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    1 \chapter{TUTORIALS ON VIEWING AND STATES}
2
3 Tutorials with illustrations are provided to give the MGED user a
4 step-by-step walk-through of the basic capabilities of the graphics
5 editor.
6 Standard UNIX login and logout procedures appropriate to each site
7 should be followed prior to
8 beginning and after ending the tutorials.
9
10 Each of the tutorials will use the solids contained the MGED database called
11 prim.g''.
12 These can be obtained by making a copy of db/prim.g''
13 from the BRL-CAD Package distribution tree.  It is important to make
14 a copy of the database and work with that, rather than using the
15 supplied one.  Changes made during the editing process are written
16 to the database when they are {\sl accepted}.
17
18 The first tutorial shows a sample invocation dialogue.  All other
19 tutorials start at the first MGED prompt ({\tt mged> }). If the user
20 wishes to continue from one tutorial to the next without leaving MGED,
21 issue the {\em press reject} and {\em press reset} commands
22 before starting a new tutorial.
23 User input will be shown in an
24 {\em emphasized} font, and MGED output will appear in a {\tt typewriter}
25 font.  If the user input is shown on the same line as a prompt, the
26 input is literal.  If the user input is shown on a line by itself,
27 it is a directive, and is entered in an appropriate fashion.
28
29 The tutorials are self-contained, and if the user wishes to proceed to
30 the next tutorial without exiting MGED,
31 the RESET button should be pressed
32 to return to the top view, where the model XYZ axes
33 map to the screen XYZ axes.
34
35 The standard recovery procedure when in the middle of an editing operation
36 is to select REJECT edit.  Control is
37 returned to the viewing state, and the user can restart with the last edit (e)
38 command used in the tutorial.
39
40 \section{States Within the Edit Process}
41
42 In this tutorial, the user will invoke MGED on a file called prim.g'';
43 attach a {\sl display manager\/}; explore the various MGED states;
44 and finally, exit MGED.  A MGED database has a treelike structure.  The
45 leaves are the individual solids, and the other nodes are groupings
46 of those solids.  The solid editing functions are concerned with defining
47 and modifying the leaves, and the object editing functions operate
48 on groups, which are Boolean combinations of solids.  One useful mental
49 model is to envision solid editing as operating directly on a leaf and
50 object editing as operating on the arc connecting a pair of nodes.  The
51 object edit will affect everything below the selected arc (this is why
52 there is an additional state transition when object editing).
53
54 \section{Viewing State}
55
56 The first task is to invoke MGED.  This tutorial will assume the user
57 has a copy of the prim.g'' database in the current directory.
58
59 \noindent
60 {\tt \$}{\em mged prim.g}\\ 61 {\tt BRL-CAD Release 3.0 Graphics Editor (MGED) Compilation 82}\\ 62 {\tt Thu Sep 22 08:08:39 EDT 1988}\\ 63 {\tt mike@video.brl.mil:/cad/.mged.4d2}\\ 64 65 \noindent 66 {\tt attach (nu|tek|tek4109|ps|plot|sgi)[nu]? }{\em sgi}\\ 67 {\tt ATTACHING sgi (SGI 4d)}\\ 68 {\tt Primitive Objects (units=mm)}\\ 69 {\tt mged> }\\ 70 71 The first three lines give information about which version of MGED is running, 72 when it was compiled, and who compiled it. The next line is the display 73 manager attach prompt. This prompt provides a list of available display 74 managers, then shows what the default will be (selected if the user answers 75 with a carriage return). In this case, the Silicon Graphics 4d display 76 manager was selected, as is noted by the following line. 77 Next the title of the database and 78 the unit of measurement used in the database are printed, 79 and finally, the first prompt is issued. 80 At this point MGED has loaded prim.g''; attached the SGI display; 81 and is awaiting commands. Attaching a display also causes what 82 is known as the MGED {\sl faceplate} to be drawn on the graphics display. 83 84 The faceplate has several features of interest. In the upper left corner 85 of the display, is a box which always shows the current MGED {\sl state}. 86 This can be one of six states: {\bf VIEWING}, {\bf SOL PICK}, 87 {\bf SOL EDIT}, {\bf OBJ PICK}, {\bf OBJ PATH}, or {\bf OBJ EDIT}. 88 89 Immediately below, is the menu area. The only menu item initially shown is 90 one labeled {\bf BUTTON MENU}. This menu item toggles the display of the 91 button menu entries when {\sl selected} (more on selection later). 92 93 At the bottom of the display are two status lines. The first line 94 contains information about the current view. 95 The entry labeled {\bf cent=} gives the {\sl model space} coordinates 96 of the dot in the center of the display. 97 The entry labeled {\bf sz=} reflects the current size in model units of 98 the {\sl viewing cube}. The viewing cube is a mathematical construct 99 centered on the dot in the center of the display. The {\bf ang=} 100 display shows the current rate of rotation in each of the three axes. 101 The bottom line is used for several kinds of information. 102 In the {\bf VIEWING} state, it displays the title of the database. 103 104 The MGED viewing features are designed to allow the user to examine 105 models at different angles. 106 Preset views can be invoked at 107 anytime by using either the menu or the button box. 108 Selecting a preset view does 109 not change the coordinates of the primitives, 110 but instead changes the angle from which these primitives are 111 displayed. Five standard views (top, right, front, 35/25, and 45/45) can 112 be obtained by using either the bottom menu on the display screen or the 113 control box. 114 Three additional views (button, left, and rear) can be obtained 115 by using the button box, but not by using the menu. 116 117 The normal or default viewing state is the top'' orientation, 118 with model +X pointing towards the right of the screen, 119 model +Y pointing towards the top of the screen, 120 and model +Z pointing out of the screen. 121 In the top'' view, the model and screen axes are the same. 122 The reset'' button and Reset Viewsize'' menu items also 123 result in a top'' view. 124 125 The following table shows the angles of rotation to obtain the other views. 126 \begin{tabular}{l l} 127 View & Angle of Rotation (from top) \\ 128 \\ 129 Top & 0, 0, 0 \\ 130 Bottom & 180, 0, 0 \\ 131 Right & 270, 0, 0 \\ 132 Left & 270, 0, 180 \\ 133 Front & 270, 0, 270 \\ 134 Rear & 270, 0, 90 \\ 135 35, 25 & 295, 0, 235 \\ 136 \end{tabular} 137 138 \noindent 139 {\tt mged>\ }{\em e arb8}\\ 140 {\tt vectorized in 0 sec}\\ 141 {\tt mged>\ }{\em size 12}\\ 142 {\tt mged> }\\ 143 144 \begin{figure} 145 \centering \includegraphics{t1-top-vw.ps} 146 \caption{arb8'' Top View.} 147 \label{t1-top-vw} 148 \end{figure} 149 150 The {\bf e} command causes the named object(s) -- a solid named arb8'' 151 in this case 152 -- to be displayed, and the {\bf size} command sets the size of the 153 viewing cube. Figure \ref{t1-top-vw} shows what the display currently 154 looks like. In this view, the X-axis is to the right, the Y-axis points 155 up, and the Z-axis is perpendicular to (poking out of) the screen. 156 157 \noindent 158 {\em Twist the {\bf Y ROT} knob clockwise and back.}\\ 159 {\em Twist the {\bf X ROT} knob counterclockwise and back.}\\ 160 161 These knobs, along with the {\bf Z ROT} knob, rotate the viewing cube. 162 Use of the rotation 163 knobs allows the user to view the model from any orientation. 164 Turning a knob clockwise causes a rotation in the positive direction, 165 while turning a knob counterclockwise causes a negative rotation 166 (right-hand rule). The knobs are rate based, not position based; 167 once a rotation has been started, it will continue until the 168 knob is returned to zero (or the {\bf zeroknobs} button is pressed). 169 Rotations are about the viewing cube (screen) axes, not the model axes. 170 Systems without knobs can use the {\bf knob} command. 171 172 \noindent 173 {\em Move the mouse (or pen) until the cursor is in the {\bf BUTTON MENU} 174 block and then press the middle mouse button (depress the pen).}\\ 175 176 \begin{figure} 177 \centering \includegraphics{t1-rot-vw.ps} 178 \caption{arb8'' Rotated View.} 179 \label{t1-rot-vw} 180 \end{figure} 181 182 Pressing the middle mouse button (or the pen) {\sl selects} something. 183 When the cursor is inside the menu area, a selection 184 causes the event described by the menu item to occur. 185 Selecting {\bf BUTTON MENU} causes the button menu to appear on the left 186 side of the screen. The {\bf BUTTON MENU} menu item is 187 a toggle; subsequent selection of this item will cause the button menu 188 to disappear. 189 Figure \ref{t1-rot-vw} shows the new display. 190 191 \noindent 192 {\em Move the cursor from the menu area to a point near the 193 upper left corner of the solid and select it (press the center mouse 194 button).}\\ 195 196 In the {\bf VIEWING} state, making a selection while outside of the menu 197 area will move the selected point to the center of the display. Look 198 carefully at the center of the display; the point just selected is now 199 located at the center dot. Use the {\bf center} command to reset any 200 translations made with the mouse. 201 202 \noindent 203 {\tt mged> }{\em center 0 0 0}\\ 204 {\tt mged> }\\ 205 206 From the {\bf VIEWING} state, the user will normally transition to either the 207 {\bf SOL PICK} or {\bf OBJ PICK} state. 208 The {\bf SOL PICK} state is selected by: 209 \begin{itemize} 210 \item Selecting the {\bf Solid Illum} button menu entry, or, 211 \item Pressing the {\bf sill} button (this button may be labeled 212 using some variation of Solid Illum''), or, 213 \item Typing {\bf press sill}. 214 \end{itemize} 215 Similar entries ({\bf Object Illum}) and ({\bf oill}) exist for transitioning 216 into the {\bf OBJ PICK} state. 217 In general, the {\bf press} command is the basic mechanism (type 218 {\bf press help} for a list of available commands). Most of the press 219 commands have been mapped onto a button box if it is available, 220 and some of the 221 most common are also mapped into the {\bf BUTTON MENU} so they can 222 accessed without letting go of the mouse. 223 224 \section{Solid Pick State} 225 226 \noindent 227 {\em Place MGED in the {\bf SOL PICK} state using one of the 228 above mechanisms.}\\ 229 230 \begin{figure} 231 \centering \includegraphics{t1-sol-pk.ps} 232 \caption{MGED In Solid Pick State.} 233 \label{t1-sol-pk} 234 \end{figure} 235 236 Upon entering the {\bf SOL PICK} state, the display will look similar to 237 Figure \ref{t1-sol-pk}. The {\bf SOL PICK} state used to select which 238 of the displayed solids is to be edited. Note that the color of the 239 solid has changed from red to white. The screen is divided into as many 240 horizontal zones as there are solids displayed, and each zone is 241 assigned to one solid. As the mouse is moved vertically through each 242 zone, the corresponding solid is highlighted (illuminated'') by 243 drawing it in white. In this instance, there is only one solid being 244 displayed, so this state is relatively uninteresting. 245 If the system being used has no mouse, there is no reason to enter the 246 {\bf SOL PICK} state. The user will instead transition directly to 247 the {\bf SOL EDIT} state using the {\bf sed} command. 248 249 \noindent 250 {\tt mged> }{\em press reject}\\ 251 {\tt mged> }{\em e ellg}\\ 252 {\tt mged> }\\ 253 {\em Press the {\bf sill} button}\\ 254 255 \begin{figure} 256 \centering \includegraphics{t1-2s-pk.ps} 257 \caption{MGED In Solid Pick with Two Solids.} 258 \label{t1-2s-pk} 259 \end{figure} 260 261 Note that the first action taken was to {\sl reject} the edit. Any time MGED 262 is not in the {\bf VIEWING} state, a {\sl reject} command (via 263 {\bf press}, button, or mouse) discards all editing changes accumulated 264 since the last transition out of the {\bf VIEWING} state, and places 265 MGED in the {\bf VIEWING} state. 266 The display should now look similar to Figure \ref{t1-2s-pk}. 267 Notice that one solid is white and 268 the name of that solid is displayed in the upper left corner of the 269 display, as well as in the bottom status line. The solid to be edited is 270 selected by moving the mouse up and down until the zone corresponding to 271 the desired solid is reached. Once the appropriate zone is reached, select it. 272 This selects a solid, and once a solid is selected, 273 MGED enters the {\bf SOL EDIT} state. 274 275 \section{Solid Edit State} 276 277 \noindent 278 {\tt mged> }{\em d ellg}\\ 279 {\tt mged> }\\ 280 {\em Select the solid called arb8''.}\\ 281 282 \begin{figure} 283 \centering \includegraphics{t1-sol-ed.ps} 284 \caption{Solid Edit State.} 285 \label{t1-sol-ed} 286 \end{figure} 287 288 The {\bf d} command removes something from the display. In this 289 case, the solid ellg'' was removed to reduce clutter. 290 The display should now look like Figure \ref{t1-sol-ed}. 291 When MGED enters the solid edit state, the following occurs: 292 \begin{itemize} 293 \item The solid selected for editing remains illuminated, 294 \item The solid is labeled, 295 \item The coordinates (or dimensions) associated with the labels, 296 and other information is displayed to the right of the menu area,. 297 \item If the solid is a member of one or more groups, a similar set 298 of coordinates called the {\sl PATH} is displayed immediately below 299 the first set of coordinates, 300 \item The {\bf *SOLID EDIT*} menu is displayed, and, 301 \item A solid specific edit menu (in this case the {\bf ARB MENU}) 302 is displayed. 303 \end{itemize} 304 305 The {\bf *SOLID EDIT*} menu provides access to generic operations (translation, rotation 306 and scaling) common to all solids. 307 The solid specific edit menu is a list of solid type specific editing operations. 308 Selecting one of the solid specific edit menus causes a submenu with solid type specific 309 choices to be displayed. To remove this submenu, select either the 310 {\bf RETURN} item in the submenu, or the {\bf edit menu} item in the 311 {\bf *SOLID EDIT*} menu. 312 313 It is in this state that the solid is altered to meet the modeler's 314 requirements. The shape, positioning, and orientation of the solid is 315 changed using numeric keyboard input, positioning of the mouse, or by 316 use of the knobs. Once the solid has been altered, the edit is 317 either accepted or rejected. Accepting the edit causes all changes 318 made to be written to the database; rejecting the edit throws them 319 away''. Either operation will terminate the edit session and return MGED 320 to the {\bf VIEWING} state. 321 322 \noindent 323 {\em Reject the edit.}\\ 324 325 \section{Object Pick State} 326 327 \noindent 328 {\em Place MGED in the {\bf OBJ PICK} state.}\\ 329 330 \begin{figure} 331 \centering \includegraphics{t1-obj-pk.ps} 332 \caption{Object Pick State.} 333 \label{t1-obj-pk} 334 \end{figure} 335 336 Figure \ref{t1-obj-pk} shows what the display looks like when in the 337 {\bf OBJ PICK} state. As with the {\bf SOL PICK} state, a single solid is 338 selected. This solid becomes the reference solid for the object edit. 339 In the {\bf OBJ PICK} state, the solid will be shown 340 as a member of one or more objects. Less obvious is the fact that the 341 local axes associated with the selected solid are the axes used for the 342 entire object during the object edit. 343 344 \section{Object Path State} 345 346 \noindent 347 {\em Select arb8''.}\\ 348 349 \begin{figure} 350 \centering \includegraphics{t1-obj-ph.ps} 351 \caption{Object Path Selection State.} 352 \label{t1-obj-ph} 353 \end{figure} 354 355 MGED transitions into the {\bf OBJ PATH} state once a solid has been 356 picked from {\bf OBJ PICK}. Figure \ref{t1-obj-ph} is the display in 357 the {\bf OBJ PATH} state. When in this state the extent of the editing 358 operation is set. Everything below the editing point is affected by the 359 edit. The editing point is shown by the {\sl MATRIX} label in the 360 display. It is shown as {\bf [MATRIX]} in the upper left part of the 361 display and as {\bf \_\_MATRIX\_\_} in the second status line. The editing 362 point is chosen with the same mechanism used by {\bf SOL PICK} and 363 {\bf OBJ PICK}. This time, there is one horizontal zone for each node in 364 the path between the root and selected leaf. Moving the mouse up and down 365 moves the editing point up and down in the tree. Once again, having a 366 simple database and only one object in view makes for a relatively 367 uninteresting situation. 368 369 \section{Object Edit State} 370 371 \noindent 372 {\em Select the editing point above arb8''.}\\ 373 374 \begin{figure} 375 \centering \includegraphics{t1-obj-ed.ps} 376 \caption{Object Edit State.} 377 \label{t1-obj-ed} 378 \end{figure} 379 380 MGED is now in the {\bf OBJ EDIT} state and the display should look like 381 Figure \ref{t1-obj-ed}. 382 When MGED enters the object edit state, the following occurs: 383 \begin{itemize} 384 \item The reference solid remains illuminated, 385 \item The reference solid is labeled, 386 \item The information associated with the labels is displayed to the right 387 of the menu area, and 388 \item The {\bf *OBJ EDIT*} menu is displayed. 389 \end{itemize} 390 391 The {\bf OBJ EDIT} state is used to modify the 392 Homogeneous Transform Matrix selected during the {\bf OBJ PATH} state. 393 Permissible operations include uniform and affine scaling of the objects, 394 as well as translation and rotation. 395 As with the {\bf SOL EDIT} state, MGED accepts changes entered using 396 the keyboard, mouse or knobs. 397 398 This concludes the first tutorial. Examples of the appearance of MGED 399 in each of the six states have been given, along with some idea of what 400 each of the states is used for. All that remains is to reject the current 401 edit, and exit MGED. Strictly speaking the {\bf q} command could be entered 402 directly, but doing so, can become a dangerous habit. 403 404 \noindent 405 {\em Select {\bf REJECT Edit} using the mouse.}\\ 406 {\em Press the {\bf reject} button.}\\ 407 {\tt mged> }{\em d arb8}\\ 408 {\tt mged> }{\em q}\\ 409 {\tt \$ }\\
410
411 \section{Editing in the Plane of the Screen}
412 \begin{figure}
413 \centering \includegraphics{plane-top1.ps}
414 \caption{A Top View of the Coordinate Axes.}
415 \label{plane-top1}
416 \end{figure}
417
418 When MGED is in a translate'' mode within an edit state,
419 the plane of the mouse or data tablet is mapped to
420 the plane of the screen, to permit moving objects in a
421 controlled way in two of the three available dimensions.
422 The orientation of the plane of the screen is determined by the
423 currently selected view.
424 In most circumstances, users will find that repositioning objects
425 is easiest when the plane of the screen is oriented in an
426 axis-aligned view.  This is most easily accomplished by utilizing
427 one of the preset views.
428 For this exercise, obtain a copy of the {\em axis.g} database,
429 and run MGED, e.g.:
430
431 \noindent{\tt
432 \$cp db/axis.g . \\ 433 \$ mged axis.g \\
434 BRL-CAD Release 3.0 Graphics Editor (MGED) Compilation 82 \\
435     Thu Sep 22 08:08:39 EDT 1988 \\
437 \\
438 attach (nu|tek|tek4109|ps|plot|sgi)[nu]? {\em sgi} \\
439 ATTACHING sgi (SGI 4d) \\
440 X,Y,Z Coordinate Axis  (units=none) \\
441 mged> {\em e axis} \\
442 vectorized in 0 sec \\
443 {\em Select Top'' in the Button menu} \\
444 mged> \\
445 }
446
447 \subsection{Top View}
448 \begin{figure}
449 \centering \includegraphics{plane-top2.ps}
450 \caption{Translating from the Top View.}
451 \label{plane-top2}
452 \end{figure}
453
454 The top view is the default view.  The orientation of the axes
455 is shown in Figure \ref{plane-top1}.
456 The surface of the viewing screen and the graphics tablet is the XY plane.
457 Edit changes using the graphics tablet will affect only the X and Y
458 coordinates of the primitive.
459
460 \noindent{\tt
461 mged> {\em sed x} \\
462 {\em Select Translate'' in the Solid Edit menu} \\
463 mged>
464 }
465
466 Select different points on the tablet with the mouse, each time
467 pressing the middle mouse button.
468 Notice how the X and Y coordinates of the V vector change,
469 but the Z coordinate does not.
470 An example of this is shown in Figure \ref{plane-top2};
471 compare the values of V with those in Figure \ref{plane-top1}.
472
473 {\em Select REJECT Edit'' in the Button menu}
474
475 \subsection{Bottom View}
476 \begin{figure}
477 \centering \includegraphics{plane-bot1.ps}
478 \caption{A Bottom View of the Coordinate Axes.}
479 \label{plane-bot1}
480 \end{figure}
481 \begin{figure}
482 \centering \includegraphics{plane-bot2.ps}
483 \caption{Translating from the Bottom View.}
484 \label{plane-bot2}
485 \end{figure}
486
487 \noindent{\tt
488 mged> {\em press bottom} \\
489 mged> {\em sed x} \\
490 {\em Select Translate'' in the Solid Edit menu} \\
491 mged>
492 }
493
494 The {\em press bottom} command selects the bottom view of the
495 model, and the new configuration of the axes can be seen in
496 Figure \ref{plane-bot1}.
497 The surface of the viewing screen and the mouse or tablet
498 are still in the XY plane.
499 Edit changes using the graphics tablet will affect only the X and Y
500 components of the solid.
501 Select different points on the tablet with the mouse and notice the
502 changes in the coordinates;
503 compare the values of V with those in Figure \ref{plane-bot2}.
504
505 {\em Select REJECT Edit'' in the Button menu}
506
507 \subsection{Right View}
508 \begin{figure}
509 \centering \includegraphics{plane-right1.ps}
510 \caption{A Right View of the Coordinate Axes.}
511 \label{plane-right1}
512 \end{figure}
513 \begin{figure}
514 \centering \includegraphics{plane-right2.ps}
515 \caption{Translating from the Right View.}
516 \label{plane-right2}
517 \end{figure}
518
519 \noindent{\tt
520 {\em Select Right'' in the Button menu} \\
521 mged> {\em sed x} \\
522 {\em Select Translate'' in the Solid Edit menu} \\
523 mged>
524 }
525
526 The right hand view has been selected. Model +X still proceeds to the right,
527 but now model +Z is at the top of the screen, and model +Y is
528 pointing out of the screen.
529 This new configuration is depicted in Figure \ref{plane-right1}.
530 The surface of the viewing screen and the graphics tablet is the XZ plane.
531 Edit changes using the graphics tablet will affect only the X and Z
532 coordinates of the solid.
533 Select different points on the tablet with the mouse and notice the
534 changes in the V coordinates;  only the X and Z components change,
535 as in Figure \ref{plane-right2}.
536
537 {\em Select REJECT Edit'' in the Button menu}
538
539 \subsection{Front View}
540 \begin{figure}
541 \centering \includegraphics{plane-front1.ps}
542 \caption{A Front View of the Coordinate Axes.}
543 \label{plane-front1}
544 \end{figure}
545 \begin{figure}
546 \centering \includegraphics{plane-front2.ps}
547 \caption{Translating from the Front View.}
548 \label{plane-front2}
549 \end{figure}
550
551 \noindent{\tt
552 {\em Select Right'' in the Button menu} \\
553 mged> {\em sed x} \\
554 {\em Select Translate'' in the Solid Edit menu} \\
555 mged>
556 }
557
558 The front view has been selected.  Model +X points out of the screen,
559 model +Y points to the right, and model +Z points towards the top
560 of the screen, as shown in Figure \ref{plane-front1},
561 which has been slightly rotated off the preset view to improve
562 the legibility of the axis labels.
563 The surface of the viewing screen and the graphics tablet is the YZ
564 plane.  Edit changes will affect only the Y and Z
565 coordinates of the primitive, as shown in Figure \ref{plane-front2}.
566 Select different points on the tablet with the mouse and notice the
567 changes in the coordinates.
568
569 {\em Select REJECT Edit'' in the Button menu}
570
571 \subsection{35, 25 View}
572 \begin{figure}
573 \centering \includegraphics{plane-35a.ps}
574 \caption{An Oblique 35,25 View of the Coordinate Axes.}
575 \label{plane-35a}
576 \end{figure}
577 \begin{figure}
578 \centering \includegraphics{plane-35b.ps}
579 \caption{Translating in the 35,25 View.}
580 \label{plane-35b}
581 \end{figure}
582
583 \noindent{\tt
584 {\em Select 35,25'' in the Button menu} \\
585 mged> {\em sed x} \\
586 {\em Select Translate'' in the Solid Edit menu} \\
587 mged>
588 }
589
590 Figure \ref{plane-35a} is the 35,25 view of the axes model.
591 The axes are no longer
592 parallel or perpendicular to the viewing surface or to the graphics tablet.
593 Edit changes using the graphics tablet will affect all of the coordinates of
594 the solid, in a manner that is visually intuitive when the solid
595 is moved around on the screen.
596 Select different points on the tablet with the mouse and notice the
597 changes in the coordinates, such as in Figure \ref{plane-35b}.
598 Note how all three components of the V vector have changed.
599
600 {\em Select REJECT Edit'' in the Button menu}