# Calculus Exploration 10: Volumes of Solids of Revolution
# 
# The following is the Maple code for the Volumes of Solids of Revolution Maplet, which should be used to both visualize the solids and obtain solutions to problems. Note that this Maplet can be used only for the disk and shell methods. You can either execute the code below or run the corresponding Maplet from the webpage.
# 
# Volumes of Solids of Revolution Maplet Code
# Click in red area and press [Enter].
# Volume of Revolution Maplet
# Copyright 2002 Waterloo Maple Inc.
# 
# This maplet plots and computes the volume of the solid of revolution generated by rotating a function f(x) around either horizontal or vertical axis.
# 
# Instructions
# 
# The user enters a function f(x), a range [a, b] on the x-axis, and the axis of revolution.  When you press the 'Plot' button, the surface of revolution is plotted.  When you press the 'Volume' button, the volume of the solid is computed and displayed in a pop-up window.
# 
# To run this maplet, click the !!! button in the tool bar.
#   
restart;
RevolutionMaplet := module()

############################################################

export iniMathML, addMathML, exportMathML, getLastMath,  
       getRevolution, getVolume, runRevolutionMaplet:
local helpStr, mlStr, save_string:

############################################################


############################################################

mlStr := "":

helpStr := 
"This maplet plots and computes the volume of the solid of revolution generated by rotating a function f(x) around the horizontal or the vertical axis.

Instructions

The user enters a function f(x), a range [a, b] on the x-axis, and the axis of revolution.  When you press the 'Plot' button, the surface of revolution is plotted.  When you press the 'Volume' button, the volume of the solid is computed and displayed in a pop-up window.":

############################################################

getLastMath:=proc()
  save_string;
end proc:

############################################################
# pre: iniEqn :: algebraic expression
# post: returns the Presentation MathML of iniEqn

iniMathML := proc(iniEqn)
  MathML:-ExportPresentation(iniEqn);
end proc:

############################################################


############################################################
# pre: mathMLStr :: string, in form of Presentation MathML
#      addEqn :: algebraic expression 

addMathML := proc(mathMLStr, addEqn)
  local tree, cmc, child, children, nl, eqnSign;
  use XMLTools in
    tree := FromString(mathMLStr);
    cmc := ContentModelCount(tree);
    child := FromString(MathML:-ExportPresentation(addEqn));
    children := ContentModel(child);
    nl := FromString("<mtext>&NewLine;</mtext>");
    eqnSign := Element("mo","=");
    tree := AddChild(tree,nl,cmc);
    tree := AddChild(tree,eqnSign,cmc+1);
    for child in children do 
      cmc := ContentModelCount(tree);
      tree := AddChild(tree,child,cmc);
    end do:
    tree := MakeElement("mrow", [], ContentModel(tree) ):
    tree := Element("math", tree):
    ToString(tree):
  end use:
end proc:

############################################################

############################################################

getVolume := proc(boo1, p_func, p_a, p_b)

  local temp, temp2, str, view, value:

  use Maplets:-Tools, Student:-Calculus1 in

    str:=p_func:
    if str="" then 
      return plots[textplot]([1,1,"No function input"], 'font'=[HELVETICA,18]):
    end if:

    temp:=p_a:
    if temp="" then 
      return plots[textplot]([1,1,"Lower limit is missing"], 'font'=[HELVETICA,18]):
    end if:
    
    temp2:=p_b:
    if temp2="" then 
      return plots[textplot]([1,1,"Upper limit is missing"], 'font'=[HELVETICA,18]):
    end if:

    str := cat(str, ", ", temp, "..", temp2):

    if not boo1 then str := cat(str, ", axis=vertical") end if:

    mlStr := iniMathML( VolumeOfRevolution(parse(str), output=integral) ):
    value := VolumeOfRevolution(parse(str)):
    mlStr := addMathML(mlStr, value):
    mlStr := addMathML(mlStr, evalf(value)):
  end use:
end proc:


############################################################

getRevolution := proc(boo1, boo2, boo3, p_func, p_a, p_b, p_x1, p_x2, p_y1, p_y2, p_z1, p_z2)

  local temp, temp2, str, view, value:

  use Maplets:-Tools, Student:-Calculus1, StringTools in

  save_string:="";

    str:=Trim(p_func):
    if str="" then 
      return plots[textplot]([1,1,"No function entered"]):
    end if:

    temp:=Trim(p_a):
    if temp="" then 
      return plots[textplot]([1,1,"Lower limit is missing"]):
    end if:
    
    temp2:=Trim(p_b):
    if temp2="" then 
      return plots[textplot]([1,1,"Upper limit is missing"]):
    end if:

    str := cat(str, ", ", temp, "..", temp2):

    if not boo1 then str := cat(str, ", axis=vertical") end if:

    if not(boo2 or boo3) then  
      return plots[textplot]( [1,1,"Select function or surface from Display Options"]):
    end if: 

    if not boo2 then str := cat(str, ", showfunction=false") end if:
    if not boo3 then str := cat(str, ", showvolume=false") end if:

    view := ["DEFAULT","DEFAULT","DEFAULT"]:

    temp:=Trim(p_x1):
    temp2:=Trim(p_x2):
    if temp <> "" and temp2 <> "" then
      view[1]:=cat(temp, "..", temp2):
    end if: 

    temp:=Trim(p_y1):
    temp2:=Trim(p_y2):
    if temp <> "" and temp2 <> "" then
      view[2]:=cat(temp, "..", temp2):
    end if: 

    temp:=Trim(p_z1):
    temp2:=Trim(p_z2):
    if temp <> "" and temp2 <> "" then
      view[3]:=cat(temp, "..", temp2):
    end if: 

    temp:=cat(", view=[", view[1], ", ", view[2], ", ", view[3], "]"):
    str := cat(str, temp):
   
    return VolumeOfRevolution(parse(str), output=plot): 

  end use:

end proc:

############################################################

############################################################

runRevolutionMaplet := proc()

local maplet, ML_opts, b, s, c, dc, lc:

b := 'border'=true:
s := 'inset'=0, 'spacing'=0:
c := 'background'="#DDFFFF":
dc := 'background'="#CCFFFF":
lc := 'background'="#EEFFFF": 

use Maplets:-Elements in

############################################################

maplet := Maplet(
  'onstartup'=RunWindow('mainWin'),

############################################################

  Font['F1']('family'="Default", 'bold'='true', 'italic'='true'),
  Font['F2']('family'="Default", 'bold'='true', 'size'=14),

############################################################

  MenuBar['MB'](
    Menu("File",
      MenuItem("Plot", 'onclick'='A1'), 
      MenuSeparator(),
      MenuItem("Close", 'onclick'=Shutdown())
    ), # end Menu/File
    Menu("Help", 
      MenuItem("About this maplet", 'onclick'=RunWindow('helpWin'))
    ) # end menu/Help
  ), # end MenuBar 

############################################################

  Window['mainWin']('resizable'='false', 
#### Changes
    'title'="Volumes of Solids of Revolution:  Disk & Shell Methods",
    'menubar'='MB',    
    
    BoxColumn(s, c,

        BoxRow(s, c, b,  
          BoxRow(s, c, b, 'caption'="Enter a function and an interval : ",  
            Label("Function: ", 'font'='F2', c),
#### Changes
            TextField['TF_func'](16, lc, 'value'=1-x^2, 'tooltip'="Enter a function"),
            Label(" a ", 'font'='F2', c), 
            Label(" = ", 'font'='F1', c), 
            TextField['TF_a']('value'=0, 3, lc, 'tooltip'="Lower limit"),
            Label(" b ", 'font'='F2', c), 
            Label(" = ", 'font'='F1', c), 
            TextField['TF_b']('value'="1", 3, lc, 'tooltip'="upper limit")
          ), # end BoxRow

          BoxRow('inset'=0, 'spacing'=3, c, b,
#### Changes  
            'caption'="Choose an axis of revolution : ", 
            RadioButton['RB']('caption'="horizontal x-axis", 
              'group'='BG_axis', 'value'=true, c), 
            RadioButton('caption'="vertical z-axis", 'group'='BG_axis', c)
          ) # end BoxColumn
        ), # end BoxRow   

        BoxRow(s, c, b,
#### Changes 
          BoxColumn(s, c, b, 'caption'="Note the xyz-coordinates with z = f(x) the blue curve and the vertical axis = z-axis.", 
            Plotter['P'](lc)
          ),
#### Changes
          BoxColumn(s,c,b,'inset'=0, 'spacing'=6, 'caption'=" Volume of the solid corresponding to plot at left.", 
              MathMLViewer['ML']('height'=370, 'width'=240, lc)
          ) # end BoxRow
        ), # end BoxRow

        BoxRow(c, s, 
         BoxColumn(s, c, b, 'caption'="To clearly see the blue curve unclick 'Show volume' below.",

         BoxRow(s, c, 
            CheckBox['CB2']('caption'="Show function", c,  
              'value'=true),
            CheckBox['CB3']('caption'="Show volume", c,  
              'value'=true)
          ), # end BoxRow

         BoxRow(s, c,    
            Label("x", 'font'='F2', c), 
            Label(" = ", 'font'='F1', c),
            TextField['x1']('width'=2, lc, 'value'=" "), 
            Label(" .. ", 'font'='F2', c),
            TextField['x2']('width'=2, lc, 'value'=" "),
#### Changes
            Label("  y", 'font'='F2', c), 
            Label(" = ", 'font'='F1', c),
            TextField['y1']('width'=2, lc, 'value'=" "),
            Label(" .. ", 'font'='F2', c),
            TextField['y2']('width'=2, lc, 'value'=" "),

            Label("  z", 'font'='F2', c), 
            Label(" = ", 'font'='F1', c),
            TextField['z1']('width'=2, lc, 'value'=" "), 
            Label(" .. ", 'font'='F2', c),
            TextField['z2']('width'=2, lc, 'value'=" ")
          ) # end BoxRow

        ), # end BoxColumn   

        BoxColumn('inset'=10, 'spacing'=10, c, 

          BoxRow('inset'=10, 'spacing'=10, c, 
             Button(" Plot ", dc, 'onclick'='A1'),
             Button("Compute Volume", dc, 'onclick'=Evaluate('target'='ML', 'function'='getVolume', 
               Argument('RB'),
               Argument('TF_func', quotedtext='true'), 
               Argument('TF_a', quotedtext='true'),
               Argument('TF_b', quotedtext='true'), 'waitforresult'='false') ),  

             Button("Close", dc, Shutdown())
        ) # end BoxRow

     ) # end BoxColumn
    ) # end BoxColumn
)
  ), # end Window

############################################################

  Window['helpWin']( 'resizable'='false',
    'title'="About the Volume of Revolution Maplet",
    BoxColumn(b, c, 'inset'=0, 'spacing'=10,
      BoxCell(
        TextBox('height'=15, 'width'=28,
          lc, 'foreground'="#333399", 
          'editable'='false', 'font'='F2', 
          'value'=helpStr
        ) # end TextBox
      ), # end BoxCell
      BoxRow(s, c,
        Button("Close", CloseWindow('helpWin'), dc)
      ) # end BoxRow
    ) # end BoxColumn
  ),  # end helpWin

############################################################

  ButtonGroup['BG_axis'](),

############################################################

Action['A1'](Evaluate('target'='P', 'function'='getRevolution', 
               Argument('RB'), 
               Argument('CB2'), 
               Argument('CB3'), 
               Argument('TF_func', quotedtext='true'), 
               Argument('TF_a', quotedtext='true'),
               Argument('TF_b', quotedtext='true'), 
               Argument('x1', quotedtext='true'),
               Argument('x2', quotedtext='true'),
#### Changes
               Argument('y1', quotedtext='true'),
               Argument('y2', quotedtext='true'),
               Argument('z1', quotedtext='true'),
               Argument('z2', quotedtext='true'), 'waitforresult'='false')) 


): # end Maplet

############################################################

Maplets:-Display(maplet):

end use: # end use
end proc: # end proc

############################################################

end module: # end module
RevolutionMaplet:-runRevolutionMaplet();

# 
#