Once a geometry file has been read into HYPERGEO and its display is active,
a number of interactive commands are available which serve to manipulate the
object and modify how it is displayed on the screen.  These commands can be
invoked by pressing the appropriate keyboard key.  Also, a number of the
commands can be executed by using a mouse to select a function box in the
program menu area.

The keyboard commands use all twenty-six letters plus several numeric and
special-purpose keys.  In some cases, a command key can be prefixed with one
of the standard keyboard modifiers (Shift, Ctrl, or Alt) to perform
additional functions.

The HYPERGEO command set can be divided into several major groupings:

  1 - Interactively set or modify display parameters:
        C, D, E, L, T, W, =, +, -, Insert, Delete,
        Page Up, Page Down, Ctrl-Page Up, Ctrl-Page Down

  2 - Toggle among possible display options:
        B, G, K, M, N, U, V, Tab, Space, Backspace

  3 - Select a particular display mode:
        A, H, P, R, S

  4 - Perform various rotations of the geometry:
        X, Y, Z, F3 thru F10, Home, End, 1 thru 6 and Alt-1 thru Alt-6
        (also, Shift, Ctrl, and Alt applied to X, Y, Z, and F5 thru F10)

  5 - Translate the geometry display or a selected 4-D vertex:
        0, the Arrow Keys

  6 - Other miscellaneous functions:
        F, I, J, O, Q, F1, F2

  7 - Menu commands using a mouse

Enter the number of the command group you wish further Help on:
(Press <Esc> to exit Help)
INTERACTIVE PARAMETERS:                                          Page 1

  C - Color of primary geometry graphics or solid-fill shade:
        For Perspective and Hidden-line display modes the color used for
        drawing the object's edges is set to one of 16 standard EGA colors.
        For Solid display mode on a system with VGA graphics it specifies a
        color to be used to generate the solid-fill shades.
  D - Delta for incrementing the W-zero intersection value (geometry units):
        This Delta value is used by the commands that translate the
        intersecting hyperplane along the W-axis (Page Up/Page Down below).
  E - Eye-to-screen viewing distance (inches):
        Sets the eye-to-screen distance used to calculate 2-D projections.
  L - Locate geometry: angular orientation or vertex coordinates:
        Rotations: specify angular displacements of coordinate axes;
        Translations: specify coordinates of selected vertex.
  T - Turn angle for incremental rotations (degrees):
        Sets the incremental angle used by the rotation commands.
  W - W-coordinate of the intersecting hyperplane (geometry units); or the
      W-coordinate of the projection viewpoint (geometry units):
        4-D Intersections: positions the hyperplane along W-axis.
        4-D Projections: positions the projection viewpoint along W-axis.
  = - Scale factor of display (screen inches per geometry unit):
        Sets the scale factor of the current display to a particular value.
  +/- - Zoom the current display scale Up/Down:
        Increases/Decreases the current display scale by 10%.
  Insert/Delete - Increase/Decrease the eye-to-screen distance by 10%:
        Reduces/Enhances the apparent perspective in the 2-D projection.
  Page Up/Page Down - Translate the intersecting hyperplane along W-axis; or
      translate the projection viewpoint along W-axis:
        4-D Intersections: Up/Down W-coordinate of hyperplane by Delta value.
        4-D Projections: Up/Down W-coordinate of projection viewpoint by 10%.
  Ctrl-Page Up/Page Down - Automated translation of intersecting hyperplane; or
      position projection viewpoint to maximum/minimum W-coordinate:
        4-D Intersections: hyperplane moves back and forth within object.
        4-D Projections: viewpoint set to greatest/least distance on W-axis.


(F1 for Help menu; 1 thru 7 for specific Help page; <Esc> to exit Help)
TOGGLES:                                                         Page 2

  B - Spectrum banding of W-coordinate: On/Off:
        With spectrum banding the color of an object's edge reflects its
        W-coordinate value:  from blue-violet for lowest W values, through
        blue, green, yellow, and orange, to red for highest W values.
  G - Toggle 4-D geometry imaging mode: Intersection/Projection/Dual:
        Cycles through the 4-D imaging modes (Dual mode combines separate
        Intersection and Projection images in one display).
        Upper-case 'G' cycles in order of Projection/Intersection/Dual;
        lower-case 'g' cycles in order of Intersection/Projection/Dual.
  K - Journal file record: On/Off:
        When recording is On, all displays are saved in a journal file;
        turning recording Off closes the journal file which may be replayed.
  M - Menu area: display On/Off
        With Menu display Off, the mouse cannot be used to execute commands.
  N - Name of geometry file: display On/Off
        The geometry file name can be shown at upper-left of main display.
  U - Toggle User Interface mode: Rotation/Translation
        The primary User Interface mode is Rotation which is available for
        all geometries; objects can be rotated in space to any orientation.
        For 4-D Projections, the User Interface mode can be toggled to
        Translation; a selected vertex may be temporarily displaced to any
        location in hyperspace; the display reflects the modified geometry.
  V - Axis vectors: display On/Off
        The projections of the unit vectors lying along the three 3-D or
        four 4-D coordinate axes may be shown in the main geometry display.
  Tab - Highlighting of a single hyperface: On/Off
        With hyperface highlighting On, all edges that belong to a single
        hyperface are drawn in a different color.  For 4-D Projections, the
        displayed edges correspond to the actual edges of the hyperface in
        the original geometry; for Intersections, the highlighted edges are
        intersections of the hyperplane with the particular hyperface.
  Space/Backspace - Cycle forward/backward thru hyperfaces for highlight:
        Steps through an arbitrary ordering of all hyperfaces in 4-D object.


(F1 for Help menu; 1 thru 7 for specific Help page; <Esc> to exit Help)
DISPLAY MODES:                                                   Page 3

HYPERGEO displays its graphical output using one of five possible methods:

  A - Anaglyph
        A two-color stereoscopic projection for use with red/blue 3D
        glasses.  Two separate Perspective projections are displayed, one in
        red and one in blue, as seen by the viewer's left and right eye.
        The stereoscopic effect produces a vivid and accurate impression of
        the three-dimensional depth of the displayed geometrical image.
  H - Hidden-line
        A normal Perspective projection is further processed to eliminate
        all edge segments that lie behind one or more faces of the object.
        This representation of opaqueness heightens the sense of depth.
  P - Perspective
        A wire-frame representation of the image as it is projected onto the
        flat surface of the computer's viewing screen.  The apparent degree
        of perspective is a function of the eye-to-screen distance; the
        closer the eye is to the screen, the greater the perspective effect.
        Perspective display is the most basic of the available modes; all
        other display modes are derived from a perspective projection.
  R - Relief
        Relief display mode combines the features of a stereoscopic anaglyph
        with hidden-line processing.  The display is a red/blue anaglyph for
        viewing with 3D glasses, with all hidden lines removed.  The 3D
        effect provides an excellent sense of the object's surface relief.
  S - Solid
        Solid display mode performs hidden-surface analysis on the object's
        structure.  Faces hidden behind the object are invisible.  Each face
        that is visible is drawn in a solid-fill color that reflects that
        face's orientation relative to a theoretical light source; the more
        directly the face is illuminated, the lighter its color.

  Note: Hidden-line, Relief, and Solid modes cannot be used with images
        produced by 4-D Projections.


(F1 for Help menu; 1 thru 7 for specific Help page; <Esc> to exit Help)
ROTATIONS:                                                       Page 4

HYPERGEO permits rotating a hyperobject about each of the six planes formed
by intersecting pairs of 4-D coordinate axes.  In addition, the 3-D image
formed from a 4-D Projection or Intersection can be rotated in three-space
around each of the three 3-D axes.  By combining the proper sequence of
rotations, a geometry can be positioned to any valid orientation.

All rotations are performed in incremental steps of the current Turn Angle
which is a parameter that may be interactively modified (the 'T' command).

  X,Y,Z - Incremental 3-D rotation about X, Y, or Z axis
    Rotates an object through the Turn Angle about the particular 3-D axis.
    (For 4-D geometries, all 3-D rotations are transient and operate only on
    the 3-D image; the hyperobject's orientation in 4-space is not altered.)
  F5 thru F10 - Incremental 4-D rotation of a plane formed by a pair of axes
    Rotates a hyperobject through the Turn Angle on a particular 4-D plane:
         F5  -  YZ plane        F6  -  XW plane
         F7  -  XZ plane        F8  -  YW plane
         F9  -  XY plane        F10 -  ZW plane
  The X,Y,Z, and F5 thru F10 commands can be modified as follows:
     Shift - Rotation in reverse direction (negative Turn Angle)
     Ctrl - Continuous rotation in forward direction
     Alt - Continuous rotation in reverse direction
  F3/F4 - Continuous random 3-D/4-D forward rotations
    Rotations either about the X, Y, and Z axes or on the YZ, XW, XZ, YW,
    XY, and ZW planes are performed in a random order.
  Home - Restore the orientation of original geometry definition
    This resets all axis angles to zero degrees.
  End - Restore orientation that existed before most recent Home command
    All axis angles are reset to their values prior to last Home command.
  1 thru 6 and Alt-1 thru Alt-6 - The twelve orthogonal 4-D orientations
    (For 3-D, only the three orientations 1, 2, and 3 are available.)

  Note: For all continuous rotation commands, press any key to stop


(F1 for Help menu; 1 thru 7 for specific Help page; <Esc> to exit Help)
TRANSLATIONS:                                                    Page 5

  0 - Center origin of geometry in display area:
    The geometry's origin is used as the center point for all rotations;
    centering the origin provides equal clearance for rotations in all
    directions.  (Note: Centering the origin is not the same as centering
    the overall image as is performed automatically at start up.  This
    distinction is greater to the extent that the geometry is defined
    asymmetrically with respect to the origin.)

  Arrow keys:
    The function of the Arrow keys depends on the User Interface mode and
    whether a 4-D Projection vertex has been selected for translation:

    For User Interface set to Rotation mode:
      The arrow keys move the displayed image right, up, left, and down.
      In this mode, the translation affects only the position of the display
      on the screen; it does not alter the 4-D geometry or its 3-D image.

    For User Interface set to Translation mode:
      Until a vertex has been selected for translation, the arrow keys
      perform the same function as in Rotation mode.

      While a vertex is selected for translation, the arrow keys are used to
      reposition it along each of the four 4-D coordinate axes:
        Right Arrow - X translation
        Up Arrow    - Y translation
        Left Arrow  - Z translation
        Down Arrow  - W translation

      Note: Shift applied to arrow key reverses translation direction.






(F1 for Help menu; 1 thru 7 for specific Help page; <Esc> to exit Help)
OTHER COMMANDS:                                                  Page 6

  F - File name of new geometry definition to be read:
    Reading in a new geometry file completely reinitializes HYPERGEO; the
    previously active geometry is cleared and the new geometry is displayed.
    Configuration file parameters and command line options are reapplied.
    The file name may include a full DOS path specification; if no extension
    is given, .BIN is assumed.
    HYPERGEO cannot directly read source geometry files (extension .GEO);
    they must first be processed into binary geometry definition files
    (extension .BIN) using the GEO2BIN utility program.
  I - Information on current geometry and display parameters:
    Displays a message window with information about the topology of the
    current geometry: the number of vertex points, edges, faces, and (for
    4-D geometries) hyperfaces.  Additional data items describe the screen
    size and resolution, and show the amount of free memory.
    (This is the same message window that appears automatically each time a
    new geometry definition file is read.)
  J - Journal file to replay:
    A journal file that has previously been recorded can be replayed.  The
    current geometry's display is temporarily overriden during the replay.
    The file name may include a full DOS path specification; if no extension
    is given, .JNL is assumed.
  O - Output graphics in PCX file format:
    The current screen image is written to a file in PCX format.  PCX is a
    standard graphics file format which can be read by many commercial
    word-processing, desk-top publishing, and presentation artwork programs.
    The file name may include a full DOS path specification; if no extension
    is given, .PCX is assumed.
  Q - Quit:
    The HYPERGEO program exits to DOS.
  F1 - Help:
    Displays the top-level Help window which contains the main Help menu.
  F2 - DOS shell:
    A DOS command screen appears temporarily (type EXIT to restore HYPERGEO).


(F1 for Help menu; 1 thru 7 for specific Help page; <Esc> to exit Help)
MENU COMMANDS USING A MOUSE:                                     Page 7
The HYPERGEO menu area displays a number of parameters that reflect the
current state of the geometry.  All of the data items shown in the menu can
be modified interactively by using a mouse (if present) to select the label
of the item in the menu.  The menu area also contains a panel of function
boxes which perform rotations and translations of the geometrical model.

The selectable functions in the HYPERGEO menu area are:

 Item Label      Key     Function
 ____________  _______   __________________________________________________

 GEOMETRY                Select the 4-D imaging mode (list dialog box)
 DISPLAY MODE            Select the display mode (list dialog box)
 EYE DIST      Ins,Del   Adjust the eye-to-screen distance (by 10%)
 SCALE           +,-     Adjust display scale factor (by 10%)
 W_INTER       Pg Up/Dn  Adjust the W-coordinate of the intersecting hyperplane
                         for 4-D Intersections (by the Delta value)
 W_PROJ        Pg Up/Dn  Adjust the W-coordinate of the projection viewpoint
                         for 4-D Projections (by 10%)
 TURN             T      Set the turn angle used by all rotations (degrees)
*AXIS ANG         L      Set the three 3-D or four 4-D axis angles (degrees)
+VERTEX           L      Set the coordinate values of the selected vertex
                         for temporary repositioning (geometry units)
 ROTATIONS:
 3-D AXIS       X,Y,Z    Rotate geometry about selected 3-D axis
*4-D PLANE    F5 to F10  Rotate geometry on selected 4-D plane
+MOVE VERTEX   X,Y,Z,W   Translate the selected vertex along coordinate axis
+Sel             Esc     Position mouse cursor to select new vertex to move
+Nxt            Enter    Select next vertex for moving

     User Interface mode:    * = Rotation;   + = Translation

Note: For mouse rotations and translations, right button is forward action
(i.e., positive angle or coordinate), and left button is reverse action.


(F1 for Help menu; 1 thru 7 for specific Help page; <Esc> to exit Help)
