Difference between revisions of "Example:compound nomograph 1"

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(→‎Compound nomograph example 1)
(→‎Source code of simple compound nomograph example)
 
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In this example we construct compound nomograph of equation
 
In this example we construct compound nomograph of equation
  
−
<math>\frac{A+B}{E}=\frac{F}{CD} \,</math>
+
<math>\frac{A+B}{E}=\frac{F}{CD}. \,</math>
  
−
just as an example. The equation is split into three equations that each are blocks:
+
The equation is split into three equations that each are blocks:
  
−
<math>A+B=R_1 \,</math>
+
{| style="background:wihte; color:black" border="1" cellpadding="5" cellspacing="0"
 +
|-
 +
| <math>A+B=R_1 \,\,\,\,\,\,\,</math> || [[type 1]]
 +
|-
 +
| <math>CD=R_2 \,\,\,\,\,\,\,</math> || [[type 2]]
 +
|-
 +
| <math>\frac{R_1}{E}= \frac{F}{R_2} \,\,\,\,\,\,\,</math> || [[type 4]]
 +
|}
  
−
<math>CD=R_2 \,</math>
 
  
−
<math>\frac{R_1}{E}= \frac{F}{R_2} \,</math>
+
It is iterative process in practice with PyNomo to construct compound nomographs.
 +
One should generate nomographs and iteratively correct for example block mirroring and axis
 +
tick sides, levels and title positions. The following is an example of final result after some
 +
ten iterations. Note the 'tag' key that defines how blocks aling with respect to each other.
 +
User has to take care that aligned scalings are really equal between blocks. Best practice
 +
may be to print in early iterations the scalings and check they are equal.
  
 
== Simple example ==
 
== Simple example ==
 
{{Infobox_nomogram1
 
{{Infobox_nomogram1
−
| name        = Simple example: Type 1  
+
| name        = Compound nomograph: example 1  
−
| image =  [[Image:Ex type1 nomo 1.png|600px]]
+
| image =  [[Image:Ex compound nomo 1.png|600px]]
−
| file = [http://nomography.org/wiki/images/a/ac/Ex_type1_nomo_1.pdf Ex_type1_nomo_1.pdf]
+
| file = [[Image:Ex compound nomo 1.pdf]]
 
}}
 
}}
−
==== Source code of simple example of type 1 ====
+
==== Source code of simple compound nomograph example ====
 
<source lang=python>
 
<source lang=python>
 
"""
 
"""
−
     ex_type1_nomo_1.py
+
     ex_compound_nomo_1.py
  
−
     Simple nomogram of type 1: F1+F2+F3=0
+
     Compound nomograph: (A+B)/E=F/(CD)
  
−
     Copyright (C) 2007-2008 Leif Roschier
+
     Copyright (C) 2007-2009 Leif Roschier
  
 
     This program is free software: you can redistribute it and/or modify
 
     This program is free software: you can redistribute it and/or modify
Line 40: Line 51:
 
     along with this program.  If not, see <http://www.gnu.org/licenses/>.
 
     along with this program.  If not, see <http://www.gnu.org/licenses/>.
 
"""
 
"""
−
from nomographer import *
+
from pynomo.nomographer import *
  
−
N_params_1={
+
# type 1
 +
A_params={
 
         'u_min':0.0,
 
         'u_min':0.0,
 
         'u_max':10.0,
 
         'u_max':10.0,
 
         'function':lambda u:u,
 
         'function':lambda u:u,
−
         'title':r'$u_2$',
+
         'title':r'$A$',
 
         'tick_levels':2,
 
         'tick_levels':2,
 
         'tick_text_levels':1,
 
         'tick_text_levels':1,
 
                 }
 
                 }
  
−
N_params_2={
+
B_params={
 
         'u_min':0.0,
 
         'u_min':0.0,
 
         'u_max':10.0,
 
         'u_max':10.0,
 
         'function':lambda u:u,
 
         'function':lambda u:u,
−
         'title':r'$u_2$',
+
         'title':r'$B$',
 
         'tick_levels':2,
 
         'tick_levels':2,
 
         'tick_text_levels':1,
 
         'tick_text_levels':1,
 
                 }
 
                 }
  
−
N_params_3={
+
R1a_params={
 
         'u_min':0.0,
 
         'u_min':0.0,
−
         'u_max':-10.0,
+
         'u_max':10.0,
 +
        'function':lambda u:-u,
 +
        'title':'',
 +
        'tick_levels':0,
 +
        'tick_text_levels':0,
 +
        'tag':'r1'
 +
                }
 +
block_1_params={
 +
            'block_type':'type_1',
 +
            'width':10.0,
 +
            'height':10.0,
 +
            'f1_params':A_params,
 +
            'f2_params':B_params,
 +
            'f3_params':R1a_params,
 +
            'isopleth_values':[[1,7,'x']]
 +
            }
 +
# type 4
 +
R1b_params={
 +
        'u_min':1.0,
 +
        'u_max':10.0,
 
         'function':lambda u:u,
 
         'function':lambda u:u,
−
         'title':r'$u_3$',
+
         'title':r'$R_1$',
−
         'tick_levels':2,
+
         'tick_levels':0,
 +
        'tick_text_levels':0,
 +
        'tick_side':'right',
 +
        'title_draw_center':True,
 +
        'title_opposite_tick':False,
 +
        'tag':'r1'
 +
                }
 +
E_params={
 +
        'u_min':1.0,
 +
        'u_max':10.0,
 +
        'function':lambda u:u,
 +
        'title':r'$E$',
 +
        'tick_levels':3,
 
         'tick_text_levels':1,
 
         'tick_text_levels':1,
 +
        'tick_side':'right',
 +
        'title_draw_center':True,
 +
        'title_opposite_tick':False,
 +
                }
 +
F_params={
 +
        'u_min':1.0,
 +
        'u_max':10.0,
 +
        'function':lambda u:u,
 +
        'title':r'$F$',
 +
        'tick_levels':3,
 +
        'tick_text_levels':1,
 +
        'tick_side':'left',
 +
        'title_draw_center':True,
 +
        'title_opposite_tick':True,
 +
                }
 +
R2a_params={
 +
        'u_min':1.0,
 +
        'u_max':10.0,
 +
        'function':lambda u:u,
 +
        'title':r'$R_2$',
 +
        'tick_levels':0,
 +
        'tick_text_levels':0,
 +
        'tick_side':'left',
 +
        'title_draw_center':True,
 +
        'title_opposite_tick':False,
 +
        'tag':'r2'
 
                 }
 
                 }
  
 +
block_2_params={
 +
                'block_type':'type_4',
 +
                'f1_params':R1b_params,
 +
                'f2_params':E_params,
 +
                'f3_params':F_params,
 +
                'f4_params':R2a_params,
 +
                'mirror_x':True,
 +
                'isopleth_values':[['x',9,4,'x']]
 +
                            }
 +
# type 2 N
 +
R2b_params={
 +
        'u_min':0.0,
 +
        'u_max':10.0,
 +
        'function':lambda u:u,
 +
        'title':r'$$',
 +
        'tick_levels':0,
 +
        'tick_text_levels':0,
 +
        'tag':'r2'
 +
                }
  
−
block_1_params={
+
C_params={
−
             'block_type':'type_1',
+
        'u_min':0.5,
 +
        'u_max':5.0,
 +
        'function':lambda u:u,
 +
        'title':r'$C$',
 +
        'tick_levels':3,
 +
        'tick_text_levels':1,
 +
        'tick_side':'left',
 +
        'scale_type':'linear smart',
 +
                }
 +
 
 +
D_params={
 +
        'u_min':1.0,
 +
        'u_max':10.0,
 +
        'function':lambda u:u,
 +
        'title':r'$D$',
 +
        'tick_levels':3,
 +
        'tick_text_levels':1,
 +
                }
 +
 
 +
block_3_params={
 +
             'block_type':'type_2',
 
             'width':10.0,
 
             'width':10.0,
 
             'height':10.0,
 
             'height':10.0,
−
             'f1_params':N_params_1,
+
             'f1_params':R2b_params,
−
             'f2_params':N_params_2,
+
             'f2_params':C_params,
−
             'f3_params':N_params_3,
+
             'f3_params':D_params,
 +
            'mirror_y':True,
 +
            'isopleth_values':[['x',1,'x']]
 
             }
 
             }
  
 
main_params={
 
main_params={
−
               'filename':'ex_type1_nomo_1.pdf',
+
               'filename':'ex_compound_nomo_1.pdf',
 
               'paper_height':10.0,
 
               'paper_height':10.0,
 
               'paper_width':10.0,
 
               'paper_width':10.0,
−
               'block_params':[block_1_params],
+
               'block_params':[block_1_params,block_2_params,block_3_params],
 
               'transformations':[('rotate',0.01),('scale paper',)],
 
               'transformations':[('rotate',0.01),('scale paper',)],
−
              'title_str':r'$u_1+u_2+u_3=0$'
 
 
               }
 
               }
 
Nomographer(main_params)
 
Nomographer(main_params)
−
</source>
 
−
 
−
== Parameters for type 1 ==
 
  
  
−
 
+
</source>
−
==== Axis parameters ====
+
−
{{Infobox_test1
+
−
| name = Specific axis parameters for type 1
+
−
| Field1a = 'function'
+
−
| Field1b = -
+
−
| Field1c = Function in the equation
+
−
 
+
−
| Field2a = 'u_min'
+
−
| Field2b = -
+
−
| Field2c = Minimum value of function variable
+
−
 
+
−
| Field3a = 'u_max'
+
−
| Field3b = -
+
−
| Field3c = Maximum value of function variable
+
−
}}
+
−
{{Axis_params}}
+
−
 
+
−
==== Block parameters ====
+
−
{{Infobox_test1
+
−
| name = Specific block parameters for type 1
+
−
| Field1a = 'block_type'
+
−
| Field1b = 'type_1'
+
−
| Field1c = This is type 1 block
+
−
 
+
−
| Field2a = 'width'
+
−
| Field2b = 10.0
+
−
| Field2c = Block width (to be scaled)
+
−
 
+
−
| Field3a = 'height'
+
−
| Field3b = 10.0
+
−
| Field3c = Block height (to be scaled)
+
−
 
+
−
| Field4a = 'f1_params'
+
−
| Field4b = --
+
−
| Field4c = Axis params for function f1
+
−
 
+
−
| Field5a = 'f2_params'
+
−
| Field5b = --
+
−
| Field5c = Axis params for function f2
+
−
 
+
−
| Field6a = 'f3_params'
+
−
| Field6b = --
+
−
| Field6c = Axis params for function f3
+
−
 
+
−
| Field7a = 'mirror_x'
+
−
| Field7b = False
+
−
| Field7c = If x-axis is mirrored
+
−
 
+
−
| Field8a = 'mirror_y'
+
−
| Field8b = False
+
−
| Field8c = If y-axis is mirrored
+
−
}}
+
−
==== General main parameters  ====
+
−
{{Infobox general params}}
+

Latest revision as of 19:12, 21 October 2009

Compound nomograph example 1

In this example we construct compound nomograph of equation

[math]\frac{A+B}{E}=\frac{F}{CD}. \,[/math]

The equation is split into three equations that each are blocks:

[math]A+B=R_1 \,\,\,\,\,\,\,[/math] type 1
[math]CD=R_2 \,\,\,\,\,\,\,[/math] type 2
[math]\frac{R_1}{E}= \frac{F}{R_2} \,\,\,\,\,\,\,[/math] type 4


It is iterative process in practice with PyNomo to construct compound nomographs. One should generate nomographs and iteratively correct for example block mirroring and axis tick sides, levels and title positions. The following is an example of final result after some ten iterations. Note the 'tag' key that defines how blocks aling with respect to each other. User has to take care that aligned scalings are really equal between blocks. Best practice may be to print in early iterations the scalings and check they are equal.

Simple example

Compound nomograph: example 1
Ex compound nomo 1.png
Generated portable document file (pdf): File:Ex compound nomo 1.pdf

Source code of simple compound nomograph example

"""
    ex_compound_nomo_1.py
 
    Compound nomograph: (A+B)/E=F/(CD)
 
    Copyright (C) 2007-2009  Leif Roschier
 
    This program is free software: you can redistribute it and/or modify
    it under the terms of the GNU General Public License as published by
    the Free Software Foundation, either version 3 of the License, or
    (at your option) any later version.
 
    This program is distributed in the hope that it will be useful,
    but WITHOUT ANY WARRANTY; without even the implied warranty of
    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
    GNU General Public License for more details.
 
    You should have received a copy of the GNU General Public License
    along with this program.  If not, see <http://www.gnu.org/licenses/>.
"""
from pynomo.nomographer import *
 
# type 1
A_params={
        'u_min':0.0,
        'u_max':10.0,
        'function':lambda u:u,
        'title':r'$A$',
        'tick_levels':2,
        'tick_text_levels':1,
                }
 
B_params={
        'u_min':0.0,
        'u_max':10.0,
        'function':lambda u:u,
        'title':r'$B$',
        'tick_levels':2,
        'tick_text_levels':1,
                }
 
R1a_params={
        'u_min':0.0,
        'u_max':10.0,
        'function':lambda u:-u,
        'title':'',
        'tick_levels':0,
        'tick_text_levels':0,
        'tag':'r1'
                }
block_1_params={
             'block_type':'type_1',
             'width':10.0,
             'height':10.0,
             'f1_params':A_params,
             'f2_params':B_params,
             'f3_params':R1a_params,
             'isopleth_values':[[1,7,'x']]
             }
# type 4
R1b_params={
        'u_min':1.0,
        'u_max':10.0,
        'function':lambda u:u,
        'title':r'$R_1$',
        'tick_levels':0,
        'tick_text_levels':0,
        'tick_side':'right',
        'title_draw_center':True,
        'title_opposite_tick':False,
        'tag':'r1'
                }
E_params={
        'u_min':1.0,
        'u_max':10.0,
        'function':lambda u:u,
        'title':r'$E$',
        'tick_levels':3,
        'tick_text_levels':1,
        'tick_side':'right',
        'title_draw_center':True,
        'title_opposite_tick':False,
                }
F_params={
        'u_min':1.0,
        'u_max':10.0,
        'function':lambda u:u,
        'title':r'$F$',
        'tick_levels':3,
        'tick_text_levels':1,
        'tick_side':'left',
        'title_draw_center':True,
        'title_opposite_tick':True,
                }
R2a_params={
        'u_min':1.0,
        'u_max':10.0,
        'function':lambda u:u,
        'title':r'$R_2$',
        'tick_levels':0,
        'tick_text_levels':0,
        'tick_side':'left',
        'title_draw_center':True,
        'title_opposite_tick':False,
        'tag':'r2'
                }
 
block_2_params={
                'block_type':'type_4',
                'f1_params':R1b_params,
                'f2_params':E_params,
                'f3_params':F_params,
                'f4_params':R2a_params,
                'mirror_x':True,
                'isopleth_values':[['x',9,4,'x']]
                             }
# type 2 N
R2b_params={
        'u_min':0.0,
        'u_max':10.0,
        'function':lambda u:u,
        'title':r'$$',
        'tick_levels':0,
        'tick_text_levels':0,
        'tag':'r2'
                }
 
C_params={
        'u_min':0.5,
        'u_max':5.0,
        'function':lambda u:u,
        'title':r'$C$',
        'tick_levels':3,
        'tick_text_levels':1,
        'tick_side':'left',
        'scale_type':'linear smart',
                }
 
D_params={
        'u_min':1.0,
        'u_max':10.0,
        'function':lambda u:u,
        'title':r'$D$',
        'tick_levels':3,
        'tick_text_levels':1,
                }
 
block_3_params={
             'block_type':'type_2',
             'width':10.0,
             'height':10.0,
             'f1_params':R2b_params,
             'f2_params':C_params,
             'f3_params':D_params,
             'mirror_y':True,
             'isopleth_values':[['x',1,'x']]
             }
 
main_params={
              'filename':'ex_compound_nomo_1.pdf',
              'paper_height':10.0,
              'paper_width':10.0,
              'block_params':[block_1_params,block_2_params,block_3_params],
              'transformations':[('rotate',0.01),('scale paper',)],
              }
Nomographer(main_params)
Retrieved from "http://pynomo.org/wiki/index.php?title=Example:compound_nomograph_1&oldid=899"