foregoing, it is an object of this invention to provide methods and apparatus to allow a preexisting imposition template to be used with a document having a finished page size different from the finished page size specified in the preexisting template. 
         [0018]    It further is an object of this invention to provide methods and apparatus to automatically modify a preexisting imposition template for use with a document having a finished page size different from the finished page size specified in the preexisting template. 
         [0019]    It additionally is an object of this invention to provide methods and apparatus to reduce the number of imposition templates that must be created and maintained for printing print jobs having varying finished page sizes. 
         [0020]    These and other objects of this invention are accomplished by providing imposition systems and methods that receive a print file having an actual page size, and a nominal imposition template specifying a nominal page size, and generate an imposition flat for printing. In particular, imposition systems and methods in accordance with this invention apply the nominal imposition template to the print file without change if the actual page size matches the nominal page size. If, however, the actual page size differs from the nominal page size, imposition systems and methods in accordance with this invention automatically modify the nominal imposition template based on the actual page size, and then apply the modified imposition template to the print file to create the imposition flat. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0021]    The above-mentioned objects and features of the present invention can be more clearly understood from the following detailed description considered in conjunction with the following drawings, in which the same reference numerals denote the same elements throughout, and in which: 
           [0022]      FIG. 1  is a diagram of a previously known imposition flat; 
           [0023]      FIG. 2  is a diagram of a previously known imposition template; 
           [0024]      FIG. 3  is a block diagram of an exemplary imposition system in accordance with this invention; 
           [0025]      FIG. 4  is a diagram of an exemplary nominal imposition template in accordance with this invention; 
           [0026]      FIG. 5A  is a diagram of an exemplary imposition layout description in accordance with this invention; 
           [0027]      FIG. 5B  is a diagram of another exemplary imposition layout description in accordance with this invention; 
           [0028]      FIG. 6  is a flowchart of an exemplary imposition process in accordance with this invention; 
           [0029]      FIG. 7  is a flow diagram of an exemplary process for creating a modified imposition template in accordance with this invention; 
           [0030]      FIG. 8A  is a flow diagram of an exemplary process for creating a modified imposition template in accordance with this invention for a book binding layout; 
           [0031]      FIG. 8B  is a flow diagram of an exemplary process for creating a modified imposition template in accordance with this invention for a non-book binding layout; 
           [0032]      FIG. 9A  is an exemplary imposition layout in accordance with this invention for a book binding template; 
           [0033]      FIG. 9B  is another exemplary imposition layout in accordance with this invention for a book binding template; 
           [0034]      FIG. 10A  is an exemplary imposition layout in accordance with this invention for a non-book binding template; 
           [0035]      FIG. 10B  is another exemplary imposition layout in accordance with this invention for a non-book binding template; 
           [0036]      FIG. 10C  is still another exemplary imposition layout in accordance with this invention for a non-book binding template; 
           [0037]      FIG. 10D  is yet another exemplary imposition layout in accordance with this invention for a non-book binding template; 
           [0038]      FIGS. 11A-11B  are exemplary modified imposition layouts in accordance with this invention corresponding to the imposition layouts of  FIGS. 9A-9B , respectively; and 
           [0039]      FIGS. 12A-12D  are exemplary modified imposition layouts in accordance with this invention corresponding to the imposition layouts of  FIGS. 10A-10D , respectively. 
       
    
    
     DETAILED DESCRIPTION 
       [0040]    Referring now to  FIG. 3 , an exemplary imposition system in accordance with this invention is described. Exemplary imposition system  40  includes imposition application  44 , which receives print file  42  and nominal imposition template  46 , and generates imposition flat  48  for printing. Imposition application  44  may be hardware and/or software that implements imposition processing in accordance with this invention, as described in more detail below. Print file  42  may be an electronic file that describes a print job in a page description language, such as portable document format (“PDF”), PostScript, page command language (“PCL”) or other similar page description language. Print file  42  includes a parameter that specifies finished page size (referred to herein as “actual page size” or “PS A ”). For example, if print file  42  includes letter-size pages, actual page size PS A =8.5″×11″. Alternatively, if print file  42  includes custom-size pages (e.g., 8″×12″), actual page size PS A =8″×12″. Persons of ordinary skill in the art will understand that other actual page sizes also may be used. 
         [0041]    Referring now to  FIG. 4 , an exemplary nominal imposition template  46  for use with imposition system  40  is described. In particular, nominal imposition template  46  may include a nominal layout description  50  and output parameters  52 . Nominal layout description  50  includes nominal pages  24  and mark objects  28 , and also may include binding edges  30  or center axes  32 , and their respective locations. Output parameters  52  include information describing various parameters used during printing and finishing of the print job. For example, output parameters  52  may include sheet size (e.g., 25″×19″), finished page size (referred to herein as “nominal page size” or “PS N ”) (e.g., 8.5″×11″), the number of rows and columns per sheet (e.g., 2 rows and 4 columns), binding style (e.g, perfect, saddle stitch) and work style (e.g., sheetwise, work and turn, work and tumble). Persons of ordinary skill in the art will understand that different or additional printing and finishing parameters may be included in output parameters  52 . 
         [0042]    Referring now to  FIGS. 5A and 5B , exemplary nominal layout descriptions  50   a  and  50   b , respectively, for use in nominal imposition template  46  are described. In particular, nominal layout description  50   a  illustrates an exemplary layout for a document that uses book binding, and nominal layout description  50   b  illustrates an exemplary layout for a document that uses a binding style other than book binding (e.g., gangup binding). Nominal layout description  50   a  includes binding edges  30 , and layout description  50   b  includes vertical and horizontal center axes  32   v  and  32   h , respectively. 
         [0043]    Each nominal page  24  may include associated mark objects  28 , such as bleed marks  28   a  and trim marks  28   b , a corresponding page location reference, such as a nominal page center (“PC N ”), and four page edges  58  (top, bottom, left and right). Each nominal page  24   a  in nominal layout description  50   a  also includes a page spine  56  that indicates the page edge  58  that will be bound during finishing. The separation between each page spine  56  and an adjacent binding edge  30  is designated as Δ s . In nominal layout description  50   b , the separation between vertical center axis  32   v  and an adjacent parallel page edge  58  is designated as Δ c , the horizontal separation between all other adjacent vertical page edges  58  is designated as Δ x , and the vertical separation between all other adjacent horizontal page edges  58  is designated as Δ y . 
         [0044]    For each page  24   a  and  24   b  in exemplary nominal layout descriptions  50   a  and  50   b , respectively, the locations of associated bleed marks  28   a  and trim marks  28   b  depend on nominal page size PS N . In this regard, bleed marks  28   a  and trim marks  28   b  are referred to herein as “page-dependent marks.” In contrast, the locations of registration marks  28   c  are not page-dependent, because their locations do not depend on page size. In accordance with this invention, imposition application  44  may be used to automatically modify imposition template  46  to accommodate a print file  42  whose actual page size PS A  does not match the nominal page size PS N  specified in nominal imposition template  46 . 
         [0045]    Referring now to  FIGS. 3 and 6 , an exemplary imposition process  60  implemented by imposition application  44  is described. In particular, beginning at step  62 , print file  42  is received. For example, a user may select print file  42  from a file directory via a graphical user interface (not shown) or other similar print file submission mechanism. Next, at step  64 , nominal imposition template  46  is received. For example, a user may select nominal imposition template  46  from a directory of previously-created imposition templates. At step  66 , actual page size PS A  is retrieved from print file  42 , and nominal page size PS N  is retrieved from nominal imposition template  46 . At step  68 , actual page size PS A  is compared to nominal page size PS N . For example, the width and height of PS A , referred to as PS A (width) and PS A  (height), respectively, may be compared to the corresponding parameters of nominal page size PS N , referred to as PS N (width) and PS N  (height), respectively. 
         [0046]    If actual page size PS A  equals nominal page size PS N  (i.e., if PS A (width)=PS N (width) and PS A  (height)=PS N  (height)), the process proceeds to step  72 , and nominal imposition template  46  is applied to print file  42  without change to create imposition flat  48 . If, however, actual page size PS A  does not equal nominal page size PS N  (e.g., if PS A (width) # PS N (width) or PS A  (height)≠PS N  (height)), the process proceeds to step  70 , wherein nominal imposition template  46  is automatically modified based on actual page size PS A  to create modified imposition template  46 ′. Modified imposition template  46 ′ includes the same number of pages and mark objects as nominal imposition template  46 , but the locations of actual pages  24 ′ and associated page-dependent mark objects  28  are modified based on actual page size PS A . Finally, at step  72 , the modified imposition template  46 ′ from step  70  is applied to print file  42  to create imposition flat  48 . 
         [0047]    Referring now to  FIG. 7 , an exemplary process  70  for automatically modifying nominal imposition template  46  is described. Beginning at step  74 , the location of the actual page center (“PC A ”) of each actual page  24 ′ is determined. As described in more detail below, the determination of the location of each actual page center PC A  depends on the binding style and finishing parameters specified in nominal imposition template  46 , and the actual page size PS A  specified in print file  42 . Next, at step  76 , for each actual page  24 ′, the locations of the associated page-dependent mark objects  28  are determined based on the location of the corresponding actual page center PC A  determined in step  74  and the actual page size PS A . Finally, at step  78 , nominal imposition template  46  is modified to position actual pages  24 ′ and their associated page-dependent mark objects  28  at the locations determined in steps  74  and  76 . 
         [0048]    As previously mentioned, the determination of the actual page center PC A  for each actual page  24 ′ depends on the binding style and finishing parameters specified in nominal imposition template  46 . In particular, if the specified binding style is book binding, a first process  74   a  may be used to determine the location of each actual page center PC A . Alternatively, if the specified binding style is anything other than book binding (e.g., gangup), a second process  74   b  may be used to determine the location of each actual page center PC A . Processes  74   a  and  74   b  each will be described in turn. 
         [0049]    Referring now to  FIGS. 8A and 9 , an exemplary process  74   a  is described for determining the location of each actual page center PC A  for a nominal imposition template  46  that specifies book binding. In particular,  FIG. 9A  illustrates an exemplary layout description  50   a   1  that includes vertical binding edges  30   v  and actual pages  24   a   1 ′, and  FIG. 9B  illustrates an exemplary layout description  50   a   2  that includes horizontal binding edge  30   h  and actual pages  24   a   2 ′. For illustrative purposes,  FIGS. 9A and 9B  also show corresponding nominal pages  24   a  and  24   b , respectively, and nominal page centers PC N (a) and PC N (b), respectively. For clarity, bleed marks  28   a  and trim marks  28   b  associated with pages  24   a  and  24   b  are not shown. 
         [0050]    Referring again to  FIG. 8A , beginning at step  80 , the spine-binding edge separation Δ s  is retrieved from nominal imposition template  46 . Next, at step  82 , one of binding edges  30  is selected for processing. At step  84 , a determination is made whether the selected binding edge  30  is vertical or horizontal. If the selected binding edge  30  is vertical, the process proceeds to step  86 , wherein for each actual page  24   a ′ adjacent to the selected binding edge  30   v , the y-coordinate of the actual page center PC A (a) is set to the y-coordinate of the corresponding nominal page center PC N (a). If, however, the selected binding edge  30  is horizontal, the process proceeds to step  88 , wherein for each actual page  24   a ′ adjacent to the selected binding edge  30   h , the x-coordinate of the actual page center PC A (a) is set to the x-coordinate of the corresponding nominal page center PC N (a). 
         [0051]    Next, at step  90 , for each actual page  24   a ′, the remaining coordinate (i.e., the x-coordinate if step  86  was used, or the y-coordinate if step  88  was used) of the corresponding actual page center PC A (a) is determined based on the location of the selected binding edge, the spine-binding edge separation Δ s  and the actual page size PS A . In this regard, the spine  56  of each actual page  24   a ″ is aligned to the spine  56  of the corresponding nominal page  24   a  to preserve spine-binding edge separation Δ s . At step  92 , a determination is made whether modified layout description  50   a ′ includes any more binding edges  30 . If so, at step  94 , a binding edge  30  is selected that has not yet been processed, and then the process returns to step  84  to process the new binding edge as described above. If, however, there are no additional binding edges  30 , the process terminates. 
         [0052]    Examples of the operation of steps  82 - 92  are now described using the exemplary layout description  50   a   1  and  50   a   2  illustrated in  FIGS. 9A and 9B , respectively. In particular, referring now to  FIGS. 8A and 9A , at step  82 , one of binding edges  30   v   1  and  30   v   2  is selected. For example, binding edge  30   v   1 , which is surrounded by adjacent actual pages  24   a   1a ″- 24   a   1d ″, may be selected. 
         [0053]    At step  84 , binding edge  30   v   1  is identified as vertical, and therefore the process proceeds to step  86 , wherein for each actual page  24   a   1a ″- 24   a   1d ″, the y-coordinate of the actual page center PC A (a 1a )-PC A (a 1d ), respectively, is set to the y-coordinate of the corresponding nominal page center PC N (a): 
         [0000]        PC   A ( a   1a ) y   =PC   N ( a   1a ) y   (1a)
 
         [0000]        PC   A ( a   1b ) y   =PC   N ( a   1b ) y   (1b)
 
         [0000]        PC   A ( a   1c ) y   =PC   N ( a   1c ) y   (1c)
 
         [0000]        PC   A ( a   1d ) y   =PC   N ( a   1d ) y   (1d)
 
         [0000]    where PC A (a 1a ) y  is the y-coordinate of PC A (a 1a ), PC N (a 1a ) y  is the y-coordinate of nominal page center PC N (a 1a ), and so on. 
         [0054]    Next, at step  90 , the x-coordinates of actual page centers PC A (a 1a )-PC A (a 1d ) are determined based on the locations of selected binding edge  30   v   1 , the spine-binding edge separation Δ s , and actual page size PS A . In this regard, the spine  56   1  of each actual page  24   a   1 ′ is aligned to the spine  56   1  of the corresponding nominal page  24   a   1  to preserve spine-binding edge separation Δ s . Thus, the x-coordinates of actual page centers PC A (a 1a )-PC A (a 1d ) are determined as follows: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         PC 
                         A 
                       
                        
                       
                         ( 
                         
                           a 
                           
                             1 
                              
                             
                                 
                             
                              
                             a 
                           
                         
                         ) 
                       
                     
                     x 
                   
                   = 
                   
                     
                       
                         
                           PC 
                           A 
                         
                          
                         
                           ( 
                           
                             a 
                             
                               1 
                                
                               
                                   
                               
                                
                               c 
                             
                           
                           ) 
                         
                       
                       x 
                     
                     = 
                     
                       
                         30 
                          
                         
                             
                         
                          
                         
                           v 
                           
                             1 
                              
                             
                                 
                             
                              
                             x 
                           
                         
                       
                       - 
                       
                         Δ 
                         s 
                       
                       - 
                       
                         
                           
                             PS 
                             A 
                           
                            
                           
                             ( 
                             width 
                             ) 
                           
                         
                         2 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     2 
                      
                     a 
                   
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         PC 
                         A 
                       
                        
                       
                         ( 
                         
                           a 
                           
                             1 
                              
                             
                                 
                             
                              
                             b 
                           
                         
                         ) 
                       
                     
                     x 
                   
                   = 
                   
                     
                       
                         
                           PC 
                           A 
                         
                          
                         
                           ( 
                           
                             a 
                             
                               1 
                                
                               
                                   
                               
                                
                               d 
                             
                           
                           ) 
                         
                       
                       x 
                     
                     = 
                     
                       
                         30 
                          
                         
                             
                         
                          
                         
                           v 
                           
                             1 
                              
                             
                                 
                             
                              
                             x 
                           
                         
                       
                       + 
                       
                         Δ 
                         s 
                       
                       + 
                       
                         
                           
                             PS 
                             A 
                           
                            
                           
                             ( 
                             width 
                             ) 
                           
                         
                         2 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     2 
                      
                     b 
                   
                   ) 
                 
               
             
           
         
       
     
         [0000]    where  30   v   1x  is the x-coordinate of binding edge  30   v   1 , and PS A (width) is the width of actual page size PS A . Thus, after completing step  90 , the x- and y-coordinates of each actual page center PC A (a 1a )-PC A (a 1d ) are known. Next, at step  92 , because layout description  50   a   1  includes an additional binding edge  30   v   2 , the process returns to step  84  to process binding edge  30   v   2 . 
         [0055]    Referring now to  FIGS. 8A and 9B , an example of process steps  82 - 92  is described using exemplary layout description  50   a   2 . Beginning at step  82 , binding edge  30   h , which is surrounded by adjacent actual pages  24   a   2a ′- 24   a   2d ′, is selected. Next, at step  84 , binding edge  30   h  is identified as horizontal, and therefore the process proceeds to step  88 , wherein for each actual page  24   a   2a ′- 24   a   2d ″, the x-coordinate of the actual page center PC A (a 2a )-PC A (a 2d ), respectively, is set to the x-coordinate of the corresponding nominal page center PC N (a): 
         [0000]        PC   A ( a   2a ) x   =PC   N ( a   2a ) x   (3a)
 
         [0000]        PC   A ( a   2b ) x   =PC   N ( a   2b ) x   (3b)
 
         [0000]        PC   A ( a   2c ) x   =PC   N ( a   2c ) x   (3c)
 
         [0000]        PC   A ( a   2d ) x   =PC   N ( a   2d ) x   (3d)
 
         [0000]    Next, at step  90 , the y-coordinates of actual page centers PC A (a 2a )-PC A (a 2d ) are determined based on the locations of selected binding edge  30   h , the spine-binding edge separation Δ s , and actual page size PS A . In this regard, the spine  56   2  of each actual page  24   a   2 ′ is aligned to the spine  56   2  of each corresponding nominal page  24   a   2  to preserve spine-binding edge separation Δ s . Thus, the y-coordinates of PC A (a 2a ) and PC A (a 2b ) are determined as follows: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         PC 
                         A 
                       
                        
                       
                         ( 
                         
                           a 
                           
                             2 
                              
                             
                                 
                             
                              
                             a 
                           
                         
                         ) 
                       
                     
                     y 
                   
                   = 
                   
                     
                       
                         
                           PC 
                           A 
                         
                          
                         
                           ( 
                           
                             a 
                             
                               2 
                                
                               
                                   
                               
                                
                               b 
                             
                           
                           ) 
                         
                       
                       y 
                     
                     = 
                     
                       
                         30 
                          
                         
                             
                         
                          
                         
                           h 
                           y 
                         
                       
                       + 
                       
                         Δ 
                         s 
                       
                       + 
                       
                         
                           
                             PS 
                             A 
                           
                            
                           
                             ( 
                             height 
                             ) 
                           
                         
                         2 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     4 
                      
                     a 
                   
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         PC 
                         A 
                       
                        
                       
                         ( 
                         
                           a 
                           
                             2 
                              
                             
                                 
                             
                              
                             c 
                           
                         
                         ) 
                       
                     
                     y 
                   
                   = 
                   
                     
                       
                         
                           PC 
                           A 
                         
                          
                         
                           ( 
                           
                             a 
                             
                               2 
                                
                               
                                   
                               
                                
                               d 
                             
                           
                           ) 
                         
                       
                       y 
                     
                     = 
                     
                       
                         30 
                          
                         
                             
                         
                          
                         hy 
                       
                       - 
                       
                         Δ 
                         s 
                       
                       - 
                       
                         
                           
                             PS 
                             A 
                           
                            
                           
                             ( 
                             height 
                             ) 
                           
                         
                         2 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     4 
                      
                     b 
                   
                   ) 
                 
               
             
           
         
       
     
         [0000]    where  30   h   y  is the y-coordinate of binding edge  30   h , and PS A (height) is the height of actual page size PS A . Therefore, after completing step  90 , the x- and y-coordinates of each actual page center PC A (a 2a )-PC A (a 2d ) are known. Next, at step  92 , because layout description  50   a   2  includes no more binding edges, the process terminates. 
         [0056]    Referring now to  FIGS. 8B and 10 , an exemplary process  74   b  is described for determining the location of each actual page center PC A  for a nominal imposition template  46  that specifies a binding style other than book binding (e.g., gangup). In particular,  FIGS. 10A-10D  illustrate various exemplary layout descriptions  50   b   1 ,  50   b   2 ,  50   b   3  and  50   b   4  that include actual pages  24   b   2 ′. For illustrative purposes,  FIGS. 10A-10D  also show corresponding nominal pages  24   b . For clarity, however, bleed marks  28   a , trim marks  28   b  and nominal page centers PC N  associated with pages  24   b  are not shown. 
         [0057]    Referring again to  FIG. 8B , beginning at step  100 , the center axis-page edge separation Δ c , the horizontal page separation Δ x , and the vertical page separation Δ y  are retrieved from nominal imposition template  46 . Next, at step  102 , for each actual page  24   b ″ located in the centermost rows and columns, the x- and y-coordinates of the actual page center PC A (b) are set to values that are centered symmetrically about vertical and horizontal center axes  32   v  and  32   h , respectively, while preserving center axis-page edge separation Δ c , horizontal page separation Δ x  and vertical page separation Δ y . Next, at step  104 , for all other actual pages  24   b ″, the x- and y-coordinates of the each actual page center PC A (b) are determined relative to the centermost actual pages  24   b ″, while preserving horizontal page separation Δ x  and vertical page separation Δ y . 
         [0058]    Examples of the operation of steps  102 - 104  are now described using the exemplary layout descriptions  50   b   1 - 50   b   4  illustrated in  FIGS. 10A-10D , respectively. In particular, referring now to  FIGS. 8B and 10A , actual pages  24   b   1a ″- 24   b   1h ″ are all located in the centermost rows and columns of layout description  50   b   1 . Thus, at step  102 , the x- and y-coordinates of actual page centers PC A (b 1a )-PC A (b 1h ), respectively, are set to values that are centered symmetrically about vertical and horizontal center axes  32   v  and  32   h , while preserving center axis-page edge separation Δ c , horizontal page separation Δ x  and vertical page separation Δ y , as follows: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         PC 
                         A 
                       
                        
                       
                         ( 
                         
                           b 
                           
                             1 
                              
                             
                                 
                             
                              
                             b 
                           
                         
                         ) 
                       
                     
                     x 
                   
                   = 
                   
                     
                       
                         
                           PC 
                           A 
                         
                          
                         
                           ( 
                           
                             b 
                             
                               1 
                                
                               
                                   
                               
                                
                               f 
                             
                           
                           ) 
                         
                       
                       x 
                     
                     = 
                     
                       
                         32 
                          
                         
                             
                         
                          
                         
                           v 
                           x 
                         
                       
                       - 
                       
                         Δ 
                          
                         
                             
                         
                          
                         c 
                       
                       - 
                       
                         
                           
                             PS 
                             A 
                           
                            
                           
                             ( 
                             width 
                             ) 
                           
                         
                         2 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     5 
                      
                     a 
                   
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         PC 
                         A 
                       
                        
                       
                         ( 
                         
                           b 
                           
                             1 
                              
                             
                                 
                             
                              
                             a 
                           
                         
                         ) 
                       
                     
                     x 
                   
                   = 
                   
                     
                       
                         
                           PC 
                           A 
                         
                          
                         
                           ( 
                           
                             b 
                             
                               1 
                                
                               
                                   
                               
                                
                               e 
                             
                           
                           ) 
                         
                       
                       x 
                     
                     = 
                     
                       
                         32 
                          
                         
                             
                         
                          
                         
                           v 
                           x 
                         
                       
                       - 
                       
                         Δ 
                          
                         
                             
                         
                          
                         c 
                       
                       - 
                       
                         Δ 
                          
                         
                             
                         
                          
                         x 
                       
                       - 
                       
                         
                           3 
                           2 
                         
                          
                         
                           [ 
                           
                             
                               PS 
                               A 
                             
                              
                             
                               ( 
                               width 
                               ) 
                             
                           
                           ] 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     5 
                      
                     
                         
                     
                      
                     b 
                   
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         
                           
                             
                               PC 
                               A 
                             
                              
                             
                               ( 
                               
                                 b 
                                 
                                   1 
                                    
                                   
                                       
                                   
                                    
                                   a 
                                 
                               
                               ) 
                             
                           
                           y 
                         
                         = 
                         
                           
                             
                               PC 
                               A 
                             
                              
                             
                               ( 
                               
                                 b 
                                 
                                   1 
                                    
                                   
                                       
                                   
                                    
                                   b 
                                 
                               
                               ) 
                             
                           
                           y 
                         
                       
                     
                   
                   
                     
                       
                         = 
                         
                           
                             
                               PC 
                               A 
                             
                              
                             
                               ( 
                               
                                 b 
                                 
                                   1 
                                    
                                   
                                       
                                   
                                    
                                   c 
                                 
                               
                               ) 
                             
                           
                           y 
                         
                       
                     
                   
                   
                     
                       
                         = 
                         
                           
                             
                               PC 
                               A 
                             
                              
                             
                               ( 
                               
                                 b 
                                 
                                   1 
                                    
                                   
                                       
                                   
                                    
                                   d 
                                 
                               
                               ) 
                             
                           
                           y 
                         
                       
                     
                   
                   
                     
                       
                         = 
                         
                           
                             32 
                              
                             
                                 
                             
                              
                             
                               h 
                               y 
                             
                           
                           + 
                           
                             
                               Δ 
                                
                               
                                   
                               
                                
                               y 
                             
                             2 
                           
                           + 
                           
                             
                               
                                 PS 
                                 A 
                               
                                
                               
                                 ( 
                                 height 
                                 ) 
                               
                             
                             2 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     5 
                      
                     c 
                   
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         PC 
                         A 
                       
                        
                       
                         ( 
                         
                           b 
                           
                             1 
                              
                             
                                 
                             
                              
                             c 
                           
                         
                         ) 
                       
                     
                     x 
                   
                   = 
                   
                     
                       
                         
                           PC 
                           A 
                         
                          
                         
                           ( 
                           
                             b 
                             
                               1 
                                
                               
                                   
                               
                                
                               g 
                             
                           
                           ) 
                         
                       
                       x 
                     
                     = 
                     
                       
                         32 
                          
                         
                             
                         
                          
                         
                           v 
                           x 
                         
                       
                       + 
                       
                         Δ 
                          
                         
                             
                         
                          
                         c 
                       
                       + 
                       
                         
                           
                             PS 
                             A 
                           
                            
                           
                             ( 
                             width 
                             ) 
                           
                         
                         2 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     5 
                      
                     d 
                   
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         PC 
                         A 
                       
                        
                       
                         ( 
                         
                           b 
                           
                             1 
                              
                             
                                 
                             
                              
                             d 
                           
                         
                         ) 
                       
                     
                     x 
                   
                   = 
                   
                     
                       
                         
                           PC 
                           A 
                         
                          
                         
                           ( 
                           
                             b 
                             
                               1 
                                
                               
                                   
                               
                                
                               h 
                             
                           
                           ) 
                         
                       
                       x 
                     
                     = 
                     
                       
                         32 
                          
                         
                             
                         
                          
                         
                           v 
                           x 
                         
                       
                       + 
                       
                         Δ 
                          
                         
                             
                         
                          
                         c 
                       
                       + 
                       
                         Δ 
                          
                         
                             
                         
                          
                         x 
                       
                       + 
                       
                         
                           3 
                           2 
                         
                          
                         
                           [ 
                           
                             
                               PS 
                               A 
                             
                              
                             
                               ( 
                               width 
                               ) 
                             
                           
                           ] 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     5 
                      
                     e 
                   
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         
                           
                             
                               PC 
                               A 
                             
                              
                             
                               ( 
                               
                                 b 
                                 
                                   1 
                                    
                                   
                                       
                                   
                                    
                                   e 
                                 
                               
                               ) 
                             
                           
                           y 
                         
                         = 
                         
                           
                             
                               PC 
                               A 
                             
                              
                             
                               ( 
                               
                                 b 
                                 
                                   1 
                                    
                                   
                                       
                                   
                                    
                                   f 
                                 
                               
                               ) 
                             
                           
                           y 
                         
                       
                     
                   
                   
                     
                       
                         = 
                         
                           
                             
                               PC 
                               A 
                             
                              
                             
                               ( 
                               
                                 b 
                                 
                                   1 
                                    
                                   
                                       
                                   
                                    
                                   g 
                                 
                               
                               ) 
                             
                           
                           y 
                         
                       
                     
                   
                   
                     
                       
                         = 
                         
                           
                             
                               PC 
                               A 
                             
                              
                             
                               ( 
                               
                                 b 
                                 
                                   1 
                                    
                                   
                                       
                                   
                                    
                                   h 
                                 
                               
                               ) 
                             
                           
                           y 
                         
                       
                     
                   
                   
                     
                       
                         = 
                         
                           
                             32 
                              
                             
                                 
                             
                              
                             
                               h 
                               y 
                             
                           
                           - 
                           
                             
                               Δ 
                                
                               
                                   
                               
                                
                               y 
                             
                             2 
                           
                           - 
                           
                             
                               
                                 PS 
                                 A 
                               
                                
                               
                                 ( 
                                 height 
                                 ) 
                               
                             
                             2 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     5 
                      
                     f 
                   
                   ) 
                 
               
             
           
         
       
     
         [0000]    where  32   v   x  is the x-coordinate of vertical center axis  32   v ,  32   h   y  is the y-coordinate of horizontal center axis  32   h , PS A (width) is the width of actual page size PS A , and PS A (height) is the height of actual page size PS A . Referring again to  FIG. 8B , at step  104 , because there are no remaining actual pages  24   b   1 ″, process  74   b  terminates. 
         [0059]    Referring now to  FIGS. 8A and 10B , exemplary process steps  102 - 104  are described using the exemplary layout description  50   b   2 , in which actual pages  24   b   2a ′- 24   b   2f ′ are all located in the centermost rows and columns. Thus, at step  102 , the x- and y-coordinates of corresponding actual page centers PC A (b 2a )-PC A (b 2f ) are set to values that are centered symmetrically about vertical and horizontal center axes  32   v  and  32   h , while preserving center axis-page edge separation Δ b  (which is zero in this instance), horizontal page separation Δ X  and vertical page separation Δ y , as follows: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         PC 
                         A 
                       
                        
                       
                         ( 
                         
                           b 
                           
                             2 
                              
                             
                                 
                             
                              
                             a 
                           
                         
                         ) 
                       
                     
                     x 
                   
                   = 
                   
                     
                       
                         
                           PC 
                           A 
                         
                          
                         
                           ( 
                           
                             b 
                             
                               2 
                                
                               
                                   
                               
                                
                               d 
                             
                           
                           ) 
                         
                       
                       x 
                     
                     = 
                     
                       
                         32 
                          
                         
                             
                         
                          
                         
                           v 
                           x 
                         
                       
                       - 
                       
                         Δ 
                          
                         
                             
                         
                          
                         x 
                       
                       - 
                       
                         
                           PS 
                           A 
                         
                          
                         
                           ( 
                           width 
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     6 
                      
                     a 
                   
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         
                           
                             
                               PC 
                               A 
                             
                              
                             
                               ( 
                               
                                 b 
                                 
                                   2 
                                    
                                   
                                       
                                   
                                    
                                   a 
                                 
                               
                               ) 
                             
                           
                           y 
                         
                         = 
                         
                           
                             
                               PC 
                               A 
                             
                              
                             
                               ( 
                               
                                 b 
                                 
                                   2 
                                    
                                   
                                       
                                   
                                    
                                   b 
                                 
                               
                               ) 
                             
                           
                           y 
                         
                       
                     
                   
                   
                     
                       
                         = 
                         
                           
                             
                               PC 
                               A 
                             
                              
                             
                               ( 
                               
                                 b 
                                 
                                   2 
                                    
                                   
                                       
                                   
                                    
                                   c 
                                 
                               
                               ) 
                             
                           
                           y 
                         
                       
                     
                   
                   
                     
                       
                         = 
                         
                           
                             32 
                              
                             
                                 
                             
                              
                             
                               h 
                               y 
                             
                           
                           + 
                           
                             
                               Δ 
                                
                               
                                   
                               
                                
                               y 
                             
                             2 
                           
                           + 
                           
                             
                               
                                 PS 
                                 A 
                               
                                
                               
                                 ( 
                                 height 
                                 ) 
                               
                             
                             2 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     6 
                      
                     
                         
                     
                      
                     b 
                   
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         PC 
                         A 
                       
                        
                       
                         ( 
                         
                           b 
                           
                             2 
                              
                             
                                 
                             
                              
                             b 
                           
                         
                         ) 
                       
                     
                     x 
                   
                   = 
                   
                     
                       
                         
                           PC 
                           A 
                         
                          
                         
                           ( 
                           
                             b 
                             
                               2 
                                
                               
                                   
                               
                                
                               e 
                             
                           
                           ) 
                         
                       
                       x 
                     
                     = 
                     
                       32 
                        
                       
                           
                       
                        
                       
                         v 
                         x 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     6 
                      
                     c 
                   
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         
                           
                             
                               PC 
                               A 
                             
                              
                             
                               ( 
                               
                                 b 
                                 
                                   2 
                                    
                                   
                                       
                                   
                                    
                                   d 
                                 
                               
                               ) 
                             
                           
                           y 
                         
                         = 
                         
                           
                             
                               PC 
                               A 
                             
                              
                             
                               ( 
                               
                                 b 
                                 
                                   2 
                                    
                                   
                                       
                                   
                                    
                                   e 
                                 
                               
                               ) 
                             
                           
                           y 
                         
                       
                     
                   
                   
                     
                       
                         = 
                         
                           
                             
                               PC 
                               A 
                             
                              
                             
                               ( 
                               
                                 b 
                                 
                                   2 
                                    
                                   
                                       
                                   
                                    
                                   f 
                                 
                               
                               ) 
                             
                           
                           y 
                         
                       
                     
                   
                   
                     
                       
                         = 
                         
                           
                             32 
                              
                             
                                 
                             
                              
                             
                               h 
                               y 
                             
                           
                           - 
                           
                             
                               Δ 
                                
                               
                                   
                               
                                
                               y 
                             
                             2 
                           
                           - 
                           
                             
                               
                                 PS 
                                 A 
                               
                                
                               
                                 ( 
                                 height 
                                 ) 
                               
                             
                             2 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     6 
                      
                     d 
                   
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         PC 
                         A 
                       
                        
                       
                         ( 
                         
                           b 
                           
                             2 
                              
                             
                                 
                             
                              
                             c 
                           
                         
                         ) 
                       
                     
                     x 
                   
                   = 
                   
                     
                       
                         
                           PC 
                           A 
                         
                          
                         
                           ( 
                           
                             b 
                             
                               2 
                                
                               
                                   
                               
                                
                               f 
                             
                           
                           ) 
                         
                       
                       x 
                     
                     = 
                     
                       
                         32 
                          
                         
                             
                         
                          
                         
                           v 
                           x 
                         
                       
                       + 
                       
                         Δ 
                          
                         
                             
                         
                          
                         x 
                       
                       + 
                       
                         
                           PS 
                           A 
                         
                          
                         
                           ( 
                           width 
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     6 
                      
                     e 
                   
                   ) 
                 
               
             
           
         
       
     
         [0060]    Referring again to  FIG. 8B , at step  104 , because there are no remaining actual pages  24   b   2 ′, process  74   b  terminates. 
         [0061]    Referring now to  FIGS. 8B and 10C , exemplary process steps  102 - 104  are described using the exemplary layout description  50   b   3 , in which actual pages  24   b   3b ′,  24   b   3c ′,  24   b   3e ′,  24   b   3f ′,  24   b   3g ′,  24   b   3h ′,  24   b   3j  and  24   b   3k ′ are all located in the centermost rows and columns. Thus, at step  102 , the x- and y-coordinates of corresponding actual page centers PC A (b 3b ), PC A (b 3c ), PC A (b 3e ), PC A (b 3f ), PC A (b 3g ), PC A (b 3h ), PC A (b 3j ) and PC A (b 3k ) are set to values that are centered symmetrically about vertical and horizontal center axes  32   v  and  32   h , respectively, while preserving center axis-page edge separation Δ b , horizontal page separation Δ X  and vertical page separation Δ y , as follows: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             
                               PC 
                               A 
                             
                              
                             
                               ( 
                               
                                 b 
                                 
                                   3 
                                    
                                   
                                       
                                   
                                    
                                   b 
                                 
                               
                               ) 
                             
                           
                           x 
                         
                         = 
                         
                           
                             
                               PC 
                               A 
                             
                              
                             
                               ( 
                               
                                 b 
                                 
                                   3 
                                    
                                   
                                       
                                   
                                    
                                   f 
                                 
                               
                               ) 
                             
                           
                           x 
                         
                       
                     
                   
                   
                     
                       
                         = 
                         
                           
                             
                               PC 
                               A 
                             
                              
                             
                               ( 
                               
                                 b 
                                 
                                   3 
                                    
                                   
                                       
                                   
                                    
                                   j 
                                 
                               
                               ) 
                             
                           
                           x 
                         
                       
                     
                   
                   
                     
                       
                         = 
                         
                           
                             32 
                              
                             
                                 
                             
                              
                             
                               v 
                               x 
                             
                           
                           - 
                           
                             Δ 
                              
                             
                                 
                             
                              
                             c 
                           
                           - 
                           
                             
                               
                                 PS 
                                 A 
                               
                                
                               
                                 ( 
                                 width 
                                 ) 
                               
                             
                             2 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     7 
                      
                     a 
                   
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         PC 
                         A 
                       
                        
                       
                         ( 
                         
                           b 
                           
                             3 
                              
                             
                                 
                             
                              
                             b 
                           
                         
                         ) 
                       
                     
                     y 
                   
                   = 
                   
                     
                       
                         
                           PC 
                           A 
                         
                          
                         
                           ( 
                           
                             b 
                             
                               3 
                                
                               
                                   
                               
                                
                               c 
                             
                           
                           ) 
                         
                       
                       y 
                     
                     = 
                     
                       
                         32 
                          
                         
                             
                         
                          
                         
                           h 
                           y 
                         
                       
                       + 
                       
                         Δ 
                          
                         
                             
                         
                          
                         y 
                       
                       + 
                       
                         
                           PS 
                           A 
                         
                          
                         
                           ( 
                           height 
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     7 
                      
                     b 
                   
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         
                           
                             
                               PC 
                               A 
                             
                              
                             
                               ( 
                               
                                 b 
                                 
                                   3 
                                    
                                   
                                       
                                   
                                    
                                   c 
                                 
                               
                               ) 
                             
                           
                           x 
                         
                         = 
                         
                           
                             
                               PC 
                               A 
                             
                              
                             
                               ( 
                               
                                 b 
                                 
                                   3 
                                    
                                   
                                       
                                   
                                    
                                   g 
                                 
                               
                               ) 
                             
                           
                           x 
                         
                       
                     
                   
                   
                     
                       
                         = 
                         
                           
                             
                               PC 
                               A 
                             
                              
                             
                               ( 
                               
                                 b 
                                 
                                   3 
                                    
                                   
                                       
                                   
                                    
                                   k 
                                 
                               
                               ) 
                             
                           
                           x 
                         
                       
                     
                   
                   
                     
                       
                         = 
                         
                           
                             32 
                              
                             
                                 
                             
                              
                             
                               v 
                               x 
                             
                           
                           + 
                           
                             Δ 
                              
                             
                                 
                             
                              
                             c 
                           
                           + 
                           
                             
                               
                                 PS 
                                 A 
                               
                                
                               
                                 ( 
                                 width 
                                 ) 
                               
                             
                             2 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     7 
                      
                     c 
                   
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         PC 
                         A 
                       
                        
                       
                         ( 
                         
                           b 
                           
                             3 
                              
                             
                                 
                             
                              
                             e 
                           
                         
                         ) 
                       
                     
                     y 
                   
                   = 
                   
                     
                       
                         
                           PC 
                           A 
                         
                          
                         
                           ( 
                           
                             b 
                             
                               3 
                                
                               
                                   
                               
                                
                               f 
                             
                           
                           ) 
                         
                       
                       y 
                     
                     = 
                     
                       
                         
                           
                             PC 
                             A 
                           
                            
                           
                             ( 
                             
                               b 
                               
                                 3 
                                  
                                 
                                     
                                 
                                  
                                 g 
                               
                             
                             ) 
                           
                         
                         y 
                       
                       = 
                       
                         
                           
                             PC 
                             A 
                           
                            
                           
                             ( 
                             
                               b 
                               
                                 3 
                                  
                                 
                                     
                                 
                                  
                                 h 
                               
                             
                             ) 
                           
                         
                         = 
                         
                           32 
                            
                           
                               
                           
                            
                           
                             h 
                             y 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     7 
                      
                     d 
                   
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         PC 
                         A 
                       
                        
                       
                         ( 
                         
                           b 
                           
                             3 
                              
                             
                                 
                             
                              
                             e 
                           
                         
                         ) 
                       
                     
                      
                     x 
                   
                   = 
                   
                     
                       32 
                        
                       
                           
                       
                        
                       
                         v 
                         x 
                       
                     
                     - 
                     
                       Δ 
                        
                       
                           
                       
                        
                       c 
                     
                     - 
                     
                       Δ 
                        
                       
                           
                       
                        
                       x 
                     
                     - 
                     
                       
                         3 
                         2 
                       
                        
                       
                         [ 
                         
                           
                             PS 
                             A 
                           
                            
                           
                             ( 
                             width 
                             ) 
                           
                         
                         ] 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     7 
                      
                     e 
                   
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         PC 
                         A 
                       
                        
                       
                         ( 
                         
                           b 
                           
                             3 
                              
                             
                                 
                             
                              
                             h 
                           
                         
                         ) 
                       
                     
                      
                     x 
                   
                   = 
                   
                     
                       32 
                        
                       
                           
                       
                        
                       
                         v 
                         x 
                       
                     
                     + 
                     
                       Δ 
                        
                       
                           
                       
                        
                       c 
                     
                     + 
                     
                       Δ 
                        
                       
                           
                       
                        
                       x 
                     
                     + 
                     
                       
                         3 
                         2 
                       
                        
                       
                         [ 
                         
                           
                             PS 
                             A 
                           
                            
                           
                             ( 
                             width 
                             ) 
                           
                         
                         ] 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     7 
                      
                     f 
                   
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         PC 
                         A 
                       
                        
                       
                         ( 
                         
                           b 
                           
                             3 
                              
                             
                                 
                             
                              
                             j 
                           
                         
                         ) 
                       
                     
                     y 
                   
                   = 
                   
                     
                       
                         
                           PC 
                           A 
                         
                          
                         
                           ( 
                           
                             b 
                             
                               3 
                                
                               
                                   
                               
                                
                               k 
                             
                           
                           ) 
                         
                       
                        
                       y 
                     
                     = 
                     
                       
                         32 
                          
                         
                             
                         
                          
                         
                           h 
                           y 
                         
                       
                       - 
                       
                         Δ 
                          
                         
                             
                         
                          
                         y 
                       
                       - 
                       
                         
                           PS 
                           A 
                         
                          
                         
                           ( 
                           height 
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     7 
                      
                     g 
                   
                   ) 
                 
               
             
           
         
       
     
         [0062]    Referring again to  FIG. 8B , at step  104 , for remaining actual pages  24   b   3a ′,  24   b   3d ′,  24   b   3i ′ and  24   b   31 , the x- and y-coordinates of corresponding actual page centers PC A (b 3a ), PC A (b 3d ), PC A (b 3i ) and PC A (b 3l ) are determined relative to centermost actual pages  24   b   3b ″,  24   b   3c %  24   b   3e ′,  24   b   3f ″,  24   b   3g ″,  24   b   3h ″,  24   b   3j ′ and  24   b   3k ″, while preserving horizontal page separation Δ x  and vertical page separation Δ y , as follows: 
         [0000]        PC   A ( b   3a ) x   =PC   A ( b   3i ) x   =PC   A ( b   3b ) x −Δ x   −PS   A (width)  (8a)
 
         [0000]        PC   A ( b   3a ) y   =PC   A ( b   3d ) y   =PC   A ( b   3e ) y +Δ y   +PS   A (height)  (8b)
 
         [0000]        PC   A ( b   3d ) x   =PC   A ( b   3l ) x   =PC   A ( b   3c ) x +Δ x   +PS   A (width)  (8c)
 
         [0000]        PC   A ( b   3i ) y   =PC   A ( b   3l ) y   =PC   A ( b   3e ) y −Δ y   −PS   A (width)  (8d)
 
         [0063]    Process  74   b  then terminates. 
         [0064]    Referring now to  FIGS. 8B and 10D , another example of process steps  102 - 104  will be described using the exemplary layout description  50   b   4 , in which actual pages  24   b   4b ′,  24   b   4d ′,  24   b   4f ″ and  24   b   4h ′ are all located in the centermost rows and columns. Thus, at step  102 , the x- and y-coordinates of corresponding actual page centers PC A (b 4b ), PC A (b 4d ), PC A (b 4e ), PC A (b 4f ) and PC A (b 4h ) are set to values that are centered symmetrically about vertical and horizontal center axes  32   v  and  32   h , respectively, while preserving center axis-page edge separation Δ c  (which is zero in this instance), horizontal page separation Δ x  and vertical page separation Δ y , as follows: 
         [0000]        PC   A ( b   4b ) x   =PC   A ( b   4e ) x   =PC   A ( b   4h ) x =32 v   x   (9a)
 
         [0000]        PC   A ( b   4b ) y =32 h   y   +Δy+PS   A (height)  (9b)
 
         [0000]        PC   A ( b   4d ) x =32 v   x   −Δx−PS   A (width)  (9c)
 
         [0000]        PC   A ( b   4d ) y   =PC   A ( b   4e ) y   =PC   A ( b   4   f ) y =32 h   y   (9d)
 
         [0000]        PC   A ( b   4f ) x =32 v   z +Δ x   +PS   A (width)  (9e)
 
         [0000]        PC   A ( b   4h ) y =32 h   y −Δ y   −PS   A (height)  (9f)
 
         [0065]    Next, at step  104 , for remaining actual pages  24   b   4a ″,  24   b   4c ″,  24   b   4g ″ and  24   b   4i , the x- and y-coordinates of corresponding actual page centers PC A (b 4a ), PC A (b 4c ), PC A (b 4g ) and PC A (b 4i ) are determined relative to centermost actual pages  24   b   4b ″,  24   b   4d ′,  24   b   4e ′,  24   b   4f ′ and  24   b   4h ′, while preserving horizontal page separation Δ x  and vertical page separation Δ y , as follows: 
         [0000]        PC   A ( b   4a ) x   =PC   A ( b   4g ) x   =PC   A ( b   4b )−Δ x   −PS   A (width)  (10a)
 
         [0000]        PC   A ( b   4a ) y   =PC   A ( b   4c ) y   =PC   A ( b   4d ) y +Δ y   +PS   A (height)  (10b)
 
         [0000]        PC   A ( b   4c ) x   =PC   A ( b   4i ) x   =PC   A ( b   4b ) x +Δ x   PS   A (width)  (10c)
 
         [0000]        PC   A ( b   4g ) y   =PC   A ( b   4i ) y   =PC   A ( bd ) y −Δ y   −PS   A (height)  (10d)
 
         [0066]    Process  74   b  then terminates. 
         [0067]    Referring again to  FIG. 7 , at the completion of step  74 , the location of the actual page center PC A  of each actual page  24 ′ has been determined. Next, at step  76 , the locations of page-dependent marks  28 ′ associated with each actual page  24 ′ are determined based on the actual page size PS A  and actual page center PC A . Persons of ordinary skill in the art will understand that any suitable technique may be used to determine such locations. Finally, at step  78 , nominal imposition template  46  is modified by locating actual pages  24 ′ and associated page-dependent marks  28 ′ at the locations determined in steps  74  and  76 . In this regard, nominal pages  24  and associated page-dependent mark objects  28  may be deleted from nominal imposition template  46  and actual pages  24 ′ and associated page-dependent marks  28 ′ may be added to nominal imposition template  46 , or nominal pages  24  and associated page-dependent mark objects  28  may be resized and repositioned as actual pages  24 ′ and associated page-dependent marks  28 ′. 
         [0068]    Exemplary modified imposition layouts  50   a   1 ′ and  50   a   2 ′ including actual pages  24   a   1a ′- 24   a   1d ′ and  24   a   2a ′- 24   a   2d ′, respectively, and their associated page-dependent mark objects  28 ′, are illustrated in  FIGS. 11A and 11B , respectively. Likewise, exemplary modified imposition layouts  50   b   1 ″,  50   b   2 ″,  50   b   3 ″ and  50   b   4 ′, including actual pages  24   b   1a ″- 24   b   1h ″,  24   b   2a ″- 24   b   2f ″,  24   b   3a ′- 24   b   31 ″ and  24   b   4a ″- 24   b   4i ′, respectively, and their associated page-dependent mark objects  28 ′, are illustrated in  FIGS. 12A-12D , respectively. 
         [0069]    The foregoing merely illustrates the principles of this invention, and various modifications can be made by persons of ordinary skill in the art without departing from the scope and spirit of this invention.