\%      ***********************
\%      *  3D Graphic window  *
\%      ***********************

\% ********** 3D Graphic window **********
\topic kh_3DWin {3D graphic window}
{\bf 3D graphic windows} are used to represent
\jump kh_Curve {curves} by their projections to
3-dimensional spaces endowed with right-handed rectangular
Cartesian coordinate systems.\par
3D space is specified by three variables or expressions
whose values are plotted along axes.
The \jump kh_3DWinCurrentAttr {current graphic attributes} dialog box
which is opened by the {\bf Attributes|Current}
command allows you to choose the variables.\par
Visible part of the space is given by minimum and maximum
values for each axis. You can set them directly in the window
(see {\bf Limits of visibility} below) or in the
\jump kh_3DWinLayout {layout dialog box} which is opened
by the {\bf Window|Layout} command.\par
CONTENT maps the visible part of the space to the window's
{\bf Graphic area} using the following two transformations.\par
\qc{$
 \system 2 l 0 0 
  {u=-x\,sin\,\varphi+y\,cos\,\varphi}
  {v=-(x\,cos\,\varphi+y\,sin\,\varphi)\,cos\,\vartheta+z\,sin\,\vartheta}
$}\par
This transformation maps 3D-points $(x,y,z)$
to a mathematical plane $(u,v)$. Two angles, 
colatitude $\vartheta$ and longitude $\varphi,$
are parameters of this transformations. They define
a vector to which the plane is orthogonal.
You can set the angles directly in the window
(see {\bf Angles} below) or in the
\jump kh_3DWinLayout {layout dialog box} which is opened
by the {\bf Window|Layout} command.
The following figure illustrates relations between
two coordinate systems.\par
\qc{\picture 0.4 contw3d.fig }\par
Mathematical coordinates $(u,v)$ are transformed then to
{\bf window coordinates} $(U,V)$:\par
\qc{$
 \system 2 l 0 0 
  {U=left+\frac{right-left}{u_{max}-u_{min}}\,(u-u_{min})}
  {V=bottom+\frac{top-bottom}{v_{max}-v_{min}}\,(v-v_{min})}
$}\par
where $left,\:top,\:right$ and $bottom$ are screen coordinates
of the window's Graphic area.
\par
You open the graphic windows with the
\jump kh_menuWindow {Window|Open|3D Graphic} command from the
\jump kh_MainWin {Main window.}\par
There are the following components in the graphics window.\par
{\desc 27
 {\bf Component\>What it does or is used for}\par
 {\bf Compute}\>\include kh_ComputeSubmenu \par
 {\sb 0 \li 1 \bf Forward}\>\include kh_ForwardItem \par
 {\sb 0 \li 1 \bf Backward}\>\include kh_BackwardItem \par
 {\sb 0 \li 1 \bf Extend}\>\include kh_ExtendItem \par
 {\bf Window}\>this menu contains commands which manipulate
  the window.\par
 {\sb 0 \li 1 \bf Redraw\+diagram}\>\include kh_RedrawDiagramItem \par
 {\sb 0 \li 1 \bf Redraw\+curve}\>\include kh_RedrawCurveItem \par
 {\sb 0 \li 1 \bf Clear}\>\include kh_ClearItem \par
 {\sb 0 \li 1 \bf Fit\+diagram}\>changes the
  {\bf limits of visibility} in such a way that all curves
  from the current diagram become totally visible.
  The command doesn't affect other windows.\par
 {\sb 0 \li 1 \bf Fit\+curve}\>changes the
  {\bf limits of visibility} in such a way that the
  current curve becomes totally visible.
  The command doesn't affect other windows.\par
 {\sb 0 \li 1 \bf Undo\+scale}\>restores the limits of visibility
  (six numbers defining the visible part of 3D space)
  for this window to their previous values. {CONTENT}
  remembers as much as last ten limits so you can go back
  more than one step (after ten steps the current limits
  are restored). {CONTENT} records the limits
  when you press the {\bf Enter} key or
  clear the window after editing them.
  \par
 {\sb 0 \li 1 \bf Undo\+rotate}\>restores
  colatitude $\vartheta$ and longitude $\varphi$
  (two angles defining rotation of the visible part of 3D space)
  for this window to their previous values. {CONTENT}
  remembers as much as last ten pairs of angles so you can go back
  more than one step (after ten steps the current angles
  are restored). {CONTENT} records the angles
  when you press the {\bf Enter} key or
  clear the window after editing them.
  \par
 {\sb 0 \li 1 \bf Layout}\>displays the
  \jump kh_3DWinLayout {layout dialog box} where
  you change various settings which control the layout
  of the window.\par
 {\sb 0 \li 1 \bf Hardcopy}\>displays the
  \jump kh_3DWinHardcopy {hardcopy dialog box} where you
  specify various option for the hardcopy of this window.\par
 {\sb 0 \li 1 \bf Duplicate}\>opens another window
  which has exactly the same attributes as the current window.
  This may be useful if you want to do some minor changes
  of attributes without restoring them back.\par
 {\sb 0 \li 1 \bf Hide}\>\include kh_HideItem \par
 {\bf Attributes}\>this menu allows you to change attributes
  used to draw and redraw curves.\par
 {\sb 0 \li 1 \bf Current}\>displays the
  \jump kh_3DWinCurrentAttr {current graphic attributes} dialog box
  where you specify attributes which will be used to draw
  the curves to be computed next.
  \par
 {\sb 0 \li 1 \bf Curve}\>displays the
  \jump kh_3DWinCurveAttr {curves graphic attributes} dialog box
  where you change attributes which are used to redraw
  the \jump kh_CurCurve {current curve.}\par
 {\bf Help}\>\include kh_HelpSubmenu \par
 {\sb 0 \li 1 \bf This\+window}\>displays
  the description of 3D graphic windows.\par
\% {\sb 0 \li 1 \bf Index}\>displays
\%  the contents of Help information.\par
 {\sb 0 \li 1 \bf Search}\>\include kh_HelpSearchItem \par
 {\bf Limits\+of\+visibility}\>is the area where you specify
  minimum and maximum values for each axis as well as
  tick sizes. To change any value in the area click it with the
  mouse and then edit it. {CONTENT} will update the
  {\bf Graphics area} when you press the {\bf Enter} key
  or perform the {Clear} command from the {Window} menu.
  Any value may be given by an expression
  constructed from numbers, parentheses, operators
  (+, -, *, /, and ^), and standard function calls
  (abs, acos, asin, atan, ceil, cos, exp, floor, log, log10,
  sin, sqrt, tan), for example sqrt(2)/2.
  As you type CONTENT tries to parse the expression
  and compute its value. If it succeeds the value
  is used. Otherwise, the prompt which is left to the input field
  is grayed to indicate that the
  text does not form correct expression.
  Use the \jump kh_3DWinLayout {layout dialog box}
  to specify whether to show the limits in the window.\par
 {\bf Angles}\>is the area where you specify the values
  of colatitude $\vartheta$ and longitude $\varphi$
  which define rotation of the visible part of the 3D space.
  The angles are measured in degrees. Each input field has
  a scroll bar attached to it. The scroll bar
  allows to increase or decrease the current value by one degree.
  Text values may be edited in the same way as the limits
  of visibility. Use the {\bf layout dialog box}
  to specify whether to show the angles in the window.\par
 {\bf Palette}\>is a horizontal bar which shows all colors
  available for drawing curves.
  To choose a color click on it with the mouse. If you specified
  more than one set of functions along the axes (see the
  \jump kh_3DWinLayout {layout dialog box}) there is
  a switch at the left of the bar which allows you to choose
  the set of functions you want to set the color for.
  A small square at the right of the bar displays the
  currently chosen color.
  The {\bf layout dialog box} allows
  you to show or hide the palette.\par
 {\bf Graphic area}\>is the part of the window where {CONTENT}
  draws computed curves. In addition you can ask {CONTENT} to
  draw enclosed box, axes, scales, and labels in the area.
  Use the \jump kh_3DWinLayout {layout dialog box} to make
  appropriate settings.\par
}
You can do \jump kh_CurveSwitch {curve switching} in the
graphics window. To choose a
\jump kh_SpecialPoint {special point} on some curve
as an \jump kh_InitialPoint {initial point} for the next
curve click the point (you may need to
redraw the \jump kh_CurDiagram {current diagram} before this).
{CONTENT} will unload current starter and generator
and load appropriate one. To make this operation possible
a {\bf marker} must be chosen for the type of special
point which can by done using the
\jump kh_SpecPointWin {special points} dialog box.
There is default marker for each type of special point.
You can also switch curves using the
\jump kh_InitPointWin {initial points} dialog box.
\par
In addition to the traditional way of changing the angles
(by typing them in) you can do it with the mouse.
Place the pointer at a point in the Graphic area
and press the left mouse button. Holding the button drag
the pointer. Horizontal movement changes the longitude $\varphi$
and vertical movement changes the colatitude $\vartheta$.
To cancel the operation release
the button elsewhere outside the area. You can restore
previous angles later by the {\bf Undo\+rotate}
command from the {\bf Window} menu.
\par
To destroy the window use the {\bf Close} command from
the {\bf System} menu of the window.\par
\end	\% kh_3DWin

\% ********** 3D hardcopy dialog box **********
\topic kh_3DWinHardcopy {hardcopy dialog box for 3D graphic window}
The {\bf hardcopy dialog box} is where you
specify various options for a hardcopy of a 3D graphic window.\par
You display the dialog box with the
\jump kh_3DWin {Window|Hardcopy} command from a graphic window.
A hardcopy is a {\bf PostScript} program which produces a copy
of the window's Graphic area with all the
\jump kh_Curve {curves} from the \jump kh_CurDiagram {current diagram}
drawn.
The hardcopy is always written into a file
and may optionally be sent to a printer.\par
There are following components in the dialog box.\par
#ifdef _UNIX
{\desc 19
#else	_UNIX
{\desc 17
#endif	_UNIX
 {\bf Component\>What it does or is used for}\par
 {\bf File}\>is where you specify the name of a file
  to which {CONTENT} will write the hardcopy.
  The file may be sent to a printer later
  (by means of appropriate {\bf copy} command.\par
 {\bf Browse}\>displays the list of available files
  which allows you to choose a file without typing
  its name. The name of the file you choose is put
  into the input field.\par
 {\bf Picture}\>is where you specify dimensions of a picture.\par
 {\li 1 \sb 0 \bf Width}\>specifies the width in current units.\par
 {\li 1 \sb 0 \bf Height}\>specifies the height in current units.\par
 {\li 1 \sb 0 \bf Unit}\>specifies the units for width and height.\par
 {\bf Font}\>contains two lists which you use to choose
  font name and its size. The font is used for all
  characters in the picture.\par
{\bf Options}\>allows you to specify some characteristics
  of the picture and where to send it. The values of three
  scale factors depend on the resolution of your printer.
  You may need to experiment to choose appropriate values for them.
  \par
 {\li 1 \sb 0 \bf Curve\+width}\>specifies the value of the
  curve width factor. It is used for all curves.\par
 {\li 1 \sb 0 \bf Line\+width}\>specifies the value of the
  line width factor. It is used for axes, grid, and frame
  of the picture.\par
 {\li 1 \sb 0 \bf Marker\+scale}\>specifies the value of the
  marker width factor. It is used to draw markers.\par
 {\li 1 \sb 0 \bf Preserve\+colors}\>when this box is checked
  {CONTENT} tries to produce a color picture by preserving
  colors set for Graphic area and curves.\par
#ifdef _UNIX
 {\li 1 \sb 0 \bf Show\+on\+screen}\>when this box is checked
  {CONTENT} shows the picture on the screen. The command
  for this is given by the value of the {\bf HCVIEWER} key which is
  in the {\bf [Visual]} section of the {\bf settings file.}\par
 {\li 1 \sb 0 \bf Send\+to\+printer}\>when this box is checked
  {CONTENT} sends the picture to a printer. The command
  for this is given by the value of the {\bf HCPRINTER} key which is
  in the {\bf [Visual]} section of the {\bf settings file.}\par
#endif _UNIX
 {\bf Buttons}\>\par
 {\li 1 \sb 0 \bf Ok}\>closes the dialog box and produces the
  hardcopy in accordance with the settings you have made.\par
 {\li 1 \sb 0 \bf Cancel}\>closes the dialog box without
  changing anything and producing the hardcopy.\par
 {\li 1 \sb 0 \bf Help}\>opens the \jump kh_HelpWin {help window} which
  displays the description of this dialog box.\par
}
\end	\% kh_3DWinHardcopy

\% ********** 3D Graphic layout dialog box **********
\topic kh_3DWinLayout {layout dialog box for 3D graphic window}
The {\bf layout dialog box} is where you specify
various settings which affects the layout of 3D graphic window.
You display the dialog box by the
\jump kh_3DWin {Window|Layout} command in 3D graphic
window. Note that the settings affect only the window
from which you perform the command.\par
The following components are in the dialog box.\par
{\desc 27
 {\bf Component\>What is does or is used for}\par
 {\bf Window\+title}\>allows you to modify the title of the window.\par
 {\bf Show\+in\+window}\>contains check boxes
  which you use to specify which components will be shown
  in the graphic window. Check appropriate boxes for
  the components you want to see in or to be able to change
  directly from the graphic window.\par
 {\sb 0 \li 1 \bf Min..Max}\>shows limits of visibility.\par
 {\sb 0 \li 1 \bf Tick}\>shows tick values.\par
 {\sb 0 \li 1 \bf Scale}\>draws scales for enclosed box using
  tick values.\par
 {\sb 0 \li 1 \bf Label}\>prints variables or expressions whose values
  are plotted along axes. The labels are placed
  near corresponding edges of the enclosed box or near axes.\par
 {\sb 0 \li 1 \bf Box}\>draws the enclosed box, i.e. all visible
 edges of the parallelepiped enclosed the visible part
 of 3D space.\par
 {\sb 0 \li 1 \bf Axis}\>draws lines corresponding
  to mathematical axes. Note that an axis is drawn only if
  zero belongs to visibility intervals of two other axes.\par
 {\sb 0 \li 1 \bf Projections}\>projects each point on three
  invisible surfaces of the enclosed box.\par
 {\sb 0 \li 1 \bf Angles}\>shows colatitude and longitude.\par
 {\bf Limits\+of\+visibility}\>is where you specify
  limits of visibility for each axis.\par
 {\sb 0 \li 1 \bf Min}\>specifies the minimum value.
  Points with the value of corresponding coordinate less
  than this value will not be drawn.\par
 {\sb 0 \li 1 \bf Max}\>specifies the maximum value.
  Points with the value of corresponding coordinate greater
  than this value will not be drawn  .\par
 {\sb 0 \li 1 \bf Tick}\>specifies the step
  used for drawing scale. 0 means you
  want {CONTENT} to calculate the value by itself
  using given minimum and maximum values.\par
 {\bf Colors}\>is where you set options related to
  colors.\par
 {\sb 0 \li 1 \bf Foreground}\>opens the {\bf Standard Color dialog box}
  which you use to select the foreground color.
  The color will be used to draw box, axes, labels, and scale.\par
 {\sb 0 \li 1 \bf Background}\>opens the {\bf Standard Color dialog box}
  which you use to select the background color for the window.\par
 {\sb 0 \li 1 \bf Show\+palette}\>sets the mode in which
  a palette will be placed in the 3D graphic window to facilitate
  selection of colors for drawing curves.\par
 {\bf Angles}\>is where you specify angles.\par
 {\sb 0 \li 1 \bf $\vartheta$}\>specifies the value of
  colatitude $\vartheta$.\par
 {\sb 0 \li 1 \bf $\varphi$}\>specifies the value of
  longitude $\varphi$.\par
 {\bf Sample\+of\+window}\>displays a sample of
  the window in accordance with the current settings.\par
 {\bf Buttons}\>\par
 {\sb 0 \li 1 \bf Ok}\>closes the dialog box and redraws
  the 3D graphic window using the settings you have made.\par
 {\sb 0 \li 1 \bf Cancel}\>closes the dialog box without
  changing the settings.\par
 {\sb 0 \li 1 \bf Help}\>opens the \jump kh_HelpWin {help window} which
  displays the description of this dialog box.\par
}
\end	\% kh_3DWinLayout

\% ********** Current graphic attributes dialog box **********
\topic kh_3DWinCurrentAttr {current attributes dialog box for 3D graphic window}
The {\bf current attributes dialog box} is where you
specify various graphic attributes of \jump kh_Curve {curves} which you
will compute next.\par
You display the dialog box by the
\jump kh_3DWin {Attributes|Current} command in a 3D graphic window. 
Note that the settings affect only the window
from which you perform the command.\par
The following components are in the dialog box. They are
listed in accordance with their positions in the box,
from the left to the right and from the top to the bottom.\par
{\desc 20
{\bf Component\>What it does or is used for}\par
{\bf Functions\+along\+axes}\>allows you to specify functions
 whose value will be plotted along axes.\par
{\sb 0 \li 1 \bf OX}\>is where you type in a function
 whose values will be plotted along the abscissa.\par
{\sb 0 \li 1 \bf OY}\>is where you type in a function
 whose values will be plotted along the ordinate.\par
{\sb 0 \li 1 \bf OZ}\>is where you type in a function
 whose values will be plotted along the vertical axis.
 There may be more than one set of functions defined for the
 window. Use the scroll bar attached to the fields to choose
 the set you want to edit.
 \par
{\sb 0 \li 1 \bf New\+functions}\>this button tells {CONTENT}
 that you want to specify one more set of functions
 whose values will be plotted along axes. Having pressed the
 button type in functions in the {\bf OX, OY,} and {\bf OZ}
 fields.\par
{\sb 0 \li 1 \bf Delete\+functions}\>this button tells {CONTENT}
 to delete the set of functions which are currently in the
 {\bf OX, OY,} and {\bf OZ} fields. Use the scroll bar
 attached to the fields to choose the set you want to delete.
 The current and total numbers of the sets are indicated in the
 left bottom corner of the group.
 \par
{\sb 0 \li 1 \bf List\+of\+names}\>contains the two-level list
 of names you can use in functions. The first level
 contains groups of names. Click the name of a group to
 see the names from the group. Click a name to insert it
 into {\bf OX, OY,} or {\bf OZ}
 field (it will be inserted into those field where the
 cursor was before you activated the list). To return to
 the first level of the list click the line which
 contains two dots.\par
{\bf Graphic\+attributes}\>allows you to set various attributes
 for the set of functions which are currently in the
 {\bf OX, OY, and} and {\bf OZ} fields. To change
 attributes of another set first choose it with the
 scroll bar attached to the fields.
 The current and total numbers of the sets are indicated in the
 left bottom corner of the function group.
 \par
{\sb 0 \li 1 \bf Set\+attributes\+of}\>allows you to choose
 attributes of what graphic element you will set.
 Choose one of the following: {\bf points},
 \jump kh_Path {paths},
 \jump kh_Trace {traces}, or
 \jump kh_Shift {shifts}.
 \par
{\sb 0 \li 2 \bf Join}\>allows you to choose the style of lines
 which join points. One of the following can be chosen:
 {\bf No,} {\bf Solid,} or {\bf Dotted.}\par
{\sb 0 \li 2 \bf Width}\>allows you to choose the width of points or lines.
 If this value is zero, the width is one pixel and fast but possibly
 not accurate device-dependent drawing algorithm will be used.
 \par
{\sb 0 \li 2 \bf Change\+Color}\>opens the {\bf Standard Color Dialog Box}
 which you use to select the color for points or lines.\par
{\bf Options}\>allows you to set additional options.\par
{\sb 0 \li 1 \bf Clear\+before\+...}\>tells {CONTENT} to
 clear window's Graphic area before drawing each point
 computed by a generator.\par
{\bf Sample\+of\+window}\>shows how curves will be drawn with
 current settings.\par
{\bf Buttons}\>\par
{\sb 0 \li 1 \bf Ok}\>remembers the graphic attributes you have set
 and closes the dialog box.\par
{\sb 0 \li 1 \bf Cancel}\>closes the dialog box without
 changing the settings.\par
{\sb 0 \li 1 \bf Help}\>opens the \jump kh_HelpWin {help window} which
 displays the description of this dialog box.\par
}
\end	\% kh_3DWinCurrentAttr

\% ********** Curve's graphics attributes dialog box **********
\topic kh_3DWinCurveAttr {curve attributes dialog box for 3D graphic window}
The {\bf curve's attributes dialog box} is where you
change various graphic attributes of the
\jump kh_CurCurve {current curve.}\par
You display the dialog box by the
\jump kh_3DWin {Attributes|Curve} command in a 3D graphic
window. Note that the settings affect only the window
from which you perform the command.\par
The following are components in the dialog box. They are
listed in accordance with their positions in the box,
from the left to the right and from the top to the bottom.\par
{\desc 16
 {\bf Component\>What it does or is used for}\par
 {\bf Curve\+segment}\>is a switch you use to choose a segment
  of the current curve whose graphics attributes you want to change
  A {\bf segment} is defined as a part of a curve between two
  successive \jump kh_SpecialPoint {special points}
  (for the purpose of this definition the first and the last
  points of a curve are considered as special points).\par
 {\bf From\+point}\>displays the \jump kh_PointType {type} of
  the first point of the current segment.\par
 {\bf To\+point}\>displays the type of
  the last point of the current segment.\par
 {\bf Attributes\+set}\>is a switch you use
  to choose which set of attributes of the given segment you want to change.
  There is one set of attributes for each set of functions
  you have specified in the
  \jump kh_3DWinCurrentAttr {current attributes} dialog box.
  There is the only set of attributes if you have one
  set of functions.
  Note that all settings below the switch are for the chosen
  attributes set of the chosen segment of the curve.\par
 {\sb 0 \li 1 \bf Add\+attributes}\>this button creates a new
  set of attributes for the chosen segment.
  Use it if you have specified new set of
  functions in the window after the curve was computed.
  This allows you to set attributes for the new functions.\par
 {\sb 0 \li 1 \bf Delete\+attributes}\>this button deletes
  the chosen set of attributes of the chosen segment.
  Use it if you have deleted a pair of functions in the window
  after the curve was computed.
  Be careful to choose those set of attribute which
  corresponds to the deleted functions.\par
{\bf Graphic\+attributes}\>allows you to change graphic attributes.
 Note that only attributes from the chosen set of the chosen
 segment are available.
 \par
{\sb 0 \li 1 \bf Set\+attributes\+of}\>allows you to choose
 attributes of what graphic element you will change.
 Choose one of the following: {\bf points},
 \jump kh_Path {paths}, or
 \jump kh_Trace {traces}.
 \par
{\sb 0 \li 2 \bf Join}\>allows you to change the style of lines
 which join points. One of the following can be chosen:
 {\bf No,} {\bf Solid,} or {\bf Dotted.}\par
{\sb 0 \li 2 \bf Width}\>allows you to change the width of points or lines.
 If this value is zero, the width is one pixel and fast but possibly
 not accurate device-dependent drawing algorithm will be used.
 \par
{\sb 0 \li 2 \bf Change\+Color}\>opens the {\bf Standard Color Dialog Box}
 which you use to change the color of points or lines.\par
 {\bf Buttons}\>\par
 {\sb 0 \li 1 \bf Ok}\>remembers the changes you have made
  and closes the dialog box.\par
 {\sb 0 \li 1 \bf Cancel}\>closes the dialog box without
  changing the attributes.\par
 {\sb 0 \li 1 \bf Help}\>opens the \jump kh_HelpWin {help window} which
  displays the description of this dialog box.\par
}
\end	\% kh_3DWinCurveAttr