\chapter{TUTORIALS ON EDITING SOLIDS}

The Solid Editing state of MGED is used to modify the fundamental
parameters of an individual solid.
Each solid must be modified individually.

\section{Solid Edit: A Six-Sided Polyhedron}

\begin{figure}
\centering \includegraphics{es8-top.ps}
\caption{Top View of ARB8.}
\label{es8-top}
\end{figure}

This section illustrates the use of commands while in
SOL EDIT state to alter the
shape of a polyhedron with six sides and 8 faces (ARB8).

\noindent{\tt
\$ {\em mged es.g} \\
BRL-CAD Release 3.0 Graphics Editor (MGED) Compilation 82 \\
    Thu Sep 22 08:08:39 EDT 1988 \\
    mike@video.brl:/cad/.mged.4d2 \\
 \\
es.g: No such file or directory \\
Create new database (y|n)[n]? {\em y} \\
attach (nu|tek|tek4109|ps|plot|sgi)[nu]? {\em sgi} \\
ATTACHING sgi (SGI 4d) \\
Untitled MGED Database (units=mm) \\
mged> {\em in arb8 rpp -1 1 -1 1 -1 1} \\
mged> {\em size 10} \\
mged>
}

Figure \ref{es8-top}
is a top view of the six-sided polyhedron.
The Z-axis perpendicular to the viewing screen.
Next, the view is rotated so that all sides can be seen.

\noindent{\tt
mged> {\em Twist ROTY knob clockwise and restore} \\
mged> {\em Twist ROTX knob counter-clockwise and restore} \\
mged>
}

\begin{figure}
\centering \includegraphics{es8-rot.ps}
\caption{A Rotated View of the ARB8.}
\label{es8-rot}
\end{figure}
Figure \ref{es8-rot} shows a better perspective of the solid.

The next step in this tutorial is to transfer to the solid edit state.
This can be accomplished in two ways:  either by going through
the SOL PICK state (``illuminate mode'') or by direct transfer via
keyboard command.
Using illuminate mode is better when the name of the solid to be
edited may not be known, while the keyboard command is generally
preferred when the name of the solid is known.

\noindent{\tt
mged> {\em Select the ``Solid Illum'' entry in the button menu} \\
mged> {\em Move the mouse out of the menu area} \\
mged> {\em Click the mouse to enter SOL EDIT state} \\
mged>
}

To perform a direct transfer from the viewing state to the solid edit state
using a keyboard command, enter:

\noindent{\tt
mged> {\em sed arb8} \\
mged>
}

\begin{figure}
\centering \includegraphics{es8-sed.ps}
\caption{An ARB8 in Solid Edit State.}
\label{es8-sed}
\end{figure}

Figure \ref{es8-sed} corresponds to the view on the display.
The ARB8 MENU is unique to the ARB primitive,
and lists operations that can only be performed on an ARB solid.
The items in the ARB8 MENU are
selected by using the mouse.
Each of the other types of solids have a
similar unique menu.
When one of these items is selected, the top level ARB8 MENU disappears,
to be replaced with the indicated subordinate menu.
The top-level menu reappears when either
the ``edit menu'' item in the SOLID EDIT menu is selected,
or the ``RETURN'' item in the subordinate menu is selected.

The  SOLID EDIT  menu applies to all
solids when in the SOL EDIT state.
The items in the  SOLID EDIT  menu are selected
by either using the mouse or by depressing the appropriate button on the
button box.
When any of the SOLID EDIT menu items are selected
(eg, ``Rotate'', ``Translate'', ``Scale''), the solid-specific menu
disappears.
Th top-level solid-specific menu reappears when
the ``edit menu'' item in the SOLID EDIT menu is selected.

The {\em p [params]} command is used to
make precise changes, where the numeric value of the parameter being
edited is know.
Values for all parameters in the ARB8
and SOLID EDIT menus can be specified by using the {\em p} command,
or by pointing and clicking with the mouse.

\begin{figure}
\centering \includegraphics{es8-tr0.ps}
\caption{Translating ARB8 Point 1 to the Origin.}
\label{es8-tr0}
\end{figure}

\subsection{Translate Operation}

\noindent{\tt
mged> {\em Select the ``Translate'' entry in the solid edit menu} \\
mged> {\em p 0 0 0} \\
mged>
}

Point 1 of the primitive is moved to point 0 0 0,
as shown in Figure \ref{es8-tr0}.

The translate solid operation is selected
by either picking ``Translate'' on the solid edit menu
with the mouse, by depressing the solid edit button on the button box,
or by entering the {\em press sed} command.
Parameters to the translate solid operation
are of the form {\em p a b c}
where {\em a}, {\em b}, and {\em c} are the new coordinates
of point 1 in the solid.
The other points are transferred to keep the same position
relative to point 1.
The general form of the new coordinates for point is

\begin{center}
\begin{verbatim}
x ' = x + a - x
y ' = y + b - y
Z ' = Z + c - Z
\end{verbatim}
\end{center}

The command

\noindent{\tt
mged> {\em p 1 -1 -1} \\
mged>
}

can be used to restore the primitive to the original position.

\subsection{Rotate Operation}

\begin{figure}
\centering \includegraphics{es8-xrot.ps}
\caption{Solid Edit Rotation of 45 Degrees about X.}
\label{es8-xrot}
\end{figure}

The rotate operation is initiated by either selecting Rotate on the menu
screen with the mouse,
by depressing the Solid Rotate button on the button box,
or by entering the {\em press srot} command on the keyboard.

\noindent{\tt
mged> {\em Select the ``Rotate'' entry in the solid edit menu} \\
mged> {\em p 45 0 0} \\
mged>
}

The parameter {\em p} command is used to make precise rotation changes.
The
command is entered in the form {\em p a b c} where
{\em a}, {\em b}, and {\em c} are the angles
(in degrees) of rotation about the x, y, and z axes respectively.  Point 1,
the vertex, remains fixed, and the solid is rotated about this point.  A
positive angle of rotation is counter-clockwise when viewed in the positive
direction along an axis.

The order of rotation is not commutative.
Rotation takes place about the
Z axis, Y axis, and X axis in that order.
Figure \ref{es8-xrot} shows the rotation of 45 degrees about the X axis.

%The following is the formula for moving point (x,y,z) through angles
%(a, b, c) to point (x', y', z')
%\begin{verbatim}
%[X'] [cos b cos c                     -cos b sin c        sin b        ][X]
%[Y']=[sin a sin b cos c +cos a sin b   cos a cos c -sin a sin b sin c -sin a cos b ][Y]
%[Z'] [sin a sin c -cos a sin b cos c   cos a sin b sin c + sin a cos c cos a cos b ][Z]
%\end{verbatim}

The values entered after the p are absolute - the rotations are applied to
the primitive as it existed when solid rotation was first selected.  Thus
entering {\em p 0 0 0} will undo any rotations
performed since solid rotation was begun.

\begin{figure}
\centering \includegraphics{es8-yrot.ps}
\caption{Solid Edit Rotation of 45 Degrees about Y.}
\label{es8-yrot}
\end{figure}

\begin{figure}
\centering \includegraphics{es8-zrot.ps}
\caption{Solid Edit Rotation of 45 Degrees about Z.}
\label{es8-zrot}
\end{figure}

\noindent{\tt
mged> {\em p 0 45 0} \\
mged>
}

Figure \ref{es8-yrot} displays the solid
after it has been rotated about the Y axis.

\noindent{\tt
mged> {\em p 0 0 45} \\
mged>
}

Figure \ref{es8-zrot} displays the solid
after it has been rotated about the Z axis.

\noindent{\tt
mged> {\em p 0 0 0} \\
mged>
}

This restores the original orientation of the solid.

\subsection{Scale Operation}

\begin{figure}
\centering \includegraphics{es8-scale.ps}
\caption{ARB8 Scale Increased by 2X.}
\label{es8-scale}
\end{figure}

\noindent{\tt
mged> {\em Select the ``Scale'' entry in the solid edit menu} \\
mged> {\em p 2} \\
mged>
}

Figure \ref{es8-scale} corresponds to the view that is shown on the display.
The scale operation may be initiated by either selecting
the Scale entry  on the menu with the mouse,
by depressing the Solid Scale button,
or by entering {\em press sscale} on the keyboard.
The parameter command {\em p n} is
used to enter a precise scale factors, where {\em n} is
the scale factor.
The coordinates of point 1 remain the same.  The distances
from point 1 to the other points are multiplied by the scale value {\em n}.
The general equations for the transformation from point p to p' are

\begin{verbatim}
    x'[i] = x[i] + n (x[i] - x[1] )
    y'[i] = y[i] + n (y[i] - y[1] )   i != 1
    z'[i] = z[i] + n (z[i] - z[1] )
\end{verbatim}

The size of the primitive may be changed by depressing the mouse at
different positions.  When the mouse is clicked, the
edited primitive is scaled about point 1 (the key point)
by an amount proportional
to the distance the mouse is from the center of the screen.  If the mouse
is above the center of the screen, the edited primitive will become larger.
If the
mouse is below the center, the primitive will become smaller.

The value of {\em n} entered is applied to the primitive as it existed when the
solid scale state was entered.

Entering {\em p 1} will return the primitive
to the size it had when the solid scale operation first started.

\noindent{\tt
mged> {\em p 1} \\
mged>
}

\begin{figure}
\centering \includegraphics{es8-edge1.ps}
\caption{ARB8 Edge 15 Moved Through (9, -2, -2).}
\label{es8-edge1}
\end{figure}

\begin{figure}
\centering \includegraphics{es8-edge2.ps}
\caption{ARB8 Edge 12 Moved Through (2, 5, -2).}
\label{es8-edge2}
\end{figure}

\begin{figure}
\centering \includegraphics{es8-edge3.ps}
\caption{ARB8 Edge 14 Moved Through (2, -2, 7).}
\label{es8-edge3}
\end{figure}

\subsection{Moving Edges}

The move edge command permits the moving of a line or edge so that the
line passes through the selected point.

\noindent{\tt
mged> {\em Select the ``edit menu'' entry in the solid edit menu} \\
mged> {\em Select the ``move edges'' entry in the ARB menu} \\
mged> {\em Select the ``move edge 15'' entry in the ARB8 edges menu} \\
mged> {\em p 9 -2 -2} \\
mged>
}

The edge 15 is moved so that it passes through the point (9, -2, -2).  The
coordinates of the new points 1 and 5 are the intersection of the new edge
with the planes 234 and 678.  Since both the old edge and new edge 15 are
parallel to the X axis,
the X coordinate of the point given by the {\em p} command
has no meaning.  The X coordinates for points 1 and 5 are not changed.
See Figure \ref{es8-edge1}.

\noindent{\tt
mged> {\em p 9 -1 -1} \\
mged>
}

This restores the original shape.
The choice of ``9'' for the X coordinate was arbitrary.

\noindent{\tt
mged> {\em Select the ``move edge 12'' entry in the ARB8 edges menu} \\
mged> {\em p 2 5 -2} \\
mged>
}

The edge 12 is parallel to the Y axis.  This command moves the points 1
and 2 so that their X and Z coordinates are 2 and -2.
See Figure \ref{es8-edge2}.
The Y coordinates are not changed.

To restore the view, enter:

\noindent{\tt
mged> {\em p 1 5 -1} \\
mged>
}

The choice of ``5'' for the Y coordinate was arbitrary.

\noindent{\tt
mged> {\em Select the ``move edge 14'' entry in the ARB8 edges menu} \\
mged> {\em p 2 -2 7} \\
mged>
}

The edge 14 is parallel to the Z axis.
This command moves the points 1
and 4 so that their X and Y coordinates are 2 and -2.
See Figure \ref{es8-edge3}.
The Z coordinates are not changed.

\noindent{\tt
mged> {\em p 1 -1 7} \\
mged>
}

This restores the original shape.
The choice of ``7'' for the Z coordinate was arbitrary.

\subsection{Extrude Command}

\begin{figure}
\centering \includegraphics{es8-ex1.ps}
\caption{ARB8 Rear Face Extruded 5 Units in -Z.}
\label{es8-ex1}
\end{figure}

\begin{figure}
\centering \includegraphics{es8-ex2.ps}
\caption{ARB8 Rear Face Extruded 3 Units in +Z.}
\label{es8-ex2}
\end{figure}

The extrude command is used to move the opposite surface a distance from
the specified surface or plate.
This command can only be used when an ARB solid is in
solid edit state.

\noindent{\tt
mged> {\em extrude 1265 5} \\
mged>
}

In Figure \ref{es8-ex1},
the plane opposite surface whose points are 1, 2, 6, and 5
is moved to a distance of 5 in the positive Z direction from plane 1265.  Note
that the points were selected counter-clockwise when viewed in the positive
direction along the Z axis.

\noindent{\tt
mged> {\em extrude 1562 3} \\
mged>
}

In Figure \ref{es8-ex2},
the plane opposite surface 1562 is moved to a distance of 3
in the negative Z direction from 1562.  Note that the points were selected
clockwise when viewed in the positive direction along the Z axis.

\noindent{\tt
mged> {\em extrude 1265 2} \\
mged>
}

This restores the original shape of this solid.

To return control to the VIEWING state, select the ``REJECT Edit''
item on the button menu, press the ``reject'' button on the button box,
or enter the command {\em press reject} on the keyboard.
Then, enter

\noindent{\tt
mged> {\em d arb8} \\
mged>
}

to drop the ARB8 from view.

\section{Solid Edit:  A Five-Sided Polyhedron}

\begin{figure}
\centering \includegraphics{es5-top.ps}
\caption{Top View of an ARB5.}
\label{es5-top}
\end{figure}

\begin{figure}
\centering \includegraphics{es5-rot.ps}
\caption{A Rotated View of the ARB5.}
\label{es5-rot}
\end{figure}

\begin{figure}
\centering \includegraphics{es5-sed.ps}
\caption{The ARB5 in Solid Edit State.}
\label{es5-sed}
\end{figure}

This tutorial illustrates the application of the SOL EDIT state to the ARB5
solid.
In this tutorial, the view is modified by using the rotation
knobs so that all sides can be seen.

\noindent{\tt
mged> {\em size 6} \\
mged> {\em in arb5 arb5} \\
Enter X, Y, Z for point 1: {\em 0 0 0} \\
Enter X, Y, Z for point 2: {\em 0 0 1} \\
Enter X, Y, Z for point 3: {\em 0 1 1} \\
Enter X, Y, Z for point 4: {\em 0 1 0} \\
Enter X, Y, Z for point 5: {\em -1 .5 .5} \\
mged>
}

Figure \ref{es5-top} is the display of arb5
in the VIEWING state that is seen when
the solid is first created.
In this view, the Z axis is perpendicular to the viewing screen.

\noindent{\tt
mged> {\em Twist ROTY knob clockwise and restore} \\
mged> {\em Twist ROTX knob counter-clockwise and restore} \\
mged>
}

These actions generate a view shown in Figure \ref{es5-rot}
that shows all sides.

\noindent{\tt
mged> {\em Select the ``Solid Illum'' entry in the button menu} \\
mged> {\em Move the mouse out of the menu area} \\
mged> {\em Click the mouse to enter SOL EDIT state} \\
mged>
}

These actions will place MGED in the SOL EDIT state
as shown in Figure \ref{es5-sed}.

\subsection{Translate Operation}

\begin{figure}
\centering \includegraphics{es5-tr.ps}
\caption{Translating an ARB5.}
\label{es5-tr}
\end{figure}

\noindent{\tt
mged> {\em Select the ``Translate'' entry in the solid edit menu} \\
mged> {\em p -1 -1 1} \\
mged>
}

This command cause point 1 to be moved to coordinates (-1, -1, 1) and the
other points are moved so that they keep the same relative position to point
1.  See Figure \ref{es5-tr}.

Enter this command to restore the solid to it's original location:

\noindent{\tt
mged> {\em p 0 0 0} \\
mged>
}

\subsection{Rotate Operation}

\begin{figure}
\centering \includegraphics{es5-xrot.ps}
\caption{ARB5 Solid Edit Rotation about X.}
\label{es5-xrot}
\end{figure}

\noindent{\tt
mged> {\em Select the ``Rotate'' entry in the solid edit menu} \\
mged> {\em p 45 0 0} \\
mged>
}

Figure \ref{es5-xrot} shows a rotation of 45 degrees
about an axis parallel to the X axis.
The rotate command is entered in the form {\em p a b c}
where {\em a}, {\em b}, and {\em c} are the angles
(in degrees) of rotation about the x, y, and z axes and intersect at point 1.
All rotation takes place about point 1.

\noindent{\tt
mged> {\em p 0 0 0} \\
mged>
}

This restores the original orientation of the solid.

\subsection{Scale Operation}

\begin{figure}
\centering \includegraphics{es5-scale.ps}
\caption{ARB5 Scale Increased by 2X.}
\label{es5-scale}
\end{figure}

\noindent{\tt
mged> {\em Select the ``Scale'' entry in the solid edit menu} \\
mged> {\em p 2} \\
mged>
}

Figure \ref{es5-scale} shows the change in the primitive.
Point 1 remains the same
and the distances of the other points from point 1 is multiplied by 2.

Entering {\em p 1} will return the primitive
to the size it had when the solid scale operation first started.

\noindent{\tt
mged> {\em p 1} \\
mged>
}

\subsection{Move Edge Command}

\begin{figure}
\centering \includegraphics{es5-edge1.ps}
\caption{ARB5 Edge 14 Moved Through (1, 1, 1).}
\label{es5-edge1}
\end{figure}

\begin{figure}
\centering \includegraphics{es5-edge2.ps}
\caption{ARB5 Point 5 Moved to (-1.5, 1, 1).}
\label{es5-edge2}
\end{figure}

\begin{figure}
\centering \includegraphics{es5-edge3.ps}
\caption{ARB5 Edge 45 Moved Through (-1.5 1 1).}
\label{es5-edge3}
\end{figure}

\begin{figure}
\centering \includegraphics{es5-edge4.ps}
\caption{ARB5 Edge 12 Moved Through (2, 1, 2).}
\label{es5-edge4}
\end{figure}

\noindent{\tt
mged> {\em Select the ``edit menu'' entry in the solid edit menu} \\
mged> {\em Select the ``move edges'' entry in the ARB menu} \\
mged> {\em Select the ``move edge 14'' entry in the ARB8 edges menu} \\
mged> {\em p 1 1 1} \\
mged>
}

The edge 14 is moved so that it moves through the point (1, 1, 1).
Note that this point is the mid-point between points 1 and 4.
See Figure \ref{es5-edge1}.

\noindent{\tt
mged> {\em p 0 2 0} \\
mged>
}

This restores the original shape.

\noindent{\tt
mged> {\em Select the ``move point 5'' entry in the ARB5 edges menu} \\
mged> {\em p -1.5 1 1} \\
mged>
}

The point 5 is moved to location -1.5, 1, 1.  See Figure \ref{es5-edge2}.

\noindent{\tt
mged> {\em p -1 .5 .5} \\
mged>
}

will restore the original shape.

\noindent{\tt
mged> {\em Select the ``move edge 45'' entry in the ARB5 edges menu} \\
mged> {\em p -1.5 1 1} \\
mged>
}

In Figure \ref{es5-edge3}, the edge 45 is moved
so that it passes through the point (-1.5, 1, 1).
Note that this point lies between the points 4 and 5.

\noindent{\tt
mged> {\em p -1 .5 .5} \\
mged>
}

This restores the original shape.

\noindent{\tt
mged> {\em Select the ``move edge 12'' entry in the ARB5 edges menu} \\
mged> {\em p 2 1 2} \\
mged>
}

In Figure \ref{es5-edge4},
the edge 12 is moved so that it passes through the point (2, 1, 2).
Note that the coordinates correspond to point 2.

The movement of the edges may yield unpredictable results when the edges
are not parallel to one of the axes.


To return control to the VIEWING state, select the ``REJECT Edit''
item on the button menu, press the ``reject'' button on the button box,
or enter the command {\em press reject} on the keyboard.
Then, enter

\noindent{\tt
mged> {\em d arb5} \\
mged>
}

to drop the ARB5 from view.

\section{Solid Edit: Alter a Cylinder}

\begin{figure}
\centering \includegraphics{esc-top.ps}
\caption{Top View of a Cylinder.}
\label{esc-top}
\end{figure}

\begin{figure}
\centering \includegraphics{esc-rot.ps}
\caption{A Rotated View of the Cylinder.}
\label{esc-rot}
\end{figure}

\begin{figure}
\centering \includegraphics{esc-sed.ps}
\caption{A Cylinder in Solid Edit State.}
\label{esc-sed}
\end{figure}

This tutorial illustrates the application of the SOL EDIT state to
cylinder solids.

\noindent{\tt
mged> {\em size 12} \\
mged> {\em in cyl rcc} \\
Enter X, Y, Z of vertex: {\em 0 0 0} \\
Enter X, Y, Z of height (H) vector: {\em 2 0 0} \\
Enter radius: {\em 1}
mged>
}

Figure \ref{esc-top} is the display of the cylinder solid
when viewed from the top.
Since the
Z axis is perpendicular to the viewing screen, a view of all sides cannot be
seen.

\noindent{\tt
mged> {\em Twist ROTY knob clockwise and restore} \\
mged> {\em Twist ROTX knob counter-clockwise and restore} \\
mged>
}

These actions generate a view, Figure \ref{esc-rot}, that shows all sides.

\noindent{\tt
mged> {\em Select the ``Solid Illum'' entry in the button menu} \\
mged> {\em Move the mouse out of the menu area} \\
mged> {\em Click the mouse to enter SOL EDIT state} \\
mged>
}

Figure \ref{esc-sed} is the view that displays the menu
for the SOL EDIT state.
The
point V is at the origin (0,0,0) in this example and is in the middle of the
circle that contains points A and B.  H is the point of the center of the
circle that contains points C and D.  The coordinates of H are the coordinates
of the vector from V to H and represent the relative position of H to V.  Mag
is the magnitude of these vectors and is represented by the formula
\begin{center}
\begin{verbatim}
Mag = sqrt( x + y + z )
\end{verbatim}
\end{center}

``H dir cos'' are the direction cosines of the vector H which
is perpendicular to plane of the points A, B, and V.  The coordinates of A
are the coordinates of the vector from V through A.  Mag is the magnitude of
the vectors from V to A.  The coordinates of B are the coordinates of the
vectors from V through B.  Mag is the magnitude of the vector from V to B.
The values for c and d are the magnitudes of the vectors from the tip of
vector H to the points C
and D respectively.
``A x B dir cos'' represents the direction cosines of the
vector ``A x B''.

\subsection{Translate Operation}

\begin{figure}
\centering \includegraphics{esc-tr.ps}
\caption{Translating Cylinder Vertex to (1, 1, 1).}
\label{esc-tr}
\end{figure}

\noindent{\tt
mged> {\em Select the ``Translate'' entry in the solid edit menu} \\
mged> {\em p 1 1 1} \\
mged>
}

The location of the vertex point V is moved to (1, 1, 1).
The locations of the other
points relative to V remains the same.  See Figure \ref{esc-tr}.

Move the mouse anywhere on the screen (outside the menu area), and click.
Notice
that the cylinder is moved so that V is placed at this location, and the
coordinates of the other points remain the same relative to V.

\noindent{\tt
mged> {\em p 0 0 0} \\
mged>
}

This restores the solid to the original location.

\subsection{Rotate Operation}

\begin{figure}
\centering \includegraphics{esc-xrot.ps}
\caption{Solid Edit Rotation of 45 Degrees about X.}
\label{esc-xrot}
\end{figure}

\begin{figure}
\centering \includegraphics{esc-yrot.ps}
\caption{Solid Edit Rotation of 45 Degrees about Y.}
\label{esc-yrot}
\end{figure}

\begin{figure}
\centering \includegraphics{esc-zrot.ps}
\caption{Solid Edit Rotation of 45 Degrees about Z.}
\label{esc-zrot}
\end{figure}

\noindent{\tt
mged> {\em Select the ``Rotate'' entry in the solid edit menu} \\
mged> {\em p 45 0 0} \\
mged>
}

When viewing in the positive X direction, the cylinder is rotated counter-
clockwise 45 degrees about an axis through point V parallel to the x axis.
See Figure \ref{esc-xrot}.

\noindent{\tt
mged> {\em p 0 45 0} \\
mged>
}

When viewing in the positive Y direction, the cylinder is rotated counter-
clockwise 45 degrees about an axis through point V parallel to the Y axis.
See Figure \ref{esc-yrot}.

\noindent{\tt
mged> {\em p 0 0 45} \\
mged>
}

When viewing in the positive Z direction, the cylinder is rotated counter-
clockwise 45 degrees about an axis through point V parallel to the Z axis.
See Figure \ref{esc-zrot}.

The command

\noindent{\tt
mged> {\em p 0 0 0} \\
mged>
}

will restore the cylinder to the original orientation.

\subsection{Scale Operation}

\begin{figure}
\centering \includegraphics{esc-scale.ps}
\caption{Cylinder Scale Increased by 1.5X.}
\label{esc-scale}
\end{figure}

\noindent{\tt
mged> {\em Select the ``Scale'' entry in the solid edit menu} \\
mged> {\em p 1.5} \\
mged>
}

The point V remains fixed, the distance H between the two end-plate ellipses
is multiplied by 1.5.
See Figure \ref{esc-scale}.

The command

\noindent{\tt
mged> {\em p 1} \\
mged>
}

restores the original scale.

\subsection{Scale H Command}

\begin{figure}
\centering \includegraphics{esc-sh.ps}
\caption{Cylinder Scale H Vector.}
\label{esc-sh}
\end{figure}

\noindent{\tt
mged> {\em Select the ``edit menu'' entry in the solid edit menu} \\
mged> {\em Select the ``scale H'' entry in the TGC menu} \\
mged> {\em p 1} \\
mged>
}

The magnitude of the vector H is reduced from 2 to 1.
See Figure \ref{esc-sh}.  The command

\noindent{\tt
mged> {\em p 2} \\
mged>
}

will restore the original shape.

\subsection{Scale A Command}

\begin{figure}
\centering \includegraphics{esc-sa.ps}
\caption{Cylinder Scale A Vector.}
\label{esc-sa}
\end{figure}

\noindent{\tt
mged> {\em Select the ``scale A'' entry in the TGC menu} \\
mged> {\em p 2} \\
mged>
}

The magnitude of the vector through point A is increased to 2, ie,
the length of the axis of the ellipse through point A is set equal to p.
See Figure \ref{esc-sa}.  The command

\noindent{\tt
mged> {\em p 1} \\
mged>
}

will restore the original shape.

\subsection{Scale B Command}

\begin{figure}
\centering \includegraphics{esc-sb.ps}
\caption{Cylinder Scale B Vector.}
\label{esc-sb}
\end{figure}

\noindent{\tt
mged> {\em Select the ``scale B'' entry in the TGC menu} \\
mged> {\em p 2} \\
mged>
}

The magnitude of the vector through point B is increased to 2, ie,
the length of the axis of the ellipse through point B is set equal to p.
See Figure \ref{esc-sb}.  The command

\noindent{\tt
mged> {\em p 1} \\
mged>
}

will restore the original shape.

\subsection{Scale C Command}

\begin{figure}
\centering \includegraphics{esc-sc.ps}
\caption{Cylinder Scale C Vector.}
\label{esc-sc}
\end{figure}

\noindent{\tt
mged> {\em Select the ``scale C'' entry in the TGC menu} \\
mged> {\em p 2} \\
mged>
}

The magnitude of the vector through point c is increased to the value of
p.  The length of the axis of the ellipse through point c is set equal to the
value of p.  See Figure \ref{esc-sc}.  The command

\noindent{\tt
mged> {\em p 1} \\
mged>
}

will restore the original shape.

\subsection{Scale D Command}

\begin{figure}
\centering \includegraphics{esc-sd.ps}
\caption{Cylinder Scale D Vector.}
\label{esc-sd}
\end{figure}

\noindent{\tt
mged> {\em Select the ``scale D'' entry in the TGC menu} \\
mged> {\em p 2} \\
mged>
}

The magnitude of the vector through point D is changed to the value of p.
The length of the axis of the ellipse through point D is set equal to the
value of p.  See Figure \ref{esc-sd}.  The command

\noindent{\tt
mged> {\em p 1} \\
mged>
}

will restore the original shape.

The scale H, A, B, C, and D commands provide for setting the magnitude
equal to the value entered by the {\em p} command.
The solid edit {\bf scale} operation provides
for multiplying {\bf all} the vectors by the value
entered by the {\em p} command.

\subsection{Move End H Command}

\begin{figure}
\centering \includegraphics{esc-mh.ps}
\caption{Cylinder Move End of H.}
\label{esc-mh}
\end{figure}

\noindent{\tt
mged> {\em Select the ``move end H'' entry in the TGC menu} \\
mged> {\em p 3} \\
mged>
}

The length of the vector H is changed to the value of p.
See Figure \ref{esc-mh}.  The command

\noindent{\tt
mged> {\em p 2} \\
mged>
}

will restore the original shape.

\subsection{Move End H (rt) Command}

\begin{figure}
\centering \includegraphics{esc-mhrt.ps}
\caption{Cylinder Move End of H \& Rotate.}
\label{esc-mhrt}
\end{figure}

\noindent{\tt
mged> {\em Select the ``move end H(rt)'' entry in the TGC menu} \\
mged> {\em p 3} \\
mged>
}

This command is similar to the ``move end H'' command except the vector
through point A is rotated so its direction is in the -Y direction.
See Figure \ref{esc-mhrt}.  The command

\noindent{\tt
mged> {\em p 2} \\
mged>
}

will restore the original shape, but not the original orientation.

To return control to the VIEWING state, select the ``REJECT Edit''
item on the button menu, press the ``reject'' button on the button box,
or enter the command {\em press reject} on the keyboard.
Then, enter

\noindent{\tt
mged> {\em d cyl} \\
mged>
}

to drop the cylinder from view.

\section{Solid Edit: Alter Ellipsoid}

\begin{figure}
\centering \includegraphics{ese-top.ps}
\caption{Top View of an Ellipsoid.}
\label{ese-top}
\end{figure}

\begin{figure}
\centering \includegraphics{ese-sed.ps}
\caption{An Ellipsoid in Solid Edit State.}
\label{ese-sed}
\end{figure}

This tutorial illustrates the application of the SOL EDIT state to the
ellipsoid primitive.

\noindent{\tt
mged> press reset
mged> {\em size 6} \\
mged> {\em in ell ellg} \\
Enter X, Y, Z of vertex: {\em 0 0 0} \\
Enter X, Y, Z of vector A: {\em 1 0 0} \\
Enter X, Y, Z of vector B: {\em 0 .3536 -0.3536} \\
Enter X, Y, Z of vector C: {\em 0 .3536  0.3536} \\
mged>
}

Figure \ref{ese-top} is the display of the primitive in the viewing state.
Since the
Z axis is perpendicular to the viewing screen, a view of all sides cannot be
seen.

\noindent{\tt
mged> {\em Twist ROTY knob clockwise and restore} \\
mged> {\em Twist ROTX knob counter-clockwise and restore} \\
mged>
}

These actions generate a view that shows all sides.

\noindent{\tt
mged> {\em Select the ``Solid Illum'' entry in the button menu} \\
mged> {\em Move the mouse out of the menu area} \\
mged> {\em Click the mouse to enter SOL EDIT state} \\
mged>
}

The display will be changed from the VIEWING MODE through the SOL PICK to
the SOL EDIT state.  Figure \ref{ese-sed} is the view that is displayed.

The coordinates of the points A, B, C, are given by the product of the
magnitude of the vector and the cosine of X, Y, and Z direction cosines.  In
the display, the coordinates are:

\begin{center}
\begin{verbatim}
A = (1, 0, 0)
B = (0, 0.3536, -0.3536)
C = (0, 0.3536,  0.3536)
\end{verbatim}
\end{center}
or
\begin{center}
\begin{verbatim}
A = ( 1* cos  0,  1* cos 90,   1* cos 90 )
B = (.5* cos 90, .5* cos 45, -.5* cos 45 )
C = (.5* cos 90, .5* cos 45,  .5* cos 45 )
\end{verbatim}
\end{center}

\subsection{Translate Operation}

\begin{figure}
\centering \includegraphics{ese-tr.ps}
\caption{Translating Ellipsoid to (-1, 1, 1).}
\label{ese-tr}
\end{figure}

\noindent{\tt
mged> {\em Select the ``Translate'' entry in the solid edit menu} \\
mged> {\em p -1 1 1} \\
mged>
}

The key point V is moved to (-1, 1, 1) and the ellipsoid maintains its
relative position to V.  See Figure \ref{ese-tr}.

While in the SOL EDIT state, the solid may be translated by
using the mouse.  These changes are not numerically exact, but they can be
useful to visually position a solid with respect to other solids.
Move the mouse to a position outside the menu area on the screen.
Click the mouse.
The center point (V) of the ellipsoid will be translated to that point.
Note that only the value of the coordinates of V are changed.
The command

\noindent{\tt
mged> {\em p 0 0 0} \\
mged>
}

will restore the original position.

\subsection{Rotate Operation}

\begin{figure}
\centering \includegraphics{ese-xrot.ps}
\caption{Solid Edit Rotation of 45 Degrees about X.}
\label{ese-xrot}
\end{figure}

\begin{figure}
\centering \includegraphics{ese-yrot.ps}
\caption{Solid Edit Rotation of 45 Degrees about Y.}
\label{ese-yrot}
\end{figure}

\begin{figure}
\centering \includegraphics{ese-zrot.ps}
\caption{Solid Edit Rotation of 45 Degrees about Z.}
\label{ese-zrot}
\end{figure}

The rotate operation is initiated by either selecting Rotate on the menu
screen with the mouse,
by depressing the Solid Rotate button on the button box,
or by entering the {\em press srot} command on the keyboard.

\noindent{\tt
mged> {\em Select the ``Rotate'' entry in the solid edit menu} \\
mged> {\em p 45 0 0} \\
mged>
}

Figure \ref{ese-xrot} shows the rotation of the ellipsoid about its X axis.
The angle of rotation is counter-clockwise when viewed in the positive X
direction.  The direction cosines of vectors VB and VC are changed by 45 .

\noindent{\tt
mged> {\em Select the ``Rotate'' entry in the solid edit menu} \\
mged> {\em p 0 45 0} \\
mged>
}

Figure \ref{ese-yrot} shows the rotation of the ellipsoid about its Y axis.
The angle
of rotation is counter-clockwise when viewed in the positive Y direction.  The
rotation is made from the original view, and the restoration of the view is
not necessary.

\noindent{\tt
mged> {\em Select the ``Rotate'' entry in the solid edit menu} \\
mged> {\em p 0 0 45} \\
mged>
}

Figure \ref{ese-zrot} shows the rotation of the ellipsoid about its Z axis.
The axis
of rotation is counter-clockwise when viewed in the positive Z direction.
The command

\noindent{\tt
mged> {\em p 0 0 0} \\
mged>
}

restores the original orientation of the solid.

\subsection{Scale Operation}

\begin{figure}
\centering \includegraphics{ese-scale.ps}
\caption{Ellipsoid Scale Decreased.}
\label{ese-scale}
\end{figure}

\noindent{\tt
mged> {\em Select the ``Scale'' entry in the solid edit menu} \\
mged> {\em p .5} \\
mged>
}

Point V is not changed,
but the distance from V to the surface of the ellipsoid is multiplied by 0.5,
because the magnitude of the vectors are multiplied by the value of 0.5.
See Figure \ref{ese-scale}.

Move the mouse to a position outside the menu area and above the X axis,
and click the mouse.
Notice that the size of the ellipsoid has grown, ie,
the magnitude of the vectors have increased.
Move the mouse to a position below the X axis, and click the mouse.
Notice that the size of the ellipsoid has increased.

The command

\noindent{\tt
mged> {\em p 1} \\
mged>
}

will restore the original scale.

NOTE:
The use
of the scale operation from the Solid Edit menu
will result in the values of all the vectors being
multiplied by the value of the scale.
Use of the scale operaton from the Ellipsoid menu
with a particular vector A, B, or C changes the
magnitude of that vector to the value of the scale.

\subsection{Scale A Command}

\begin{figure}
\centering \includegraphics{ese-sa.ps}
\caption{Ellipsoid Scale A Vector.}
\label{ese-sa}
\end{figure}

\noindent{\tt
mged> {\em Select the ``edit menu'' entry in the solid edit menu} \\
mged> {\em Select the ``scale A'' entry in the ellipsoid menu} \\
mged> {\em p 1.5} \\
mged>
}

The magnitude of the vector to point A is set equal to the value of p
(eg 1.5).
The components of the vector are (1.5, 0, 0) since the vector was
parallel to the X axis.  See Figure \ref{ese-sa}.  The command

\noindent{\tt
mged> {\em Select the ``scale A'' entry in the TGC menu} \\
mged> {\em p 1} \\
mged>
}

will restore the original shape.

\subsection{Scale B Command}

\begin{figure}
\centering \includegraphics{ese-sb.ps}
\caption{Ellipsoid Scale B Vector.}
\label{ese-sb}
\end{figure}

\noindent{\tt
mged> {\em Select the ``scale B'' entry in the Ellipsoid menu} \\
mged> {\em p 1.5} \\
mged>
}

The magnitude of the vector to point B is set equal to the value of p
(eg 1.5).
The coordinates of the vector are the product of p and the
direction cosines of B.  See Figure \ref{ese-sb}.  The command

\noindent{\tt
mged> {\em p 0.5} \\
mged>
}

will restore the original shape.

\subsection{Scale C Command}

\begin{figure}
\centering \includegraphics{ese-sc.ps}
\caption{Ellipsoid Scale C Vector.}
\label{ese-sc}
\end{figure}

\noindent{\tt
mged> {\em Select the ``scale C'' entry in the Ellipsoid menu} \\
mged> {\em p 1.5} \\
mged>
}

The magnitude of the vector to point C is set equal to the value of p
(ie, 1.5).
The coordinates of the vector are the product of p and the
direction cosines of C.  See Figure \ref{ese-sc}.  The command

\noindent{\tt
mged> {\em p 0.5} \\
mged>
}

will restore the original shape.

To return control to the VIEWING state, select the ``REJECT Edit''
item on the button menu, press the ``reject'' button on the button box,
or enter the command {\em press reject} on the keyboard.
Then, enter

\noindent{\tt
mged> {\em d ell} \\
mged>
}

to drop the ellipsoid from view.

\section{Solid Edit: Alter Torus}

\begin{figure}
\centering \includegraphics{est-top.ps}
\caption{Top View of a Torus.}
\label{est-top}
\end{figure}

\begin{figure}
\centering \includegraphics{est-sed.ps}
\caption{The Torus in Solid Edit State.}
\label{est-sed}
\end{figure}

This tutorial illustrates the application of the SOL EDIT state to the
torus solid.

\noindent{\tt
mged> {\em size 6} \\
mged> {\em in tor tor} \\
Enter X, Y, Z of vertex: {\em 0 0 0} \\
Enter X, Y, Z of normal vector: {\em 0 1 0} \\
Enter radius 1: {\em 1} \\
Enter radius 2: {\em 0.2} \\
mged>
}

Figure \ref{est-top} is the display of the torus solid in viewing state.
Since the
Z-axis is perpendicular to the viewing screen, a view of all sides cannot be
seen.

\noindent{\tt
mged> {\em Twist ROTY knob clockwise and restore} \\
mged> {\em Twist ROTX knob counter-clockwise and restore} \\
mged>
}

These actions generate a view of the torus that shows all sides,
as shown in Figure \ref{est-sed}.

\noindent{\tt
mged> {\em Select the ``Solid Illum'' entry in the button menu} \\
mged> {\em Move the mouse out of the menu area} \\
mged> {\em Click the mouse to enter SOL EDIT state} \\
mged>
}

The torus is a ring whose cross-section is a circle.  The distance from
the vertex to the center of the cross-section is r1 and r2 is the radius of
the circular cross section.

Let the points I and O be the intersection of the line x=-z and the torus.
Then,
\begin{center}
\begin{verbatim}
I = (-(r2-r1) cos 45, 0, (r2-r1) cos 45 )
O = (-(r2+r1) cos 45, 0, (r2+r1) cos 45 )
\end{verbatim}
\end{center}

\subsection{Translate Operation}

\begin{figure}
\centering \includegraphics{est-tr.ps}
\caption{Translating a Torus.}
\label{est-tr}
\end{figure}

\noindent{\tt
mged> {\em Select the ``Translate'' entry in the solid edit menu} \\
mged> {\em p -.5 -1 .5} \\
mged>
}

The vertex V of the torus is moved to (-.5, -1, .5).
See figure \ref{est-tr}.  The
coordinates of the other points remain the same, relative to the vertex.
The command

\noindent{\tt
mged> {\em p 0 0 0} \\
mged>
}

will restore the original position.

\subsection{Rotate Operation}

\begin{figure}
\centering \includegraphics{est-xrot.ps}
\caption{Torus Solid Edit Rotation about X.}
\label{est-xrot}
\end{figure}

\begin{figure}
\centering \includegraphics{est-yrot.ps}
\caption{Torus Solid Edit Rotation about Y.}
\label{est-yrot}
\end{figure}

\begin{figure}
\centering \includegraphics{est-zrot.ps}
\caption{Torus Solid Edit Rotation about Z.}
\label{est-zrot}
\end{figure}

\noindent{\tt
mged> {\em Select the ``Rotate'' entry in the solid edit menu} \\
mged> {\em p 45 0 0} \\
mged>
}

The torus is rotated 45 degrees counter-clockwise about the positive X axis.
The
coordinates of the points I and H are transformed using the following matrix:
\begin{verbatim}
    [x'] [1   0      0   ] [x]
    [y']=[0  .7071 -.7071] [y]
    [z'] [0  .7071  .7071] [z]
\end{verbatim}
See Figure \ref{est-xrot}.

\noindent{\tt
mged> {\em p 0 45 0} \\
mged>
}

The torus is rotated 45 degrees counter-clockwise about the positive Y axis.
See Figure \ref{est-yrot}.

\noindent{\tt
mged> {\em p 0 0 45} \\
mged>
}

The torus is rotated 45 degrees counter-clockwise about the positive Z axis.
See Figure \ref{est-zrot}.
The original orientation is restored by entering

\noindent{\tt
mged> {\em p 0 0 0} \\
mged>
}

\subsection{Scale Operation}

\begin{figure}
\centering \includegraphics{est-scale.ps}
\caption{Torus Scale Increased.}
\label{est-scale}
\end{figure}

\noindent{\tt
mged> {\em Select the ``Scale'' entry in the solid edit menu} \\
mged> {\em p 1.5} \\
mged>
}

The vertex remains the same and all distances from the vertex are
multiplied by 1.5, the value entered with p.  See Figure \ref{est-scale}.
To return to the original scale, enter

\noindent{\tt
mged> {\em p 1} \\
mged>
}

\subsection{Scale Radius 1 Command}

\begin{figure}
\centering \includegraphics{est-sr1.ps}
\caption{Scale Torus Radius 1.}
\label{est-sr1}
\end{figure}

\noindent{\tt
mged> {\em Select the ``edit menu'' entry in the solid edit menu} \\
mged> {\em Select the ``scale radius 1'' entry in the TORUS menu} \\
mged> {\em p 1.5} \\
mged>
}

The distance from the vertex to the center of the cross-section of the
ring is set equal to the values given with {\em p}, eg, 1.5.
See Figure \ref{est-sr1}.
The original scale can be restored with

\noindent{\tt
mged> {\em p 1} \\
mged>
}

\subsection{Scale Radius 2 Command}

\begin{figure}
\centering \includegraphics{est-sr2.ps}
\caption{Scale Torus Radius 2.}
\label{est-sr2}
\end{figure}

\noindent{\tt
mged> {\em Select the ``edit menu'' entry in the solid edit menu} \\
mged> {\em Select the ``scale radius 2'' entry in the TORUS menu} \\
mged> {\em p 0.5} \\
mged>
}

The distance from the center of the cross-section of the ring is set equal
to the value given with {\em p}, eg 0.5.
This value must remain less than the value for r1.
See Figure \ref{est-sr2}.
The command

\noindent{\tt
mged> {\em p 0.2} \\
mged>
}

will restore the original shape.

To return control to the VIEWING state, select the ``REJECT Edit''
item on the button menu, press the ``reject'' button on the button box,
or enter the command {\em press reject} on the keyboard.
Then, enter

\noindent{\tt
mged> {\em d tor} \\
mged>
}

to drop the torus from view.
