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    1 \chapter{TUTORIALS ON EDITING SOLIDS}
2
3 The Solid Editing state of MGED is used to modify the fundamental
4 parameters of an individual solid.
5 Each solid must be modified individually.
6
7 \section{Solid Edit: A Six-Sided Polyhedron}
8
9 \begin{figure}
10 \centering \includegraphics{es8-top.ps}
11 \caption{Top View of ARB8.}
12 \label{es8-top}
13 \end{figure}
14
15 This section illustrates the use of commands while in
16 SOL EDIT state to alter the
17 shape of a polyhedron with six sides and 8 faces (ARB8).
18
19 \noindent{\tt
20 \\$ {\em mged es.g} \\
21 BRL-CAD Release 3.0 Graphics Editor (MGED) Compilation 82 \\
22     Thu Sep 22 08:08:39 EDT 1988 \\
24  \\
25 es.g: No such file or directory \\
26 Create new database (y|n)[n]? {\em y} \\
27 attach (nu|tek|tek4109|ps|plot|sgi)[nu]? {\em sgi} \\
28 ATTACHING sgi (SGI 4d) \\
29 Untitled MGED Database (units=mm) \\
30 mged> {\em in arb8 rpp -1 1 -1 1 -1 1} \\
31 mged> {\em size 10} \\
32 mged>
33 }
34
35 Figure \ref{es8-top}
36 is a top view of the six-sided polyhedron.
37 The Z-axis perpendicular to the viewing screen.
38 Next, the view is rotated so that all sides can be seen.
39
40 \noindent{\tt
41 mged> {\em Twist ROTY knob clockwise and restore} \\
42 mged> {\em Twist ROTX knob counter-clockwise and restore} \\
43 mged>
44 }
45
46 \begin{figure}
47 \centering \includegraphics{es8-rot.ps}
48 \caption{A Rotated View of the ARB8.}
49 \label{es8-rot}
50 \end{figure}
51 Figure \ref{es8-rot} shows a better perspective of the solid.
52
53 The next step in this tutorial is to transfer to the solid edit state.
54 This can be accomplished in two ways:  either by going through
55 the SOL PICK state (illuminate mode'') or by direct transfer via
56 keyboard command.
57 Using illuminate mode is better when the name of the solid to be
58 edited may not be known, while the keyboard command is generally
59 preferred when the name of the solid is known.
60
61 \noindent{\tt
62 mged> {\em Select the Solid Illum'' entry in the button menu} \\
63 mged> {\em Move the mouse out of the menu area} \\
64 mged> {\em Click the mouse to enter SOL EDIT state} \\
65 mged>
66 }
67
68 To perform a direct transfer from the viewing state to the solid edit state
69 using a keyboard command, enter:
70
71 \noindent{\tt
72 mged> {\em sed arb8} \\
73 mged>
74 }
75
76 \begin{figure}
77 \centering \includegraphics{es8-sed.ps}
78 \caption{An ARB8 in Solid Edit State.}
79 \label{es8-sed}
80 \end{figure}
81
82 Figure \ref{es8-sed} corresponds to the view on the display.
83 The ARB8 MENU is unique to the ARB primitive,
84 and lists operations that can only be performed on an ARB solid.
85 The items in the ARB8 MENU are
86 selected by using the mouse.
87 Each of the other types of solids have a
88 similar unique menu.
89 When one of these items is selected, the top level ARB8 MENU disappears,
90 to be replaced with the indicated subordinate menu.
91 The top-level menu reappears when either
92 the edit menu'' item in the SOLID EDIT menu is selected,
93 or the RETURN'' item in the subordinate menu is selected.
94
95 The  SOLID EDIT  menu applies to all
96 solids when in the SOL EDIT state.
97 The items in the  SOLID EDIT  menu are selected
98 by either using the mouse or by depressing the appropriate button on the
99 button box.
100 When any of the SOLID EDIT menu items are selected
101 (e.g., Rotate'', Translate'', Scale''), the solid-specific menu
102 disappears.
103 Th top-level solid-specific menu reappears when
104 the edit menu'' item in the SOLID EDIT menu is selected.
105
106 The {\em p [params]} command is used to
107 make precise changes, where the numeric value of the parameter being
108 edited is know.
109 Values for all parameters in the ARB8
110 and SOLID EDIT menus can be specified by using the {\em p} command,
111 or by pointing and clicking with the mouse.
112
113 \begin{figure}
114 \centering \includegraphics{es8-tr0.ps}
115 \caption{Translating ARB8 Point 1 to the Origin.}
116 \label{es8-tr0}
117 \end{figure}
118
119 \subsection{Translate Operation}
120
121 \noindent{\tt
122 mged> {\em Select the Translate'' entry in the solid edit menu} \\
123 mged> {\em p 0 0 0} \\
124 mged>
125 }
126
127 Point 1 of the primitive is moved to point 0 0 0,
128 as shown in Figure \ref{es8-tr0}.
129
130 The translate solid operation is selected
131 by either picking Translate'' on the solid edit menu
132 with the mouse, by depressing the solid edit button on the button box,
133 or by entering the {\em press sed} command.
134 Parameters to the translate solid operation
135 are of the form {\em p a b c}
136 where {\em a}, {\em b}, and {\em c} are the new coordinates
137 of point 1 in the solid.
138 The other points are transferred to keep the same position
139 relative to point 1.
140 The general form of the new coordinates for point is
141
142 \begin{center}
143 \begin{verbatim}
144 x ' = x + a - x
145 y ' = y + b - y
146 Z ' = Z + c - Z
147 \end{verbatim}
148 \end{center}
149
150 The command
151
152 \noindent{\tt
153 mged> {\em p 1 -1 -1} \\
154 mged>
155 }
156
157 can be used to restore the primitive to the original position.
158
159 \subsection{Rotate Operation}
160
161 \begin{figure}
162 \centering \includegraphics{es8-xrot.ps}
163 \caption{Solid Edit Rotation of 45 Degrees about X.}
164 \label{es8-xrot}
165 \end{figure}
166
167 The rotate operation is initiated by either selecting Rotate on the menu
168 screen with the mouse,
169 by depressing the Solid Rotate button on the button box,
170 or by entering the {\em press srot} command on the keyboard.
171
172 \noindent{\tt
173 mged> {\em Select the Rotate'' entry in the solid edit menu} \\
174 mged> {\em p 45 0 0} \\
175 mged>
176 }
177
178 The parameter {\em p} command is used to make precise rotation changes.
179 The
180 command is entered in the form {\em p a b c} where
181 {\em a}, {\em b}, and {\em c} are the angles
182 (in degrees) of rotation about the x, y, and z axes respectively.  Point 1,
183 the vertex, remains fixed, and the solid is rotated about this point.  A
184 positive angle of rotation is counter-clockwise when viewed in the positive
185 direction along an axis.
186
187 The order of rotation is not commutative.
188 Rotation takes place about the
189 Z axis, Y axis, and X axis in that order.
190 Figure \ref{es8-xrot} shows the rotation of 45 degrees about the X axis.
191
192 %The following is the formula for moving point (x,y,z) through angles
193 %(a, b, c) to point (x', y', z')
194 %\begin{verbatim}
195 %[X'] [cos b cos c                     -cos b sin c        sin b        ][X]
196 %[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]
197 %[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]
198 %\end{verbatim}
199
200 The values entered after the p are absolute - the rotations are applied to
201 the primitive as it existed when solid rotation was first selected.  Thus
202 entering {\em p 0 0 0} will undo any rotations
203 performed since solid rotation was begun.
204
205 \begin{figure}
206 \centering \includegraphics{es8-yrot.ps}
207 \caption{Solid Edit Rotation of 45 Degrees about Y.}
208 \label{es8-yrot}
209 \end{figure}
210
211 \begin{figure}
212 \centering \includegraphics{es8-zrot.ps}
213 \caption{Solid Edit Rotation of 45 Degrees about Z.}
214 \label{es8-zrot}
215 \end{figure}
216
217 \noindent{\tt
218 mged> {\em p 0 45 0} \\
219 mged>
220 }
221
222 Figure \ref{es8-yrot} displays the solid
223 after it has been rotated about the Y axis.
224
225 \noindent{\tt
226 mged> {\em p 0 0 45} \\
227 mged>
228 }
229
230 Figure \ref{es8-zrot} displays the solid
231 after it has been rotated about the Z axis.
232
233 \noindent{\tt
234 mged> {\em p 0 0 0} \\
235 mged>
236 }
237
238 This restores the original orientation of the solid.
239
240 \subsection{Scale Operation}
241
242 \begin{figure}
243 \centering \includegraphics{es8-scale.ps}
244 \caption{ARB8 Scale Increased by 2X.}
245 \label{es8-scale}
246 \end{figure}
247
248 \noindent{\tt
249 mged> {\em Select the Scale'' entry in the solid edit menu} \\
250 mged> {\em p 2} \\
251 mged>
252 }
253
254 Figure \ref{es8-scale} corresponds to the view that is shown on the display.
255 The scale operation may be initiated by either selecting
256 the Scale entry  on the menu with the mouse,
257 by depressing the Solid Scale button,
258 or by entering {\em press sscale} on the keyboard.
259 The parameter command {\em p n} is
260 used to enter a precise scale factors, where {\em n} is
261 the scale factor.
262 The coordinates of point 1 remain the same.  The distances
263 from point 1 to the other points are multiplied by the scale value {\em n}.
264 The general equations for the transformation from point p to p' are
265
266 \begin{verbatim}
267     x'[i] = x[i] + n (x[i] - x[1] )
268     y'[i] = y[i] + n (y[i] - y[1] )   i != 1
269     z'[i] = z[i] + n (z[i] - z[1] )
270 \end{verbatim}
271
272 The size of the primitive may be changed by depressing the mouse at
273 different positions.  When the mouse is clicked, the
274 edited primitive is scaled about point 1 (the key point)
275 by an amount proportional
276 to the distance the mouse is from the center of the screen.  If the mouse
277 is above the center of the screen, the edited primitive will become larger.
278 If the
279 mouse is below the center, the primitive will become smaller.
280
281 The value of {\em n} entered is applied to the primitive as it existed when the
282 solid scale state was entered.
283
284 Entering {\em p 1} will return the primitive
285 to the size it had when the solid scale operation first started.
286
287 \noindent{\tt
288 mged> {\em p 1} \\
289 mged>
290 }
291
292 \begin{figure}
293 \centering \includegraphics{es8-edge1.ps}
294 \caption{ARB8 Edge 15 Moved Through (9, -2, -2).}
295 \label{es8-edge1}
296 \end{figure}
297
298 \begin{figure}
299 \centering \includegraphics{es8-edge2.ps}
300 \caption{ARB8 Edge 12 Moved Through (2, 5, -2).}
301 \label{es8-edge2}
302 \end{figure}
303
304 \begin{figure}
305 \centering \includegraphics{es8-edge3.ps}
306 \caption{ARB8 Edge 14 Moved Through (2, -2, 7).}
307 \label{es8-edge3}
308 \end{figure}
309
310 \subsection{Moving Edges}
311
312 The move edge command permits the moving of a line or edge so that the
313 line passes through the selected point.
314
315 \noindent{\tt
316 mged> {\em Select the edit menu'' entry in the solid edit menu} \\
317 mged> {\em Select the move edges'' entry in the ARB menu} \\
318 mged> {\em Select the move edge 15'' entry in the ARB8 edges menu} \\
319 mged> {\em p 9 -2 -2} \\
320 mged>
321 }
322
323 The edge 15 is moved so that it passes through the point (9, -2, -2).  The
324 coordinates of the new points 1 and 5 are the intersection of the new edge
325 with the planes 234 and 678.  Since both the old edge and new edge 15 are
326 parallel to the X axis,
327 the X coordinate of the point given by the {\em p} command
328 has no meaning.  The X coordinates for points 1 and 5 are not changed.
329 See Figure \ref{es8-edge1}.
330
331 \noindent{\tt
332 mged> {\em p 9 -1 -1} \\
333 mged>
334 }
335
336 This restores the original shape.
337 The choice of 9'' for the X coordinate was arbitrary.
338
339 \noindent{\tt
340 mged> {\em Select the move edge 12'' entry in the ARB8 edges menu} \\
341 mged> {\em p 2 5 -2} \\
342 mged>
343 }
344
345 The edge 12 is parallel to the Y axis.  This command moves the points 1
346 and 2 so that their X and Z coordinates are 2 and -2.
347 See Figure \ref{es8-edge2}.
348 The Y coordinates are not changed.
349
350 To restore the view, enter:
351
352 \noindent{\tt
353 mged> {\em p 1 5 -1} \\
354 mged>
355 }
356
357 The choice of 5'' for the Y coordinate was arbitrary.
358
359 \noindent{\tt
360 mged> {\em Select the move edge 14'' entry in the ARB8 edges menu} \\
361 mged> {\em p 2 -2 7} \\
362 mged>
363 }
364
365 The edge 14 is parallel to the Z axis.
366 This command moves the points 1
367 and 4 so that their X and Y coordinates are 2 and -2.
368 See Figure \ref{es8-edge3}.
369 The Z coordinates are not changed.
370
371 \noindent{\tt
372 mged> {\em p 1 -1 7} \\
373 mged>
374 }
375
376 This restores the original shape.
377 The choice of 7'' for the Z coordinate was arbitrary.
378
379 \subsection{Extrude Command}
380
381 \begin{figure}
382 \centering \includegraphics{es8-ex1.ps}
383 \caption{ARB8 Rear Face Extruded 5 Units in -Z.}
384 \label{es8-ex1}
385 \end{figure}
386
387 \begin{figure}
388 \centering \includegraphics{es8-ex2.ps}
389 \caption{ARB8 Rear Face Extruded 3 Units in +Z.}
390 \label{es8-ex2}
391 \end{figure}
392
393 The extrude command is used to move the opposite surface a distance from
394 the specified surface or plate.
395 This command can only be used when an ARB solid is in
396 solid edit state.
397
398 \noindent{\tt
399 mged> {\em extrude 1265 5} \\
400 mged>
401 }
402
403 In Figure \ref{es8-ex1},
404 the plane opposite surface whose points are 1, 2, 6, and 5
405 is moved to a distance of 5 in the positive Z direction from plane 1265.  Note
406 that the points were selected counter-clockwise when viewed in the positive
407 direction along the Z axis.
408
409 \noindent{\tt
410 mged> {\em extrude 1562 3} \\
411 mged>
412 }
413
414 In Figure \ref{es8-ex2},
415 the plane opposite surface 1562 is moved to a distance of 3
416 in the negative Z direction from 1562.  Note that the points were selected
417 clockwise when viewed in the positive direction along the Z axis.
418
419 \noindent{\tt
420 mged> {\em extrude 1265 2} \\
421 mged>
422 }
423
424 This restores the original shape of this solid.
425
426 To return control to the VIEWING state, select the REJECT Edit''
427 item on the button menu, press the reject'' button on the button box,
428 or enter the command {\em press reject} on the keyboard.
429 Then, enter
430
431 \noindent{\tt
432 mged> {\em d arb8} \\
433 mged>
434 }
435
436 to drop the ARB8 from view.
437
438 \section{Solid Edit:  A Five-Sided Polyhedron}
439
440 \begin{figure}
441 \centering \includegraphics{es5-top.ps}
442 \caption{Top View of an ARB5.}
443 \label{es5-top}
444 \end{figure}
445
446 \begin{figure}
447 \centering \includegraphics{es5-rot.ps}
448 \caption{A Rotated View of the ARB5.}
449 \label{es5-rot}
450 \end{figure}
451
452 \begin{figure}
453 \centering \includegraphics{es5-sed.ps}
454 \caption{The ARB5 in Solid Edit State.}
455 \label{es5-sed}
456 \end{figure}
457
458 This tutorial illustrates the application of the SOL EDIT state to the ARB5
459 solid.
460 In this tutorial, the view is modified by using the rotation
461 knobs so that all sides can be seen.
462
463 \noindent{\tt
464 mged> {\em size 6} \\
465 mged> {\em in arb5 arb5} \\
466 Enter X, Y, Z for point 1: {\em 0 0 0} \\
467 Enter X, Y, Z for point 2: {\em 0 0 1} \\
468 Enter X, Y, Z for point 3: {\em 0 1 1} \\
469 Enter X, Y, Z for point 4: {\em 0 1 0} \\
470 Enter X, Y, Z for point 5: {\em -1 .5 .5} \\
471 mged>
472 }
473
474 Figure \ref{es5-top} is the display of arb5
475 in the VIEWING state that is seen when
476 the solid is first created.
477 In this view, the Z axis is perpendicular to the viewing screen.
478
479 \noindent{\tt
480 mged> {\em Twist ROTY knob clockwise and restore} \\
481 mged> {\em Twist ROTX knob counter-clockwise and restore} \\
482 mged>
483 }
484
485 These actions generate a view shown in Figure \ref{es5-rot}
486 that shows all sides.
487
488 \noindent{\tt
489 mged> {\em Select the Solid Illum'' entry in the button menu} \\
490 mged> {\em Move the mouse out of the menu area} \\
491 mged> {\em Click the mouse to enter SOL EDIT state} \\
492 mged>
493 }
494
495 These actions will place MGED in the SOL EDIT state
496 as shown in Figure \ref{es5-sed}.
497
498 \subsection{Translate Operation}
499
500 \begin{figure}
501 \centering \includegraphics{es5-tr.ps}
502 \caption{Translating an ARB5.}
503 \label{es5-tr}
504 \end{figure}
505
506 \noindent{\tt
507 mged> {\em Select the Translate'' entry in the solid edit menu} \\
508 mged> {\em p -1 -1 1} \\
509 mged>
510 }
511
512 This command cause point 1 to be moved to coordinates (-1, -1, 1) and the
513 other points are moved so that they keep the same relative position to point
514 1.  See Figure \ref{es5-tr}.
515
516 Enter this command to restore the solid to its original location:
517
518 \noindent{\tt
519 mged> {\em p 0 0 0} \\
520 mged>
521 }
522
523 \subsection{Rotate Operation}
524
525 \begin{figure}
526 \centering \includegraphics{es5-xrot.ps}
527 \caption{ARB5 Solid Edit Rotation about X.}
528 \label{es5-xrot}
529 \end{figure}
530
531 \noindent{\tt
532 mged> {\em Select the Rotate'' entry in the solid edit menu} \\
533 mged> {\em p 45 0 0} \\
534 mged>
535 }
536
537 Figure \ref{es5-xrot} shows a rotation of 45 degrees
538 about an axis parallel to the X axis.
539 The rotate command is entered in the form {\em p a b c}
540 where {\em a}, {\em b}, and {\em c} are the angles
541 (in degrees) of rotation about the x, y, and z axes and intersect at point 1.
542 All rotation takes place about point 1.
543
544 \noindent{\tt
545 mged> {\em p 0 0 0} \\
546 mged>
547 }
548
549 This restores the original orientation of the solid.
550
551 \subsection{Scale Operation}
552
553 \begin{figure}
554 \centering \includegraphics{es5-scale.ps}
555 \caption{ARB5 Scale Increased by 2X.}
556 \label{es5-scale}
557 \end{figure}
558
559 \noindent{\tt
560 mged> {\em Select the Scale'' entry in the solid edit menu} \\
561 mged> {\em p 2} \\
562 mged>
563 }
564
565 Figure \ref{es5-scale} shows the change in the primitive.
566 Point 1 remains the same
567 and the distances of the other points from point 1 is multiplied by 2.
568
569 Entering {\em p 1} will return the primitive
570 to the size it had when the solid scale operation first started.
571
572 \noindent{\tt
573 mged> {\em p 1} \\
574 mged>
575 }
576
577 \subsection{Move Edge Command}
578
579 \begin{figure}
580 \centering \includegraphics{es5-edge1.ps}
581 \caption{ARB5 Edge 14 Moved Through (1, 1, 1).}
582 \label{es5-edge1}
583 \end{figure}
584
585 \begin{figure}
586 \centering \includegraphics{es5-edge2.ps}
587 \caption{ARB5 Point 5 Moved to (-1.5, 1, 1).}
588 \label{es5-edge2}
589 \end{figure}
590
591 \begin{figure}
592 \centering \includegraphics{es5-edge3.ps}
593 \caption{ARB5 Edge 45 Moved Through (-1.5 1 1).}
594 \label{es5-edge3}
595 \end{figure}
596
597 \begin{figure}
598 \centering \includegraphics{es5-edge4.ps}
599 \caption{ARB5 Edge 12 Moved Through (2, 1, 2).}
600 \label{es5-edge4}
601 \end{figure}
602
603 \noindent{\tt
604 mged> {\em Select the edit menu'' entry in the solid edit menu} \\
605 mged> {\em Select the move edges'' entry in the ARB menu} \\
606 mged> {\em Select the move edge 14'' entry in the ARB8 edges menu} \\
607 mged> {\em p 1 1 1} \\
608 mged>
609 }
610
611 The edge 14 is moved so that it moves through the point (1, 1, 1).
612 Note that this point is the mid-point between points 1 and 4.
613 See Figure \ref{es5-edge1}.
614
615 \noindent{\tt
616 mged> {\em p 0 2 0} \\
617 mged>
618 }
619
620 This restores the original shape.
621
622 \noindent{\tt
623 mged> {\em Select the move point 5'' entry in the ARB5 edges menu} \\
624 mged> {\em p -1.5 1 1} \\
625 mged>
626 }
627
628 The point 5 is moved to location -1.5, 1, 1.  See Figure \ref{es5-edge2}.
629
630 \noindent{\tt
631 mged> {\em p -1 .5 .5} \\
632 mged>
633 }
634
635 will restore the original shape.
636
637 \noindent{\tt
638 mged> {\em Select the move edge 45'' entry in the ARB5 edges menu} \\
639 mged> {\em p -1.5 1 1} \\
640 mged>
641 }
642
643 In Figure \ref{es5-edge3}, the edge 45 is moved
644 so that it passes through the point (-1.5, 1, 1).
645 Note that this point lies between the points 4 and 5.
646
647 \noindent{\tt
648 mged> {\em p -1 .5 .5} \\
649 mged>
650 }
651
652 This restores the original shape.
653
654 \noindent{\tt
655 mged> {\em Select the move edge 12'' entry in the ARB5 edges menu} \\
656 mged> {\em p 2 1 2} \\
657 mged>
658 }
659
660 In Figure \ref{es5-edge4},
661 the edge 12 is moved so that it passes through the point (2, 1, 2).
662 Note that the coordinates correspond to point 2.
663
664 The movement of the edges may yield unpredictable results when the edges
665 are not parallel to one of the axes.
666
667
668 To return control to the VIEWING state, select the REJECT Edit''
669 item on the button menu, press the reject'' button on the button box,
670 or enter the command {\em press reject} on the keyboard.
671 Then, enter
672
673 \noindent{\tt
674 mged> {\em d arb5} \\
675 mged>
676 }
677
678 to drop the ARB5 from view.
679
680 \section{Solid Edit: Alter a Cylinder}
681
682 \begin{figure}
683 \centering \includegraphics{esc-top.ps}
684 \caption{Top View of a Cylinder.}
685 \label{esc-top}
686 \end{figure}
687
688 \begin{figure}
689 \centering \includegraphics{esc-rot.ps}
690 \caption{A Rotated View of the Cylinder.}
691 \label{esc-rot}
692 \end{figure}
693
694 \begin{figure}
695 \centering \includegraphics{esc-sed.ps}
696 \caption{A Cylinder in Solid Edit State.}
697 \label{esc-sed}
698 \end{figure}
699
700 This tutorial illustrates the application of the SOL EDIT state to
701 cylinder solids.
702
703 \noindent{\tt
704 mged> {\em size 12} \\
705 mged> {\em in cyl rcc} \\
706 Enter X, Y, Z of vertex: {\em 0 0 0} \\
707 Enter X, Y, Z of height (H) vector: {\em 2 0 0} \\
708 Enter radius: {\em 1}
709 mged>
710 }
711
712 Figure \ref{esc-top} is the display of the cylinder solid
713 when viewed from the top.
714 Since the
715 Z axis is perpendicular to the viewing screen, a view of all sides cannot be
716 seen.
717
718 \noindent{\tt
719 mged> {\em Twist ROTY knob clockwise and restore} \\
720 mged> {\em Twist ROTX knob counter-clockwise and restore} \\
721 mged>
722 }
723
724 These actions generate a view, Figure \ref{esc-rot}, that shows all sides.
725
726 \noindent{\tt
727 mged> {\em Select the Solid Illum'' entry in the button menu} \\
728 mged> {\em Move the mouse out of the menu area} \\
729 mged> {\em Click the mouse to enter SOL EDIT state} \\
730 mged>
731 }
732
733 Figure \ref{esc-sed} is the view that displays the menu
734 for the SOL EDIT state.
735 The
736 point V is at the origin (0,0,0) in this example and is in the middle of the
737 circle that contains points A and B.  H is the point of the center of the
738 circle that contains points C and D.  The coordinates of H are the coordinates
739 of the vector from V to H and represent the relative position of H to V.  Mag
740 is the magnitude of these vectors and is represented by the formula
741 \begin{center}
742 \begin{verbatim}
743 Mag = sqrt( x + y + z )
744 \end{verbatim}
745 \end{center}
746
747 H dir cos'' are the direction cosines of the vector H which
748 is perpendicular to plane of the points A, B, and V.  The coordinates of A
749 are the coordinates of the vector from V through A.  Mag is the magnitude of
750 the vectors from V to A.  The coordinates of B are the coordinates of the
751 vectors from V through B.  Mag is the magnitude of the vector from V to B.
752 The values for c and d are the magnitudes of the vectors from the tip of
753 vector H to the points C
754 and D respectively.
755 A x B dir cos'' represents the direction cosines of the
756 vector A x B''.
757
758 \subsection{Translate Operation}
759
760 \begin{figure}
761 \centering \includegraphics{esc-tr.ps}
762 \caption{Translating Cylinder Vertex to (1, 1, 1).}
763 \label{esc-tr}
764 \end{figure}
765
766 \noindent{\tt
767 mged> {\em Select the Translate'' entry in the solid edit menu} \\
768 mged> {\em p 1 1 1} \\
769 mged>
770 }
771
772 The location of the vertex point V is moved to (1, 1, 1).
773 The locations of the other
774 points relative to V remains the same.  See Figure \ref{esc-tr}.
775
776 Move the mouse anywhere on the screen (outside the menu area), and click.
777 Notice
778 that the cylinder is moved so that V is placed at this location, and the
779 coordinates of the other points remain the same relative to V.
780
781 \noindent{\tt
782 mged> {\em p 0 0 0} \\
783 mged>
784 }
785
786 This restores the solid to the original location.
787
788 \subsection{Rotate Operation}
789
790 \begin{figure}
791 \centering \includegraphics{esc-xrot.ps}
792 \caption{Solid Edit Rotation of 45 Degrees about X.}
793 \label{esc-xrot}
794 \end{figure}
795
796 \begin{figure}
797 \centering \includegraphics{esc-yrot.ps}
798 \caption{Solid Edit Rotation of 45 Degrees about Y.}
799 \label{esc-yrot}
800 \end{figure}
801
802 \begin{figure}
803 \centering \includegraphics{esc-zrot.ps}
804 \caption{Solid Edit Rotation of 45 Degrees about Z.}
805 \label{esc-zrot}
806 \end{figure}
807
808 \noindent{\tt
809 mged> {\em Select the Rotate'' entry in the solid edit menu} \\
810 mged> {\em p 45 0 0} \\
811 mged>
812 }
813
814 When viewing in the positive X direction, the cylinder is rotated counter-
815 clockwise 45 degrees about an axis through point V parallel to the x axis.
816 See Figure \ref{esc-xrot}.
817
818 \noindent{\tt
819 mged> {\em p 0 45 0} \\
820 mged>
821 }
822
823 When viewing in the positive Y direction, the cylinder is rotated counter-
824 clockwise 45 degrees about an axis through point V parallel to the Y axis.
825 See Figure \ref{esc-yrot}.
826
827 \noindent{\tt
828 mged> {\em p 0 0 45} \\
829 mged>
830 }
831
832 When viewing in the positive Z direction, the cylinder is rotated counter-
833 clockwise 45 degrees about an axis through point V parallel to the Z axis.
834 See Figure \ref{esc-zrot}.
835
836 The command
837
838 \noindent{\tt
839 mged> {\em p 0 0 0} \\
840 mged>
841 }
842
843 will restore the cylinder to the original orientation.
844
845 \subsection{Scale Operation}
846
847 \begin{figure}
848 \centering \includegraphics{esc-scale.ps}
849 \caption{Cylinder Scale Increased by 1.5X.}
850 \label{esc-scale}
851 \end{figure}
852
853 \noindent{\tt
854 mged> {\em Select the Scale'' entry in the solid edit menu} \\
855 mged> {\em p 1.5} \\
856 mged>
857 }
858
859 The point V remains fixed, the distance H between the two end-plate ellipses
860 is multiplied by 1.5.
861 See Figure \ref{esc-scale}.
862
863 The command
864
865 \noindent{\tt
866 mged> {\em p 1} \\
867 mged>
868 }
869
870 restores the original scale.
871
872 \subsection{Scale H Command}
873
874 \begin{figure}
875 \centering \includegraphics{esc-sh.ps}
876 \caption{Cylinder Scale H Vector.}
877 \label{esc-sh}
878 \end{figure}
879
880 \noindent{\tt
881 mged> {\em Select the edit menu'' entry in the solid edit menu} \\
882 mged> {\em Select the scale H'' entry in the TGC menu} \\
883 mged> {\em p 1} \\
884 mged>
885 }
886
887 The magnitude of the vector H is reduced from 2 to 1.
888 See Figure \ref{esc-sh}.  The command
889
890 \noindent{\tt
891 mged> {\em p 2} \\
892 mged>
893 }
894
895 will restore the original shape.
896
897 \subsection{Scale A Command}
898
899 \begin{figure}
900 \centering \includegraphics{esc-sa.ps}
901 \caption{Cylinder Scale A Vector.}
902 \label{esc-sa}
903 \end{figure}
904
905 \noindent{\tt
906 mged> {\em Select the scale A'' entry in the TGC menu} \\
907 mged> {\em p 2} \\
908 mged>
909 }
910
911 The magnitude of the vector through point A is increased to 2, i.e.,
912 the length of the axis of the ellipse through point A is set equal to p.
913 See Figure \ref{esc-sa}.  The command
914
915 \noindent{\tt
916 mged> {\em p 1} \\
917 mged>
918 }
919
920 will restore the original shape.
921
922 \subsection{Scale B Command}
923
924 \begin{figure}
925 \centering \includegraphics{esc-sb.ps}
926 \caption{Cylinder Scale B Vector.}
927 \label{esc-sb}
928 \end{figure}
929
930 \noindent{\tt
931 mged> {\em Select the scale B'' entry in the TGC menu} \\
932 mged> {\em p 2} \\
933 mged>
934 }
935
936 The magnitude of the vector through point B is increased to 2, i.e.,
937 the length of the axis of the ellipse through point B is set equal to p.
938 See Figure \ref{esc-sb}.  The command
939
940 \noindent{\tt
941 mged> {\em p 1} \\
942 mged>
943 }
944
945 will restore the original shape.
946
947 \subsection{Scale C Command}
948
949 \begin{figure}
950 \centering \includegraphics{esc-sc.ps}
951 \caption{Cylinder Scale C Vector.}
952 \label{esc-sc}
953 \end{figure}
954
955 \noindent{\tt
956 mged> {\em Select the scale C'' entry in the TGC menu} \\
957 mged> {\em p 2} \\
958 mged>
959 }
960
961 The magnitude of the vector through point c is increased to the value of
962 p.  The length of the axis of the ellipse through point c is set equal to the
963 value of p.  See Figure \ref{esc-sc}.  The command
964
965 \noindent{\tt
966 mged> {\em p 1} \\
967 mged>
968 }
969
970 will restore the original shape.
971
972 \subsection{Scale D Command}
973
974 \begin{figure}
975 \centering \includegraphics{esc-sd.ps}
976 \caption{Cylinder Scale D Vector.}
977 \label{esc-sd}
978 \end{figure}
979
980 \noindent{\tt
981 mged> {\em Select the scale D'' entry in the TGC menu} \\
982 mged> {\em p 2} \\
983 mged>
984 }
985
986 The magnitude of the vector through point D is changed to the value of p.
987 The length of the axis of the ellipse through point D is set equal to the
988 value of p.  See Figure \ref{esc-sd}.  The command
989
990 \noindent{\tt
991 mged> {\em p 1} \\
992 mged>
993 }
994
995 will restore the original shape.
996
997 The scale H, A, B, C, and D commands provide for setting the magnitude
998 equal to the value entered by the {\em p} command.
999 The solid edit {\bf scale} operation provides
1000 for multiplying {\bf all} the vectors by the value
1001 entered by the {\em p} command.
1002
1003 \subsection{Move End H Command}
1004
1005 \begin{figure}
1006 \centering \includegraphics{esc-mh.ps}
1007 \caption{Cylinder Move End of H.}
1008 \label{esc-mh}
1009 \end{figure}
1010
1011 \noindent{\tt
1012 mged> {\em Select the move end H'' entry in the TGC menu} \\
1013 mged> {\em p 3} \\
1014 mged>
1015 }
1016
1017 The length of the vector H is changed to the value of p.
1018 See Figure \ref{esc-mh}.  The command
1019
1020 \noindent{\tt
1021 mged> {\em p 2} \\
1022 mged>
1023 }
1024
1025 will restore the original shape.
1026
1027 \subsection{Move End H (rt) Command}
1028
1029 \begin{figure}
1030 \centering \includegraphics{esc-mhrt.ps}
1031 \caption{Cylinder Move End of H \& Rotate.}
1032 \label{esc-mhrt}
1033 \end{figure}
1034
1035 \noindent{\tt
1036 mged> {\em Select the move end H(rt)'' entry in the TGC menu} \\
1037 mged> {\em p 3} \\
1038 mged>
1039 }
1040
1041 This command is similar to the move end H'' command except the vector
1042 through point A is rotated so its direction is in the -Y direction.
1043 See Figure \ref{esc-mhrt}.  The command
1044
1045 \noindent{\tt
1046 mged> {\em p 2} \\
1047 mged>
1048 }
1049
1050 will restore the original shape, but not the original orientation.
1051
1052 To return control to the VIEWING state, select the REJECT Edit''
1053 item on the button menu, press the reject'' button on the button box,
1054 or enter the command {\em press reject} on the keyboard.
1055 Then, enter
1056
1057 \noindent{\tt
1058 mged> {\em d cyl} \\
1059 mged>
1060 }
1061
1062 to drop the cylinder from view.
1063
1064 \section{Solid Edit: Alter Ellipsoid}
1065
1066 \begin{figure}
1067 \centering \includegraphics{ese-top.ps}
1068 \caption{Top View of an Ellipsoid.}
1069 \label{ese-top}
1070 \end{figure}
1071
1072 \begin{figure}
1073 \centering \includegraphics{ese-sed.ps}
1074 \caption{An Ellipsoid in Solid Edit State.}
1075 \label{ese-sed}
1076 \end{figure}
1077
1078 This tutorial illustrates the application of the SOL EDIT state to the
1079 ellipsoid primitive.
1080
1081 \noindent{\tt
1082 mged> press reset
1083 mged> {\em size 6} \\
1084 mged> {\em in ell ellg} \\
1085 Enter X, Y, Z of vertex: {\em 0 0 0} \\
1086 Enter X, Y, Z of vector A: {\em 1 0 0} \\
1087 Enter X, Y, Z of vector B: {\em 0 .3536 -0.3536} \\
1088 Enter X, Y, Z of vector C: {\em 0 .3536  0.3536} \\
1089 mged>
1090 }
1091
1092 Figure \ref{ese-top} is the display of the primitive in the viewing state.
1093 Since the
1094 Z axis is perpendicular to the viewing screen, a view of all sides cannot be
1095 seen.
1096
1097 \noindent{\tt
1098 mged> {\em Twist ROTY knob clockwise and restore} \\
1099 mged> {\em Twist ROTX knob counter-clockwise and restore} \\
1100 mged>
1101 }
1102
1103 These actions generate a view that shows all sides.
1104
1105 \noindent{\tt
1106 mged> {\em Select the Solid Illum'' entry in the button menu} \\
1107 mged> {\em Move the mouse out of the menu area} \\
1108 mged> {\em Click the mouse to enter SOL EDIT state} \\
1109 mged>
1110 }
1111
1112 The display will be changed from the VIEWING MODE through the SOL PICK to
1113 the SOL EDIT state.  Figure \ref{ese-sed} is the view that is displayed.
1114
1115 The coordinates of the points A, B, C, are given by the product of the
1116 magnitude of the vector and the cosine of X, Y, and Z direction cosines.  In
1117 the display, the coordinates are:
1118
1119 \begin{center}
1120 \begin{verbatim}
1121 A = (1, 0, 0)
1122 B = (0, 0.3536, -0.3536)
1123 C = (0, 0.3536,  0.3536)
1124 \end{verbatim}
1125 \end{center}
1126 or
1127 \begin{center}
1128 \begin{verbatim}
1129 A = ( 1* cos  0,  1* cos 90,   1* cos 90 )
1130 B = (.5* cos 90, .5* cos 45, -.5* cos 45 )
1131 C = (.5* cos 90, .5* cos 45,  .5* cos 45 )
1132 \end{verbatim}
1133 \end{center}
1134
1135 \subsection{Translate Operation}
1136
1137 \begin{figure}
1138 \centering \includegraphics{ese-tr.ps}
1139 \caption{Translating Ellipsoid to (-1, 1, 1).}
1140 \label{ese-tr}
1141 \end{figure}
1142
1143 \noindent{\tt
1144 mged> {\em Select the Translate'' entry in the solid edit menu} \\
1145 mged> {\em p -1 1 1} \\
1146 mged>
1147 }
1148
1149 The key point V is moved to (-1, 1, 1) and the ellipsoid maintains its
1150 relative position to V.  See Figure \ref{ese-tr}.
1151
1152 While in the SOL EDIT state, the solid may be translated by
1153 using the mouse.  These changes are not numerically exact, but they can be
1154 useful to visually position a solid with respect to other solids.
1155 Move the mouse to a position outside the menu area on the screen.
1156 Click the mouse.
1157 The center point (V) of the ellipsoid will be translated to that point.
1158 Note that only the value of the coordinates of V are changed.
1159 The command
1160
1161 \noindent{\tt
1162 mged> {\em p 0 0 0} \\
1163 mged>
1164 }
1165
1166 will restore the original position.
1167
1168 \subsection{Rotate Operation}
1169
1170 \begin{figure}
1171 \centering \includegraphics{ese-xrot.ps}
1172 \caption{Solid Edit Rotation of 45 Degrees about X.}
1173 \label{ese-xrot}
1174 \end{figure}
1175
1176 \begin{figure}
1177 \centering \includegraphics{ese-yrot.ps}
1178 \caption{Solid Edit Rotation of 45 Degrees about Y.}
1179 \label{ese-yrot}
1180 \end{figure}
1181
1182 \begin{figure}
1183 \centering \includegraphics{ese-zrot.ps}
1184 \caption{Solid Edit Rotation of 45 Degrees about Z.}
1185 \label{ese-zrot}
1186 \end{figure}
1187
1188 The rotate operation is initiated by either selecting Rotate on the menu
1189 screen with the mouse,
1190 by depressing the Solid Rotate button on the button box,
1191 or by entering the {\em press srot} command on the keyboard.
1192
1193 \noindent{\tt
1194 mged> {\em Select the Rotate'' entry in the solid edit menu} \\
1195 mged> {\em p 45 0 0} \\
1196 mged>
1197 }
1198
1199 Figure \ref{ese-xrot} shows the rotation of the ellipsoid about its X axis.
1200 The angle of rotation is counter-clockwise when viewed in the positive X
1201 direction.  The direction cosines of vectors VB and VC are changed by 45 .
1202
1203 \noindent{\tt
1204 mged> {\em Select the Rotate'' entry in the solid edit menu} \\
1205 mged> {\em p 0 45 0} \\
1206 mged>
1207 }
1208
1209 Figure \ref{ese-yrot} shows the rotation of the ellipsoid about its Y axis.
1210 The angle
1211 of rotation is counter-clockwise when viewed in the positive Y direction.  The
1212 rotation is made from the original view, and the restoration of the view is
1213 not necessary.
1214
1215 \noindent{\tt
1216 mged> {\em Select the Rotate'' entry in the solid edit menu} \\
1217 mged> {\em p 0 0 45} \\
1218 mged>
1219 }
1220
1221 Figure \ref{ese-zrot} shows the rotation of the ellipsoid about its Z axis.
1222 The axis
1223 of rotation is counter-clockwise when viewed in the positive Z direction.
1224 The command
1225
1226 \noindent{\tt
1227 mged> {\em p 0 0 0} \\
1228 mged>
1229 }
1230
1231 restores the original orientation of the solid.
1232
1233 \subsection{Scale Operation}
1234
1235 \begin{figure}
1236 \centering \includegraphics{ese-scale.ps}
1237 \caption{Ellipsoid Scale Decreased.}
1238 \label{ese-scale}
1239 \end{figure}
1240
1241 \noindent{\tt
1242 mged> {\em Select the Scale'' entry in the solid edit menu} \\
1243 mged> {\em p .5} \\
1244 mged>
1245 }
1246
1247 Point V is not changed,
1248 but the distance from V to the surface of the ellipsoid is multiplied by 0.5,
1249 because the magnitude of the vectors are multiplied by the value of 0.5.
1250 See Figure \ref{ese-scale}.
1251
1252 Move the mouse to a position outside the menu area and above the X axis,
1253 and click the mouse.
1254 Notice that the size of the ellipsoid has grown, i.e.,
1255 the magnitude of the vectors have increased.
1256 Move the mouse to a position below the X axis, and click the mouse.
1257 Notice that the size of the ellipsoid has increased.
1258
1259 The command
1260
1261 \noindent{\tt
1262 mged> {\em p 1} \\
1263 mged>
1264 }
1265
1266 will restore the original scale.
1267
1268 NOTE:
1269 The use
1270 of the scale operation from the Solid Edit menu
1271 will result in the values of all the vectors being
1272 multiplied by the value of the scale.
1273 Use of the scale operaton from the Ellipsoid menu
1274 with a particular vector A, B, or C changes the
1275 magnitude of that vector to the value of the scale.
1276
1277 \subsection{Scale A Command}
1278
1279 \begin{figure}
1280 \centering \includegraphics{ese-sa.ps}
1281 \caption{Ellipsoid Scale A Vector.}
1282 \label{ese-sa}
1283 \end{figure}
1284
1285 \noindent{\tt
1286 mged> {\em Select the edit menu'' entry in the solid edit menu} \\
1287 mged> {\em Select the scale A'' entry in the ellipsoid menu} \\
1288 mged> {\em p 1.5} \\
1289 mged>
1290 }
1291
1292 The magnitude of the vector to point A is set equal to the value of p
1293 (e.g. 1.5).
1294 The components of the vector are (1.5, 0, 0) since the vector was
1295 parallel to the X axis.  See Figure \ref{ese-sa}.  The command
1296
1297 \noindent{\tt
1298 mged> {\em Select the scale A'' entry in the TGC menu} \\
1299 mged> {\em p 1} \\
1300 mged>
1301 }
1302
1303 will restore the original shape.
1304
1305 \subsection{Scale B Command}
1306
1307 \begin{figure}
1308 \centering \includegraphics{ese-sb.ps}
1309 \caption{Ellipsoid Scale B Vector.}
1310 \label{ese-sb}
1311 \end{figure}
1312
1313 \noindent{\tt
1314 mged> {\em Select the scale B'' entry in the Ellipsoid menu} \\
1315 mged> {\em p 1.5} \\
1316 mged>
1317 }
1318
1319 The magnitude of the vector to point B is set equal to the value of p
1320 (e.g. 1.5).
1321 The coordinates of the vector are the product of p and the
1322 direction cosines of B.  See Figure \ref{ese-sb}.  The command
1323
1324 \noindent{\tt
1325 mged> {\em p 0.5} \\
1326 mged>
1327 }
1328
1329 will restore the original shape.
1330
1331 \subsection{Scale C Command}
1332
1333 \begin{figure}
1334 \centering \includegraphics{ese-sc.ps}
1335 \caption{Ellipsoid Scale C Vector.}
1336 \label{ese-sc}
1337 \end{figure}
1338
1339 \noindent{\tt
1340 mged> {\em Select the scale C'' entry in the Ellipsoid menu} \\
1341 mged> {\em p 1.5} \\
1342 mged>
1343 }
1344
1345 The magnitude of the vector to point C is set equal to the value of p
1346 (i.e., 1.5).
1347 The coordinates of the vector are the product of p and the
1348 direction cosines of C.  See Figure \ref{ese-sc}.  The command
1349
1350 \noindent{\tt
1351 mged> {\em p 0.5} \\
1352 mged>
1353 }
1354
1355 will restore the original shape.
1356
1357 To return control to the VIEWING state, select the REJECT Edit''
1358 item on the button menu, press the reject'' button on the button box,
1359 or enter the command {\em press reject} on the keyboard.
1360 Then, enter
1361
1362 \noindent{\tt
1363 mged> {\em d ell} \\
1364 mged>
1365 }
1366
1367 to drop the ellipsoid from view.
1368
1369 \section{Solid Edit: Alter Torus}
1370
1371 \begin{figure}
1372 \centering \includegraphics{est-top.ps}
1373 \caption{Top View of a Torus.}
1374 \label{est-top}
1375 \end{figure}
1376
1377 \begin{figure}
1378 \centering \includegraphics{est-sed.ps}
1379 \caption{The Torus in Solid Edit State.}
1380 \label{est-sed}
1381 \end{figure}
1382
1383 This tutorial illustrates the application of the SOL EDIT state to the
1384 torus solid.
1385
1386 \noindent{\tt
1387 mged> {\em size 6} \\
1388 mged> {\em in tor tor} \\
1389 Enter X, Y, Z of vertex: {\em 0 0 0} \\
1390 Enter X, Y, Z of normal vector: {\em 0 1 0} \\
1391 Enter radius 1: {\em 1} \\
1392 Enter radius 2: {\em 0.2} \\
1393 mged>
1394 }
1395
1396 Figure \ref{est-top} is the display of the torus solid in viewing state.
1397 Since the
1398 Z-axis is perpendicular to the viewing screen, a view of all sides cannot be
1399 seen.
1400
1401 \noindent{\tt
1402 mged> {\em Twist ROTY knob clockwise and restore} \\
1403 mged> {\em Twist ROTX knob counter-clockwise and restore} \\
1404 mged>
1405 }
1406
1407 These actions generate a view of the torus that shows all sides,
1408 as shown in Figure \ref{est-sed}.
1409
1410 \noindent{\tt
1411 mged> {\em Select the Solid Illum'' entry in the button menu} \\
1412 mged> {\em Move the mouse out of the menu area} \\
1413 mged> {\em Click the mouse to enter SOL EDIT state} \\
1414 mged>
1415 }
1416
1417 The torus is a ring whose cross-section is a circle.  The distance from
1418 the vertex to the center of the cross-section is r1 and r2 is the radius of
1419 the circular cross section.
1420
1421 Let the points I and O be the intersection of the line x=-z and the torus.
1422 Then,
1423 \begin{center}
1424 \begin{verbatim}
1425 I = (-(r2-r1) cos 45, 0, (r2-r1) cos 45 )
1426 O = (-(r2+r1) cos 45, 0, (r2+r1) cos 45 )
1427 \end{verbatim}
1428 \end{center}
1429
1430 \subsection{Translate Operation}
1431
1432 \begin{figure}
1433 \centering \includegraphics{est-tr.ps}
1434 \caption{Translating a Torus.}
1435 \label{est-tr}
1436 \end{figure}
1437
1438 \noindent{\tt
1439 mged> {\em Select the Translate'' entry in the solid edit menu} \\
1440 mged> {\em p -.5 -1 .5} \\
1441 mged>
1442 }
1443
1444 The vertex V of the torus is moved to (-.5, -1, .5).
1445 See figure \ref{est-tr}.  The
1446 coordinates of the other points remain the same, relative to the vertex.
1447 The command
1448
1449 \noindent{\tt
1450 mged> {\em p 0 0 0} \\
1451 mged>
1452 }
1453
1454 will restore the original position.
1455
1456 \subsection{Rotate Operation}
1457
1458 \begin{figure}
1459 \centering \includegraphics{est-xrot.ps}
1460 \caption{Torus Solid Edit Rotation about X.}
1461 \label{est-xrot}
1462 \end{figure}
1463
1464 \begin{figure}
1465 \centering \includegraphics{est-yrot.ps}
1466 \caption{Torus Solid Edit Rotation about Y.}
1467 \label{est-yrot}
1468 \end{figure}
1469
1470 \begin{figure}
1471 \centering \includegraphics{est-zrot.ps}
1472 \caption{Torus Solid Edit Rotation about Z.}
1473 \label{est-zrot}
1474 \end{figure}
1475
1476 \noindent{\tt
1477 mged> {\em Select the Rotate'' entry in the solid edit menu} \\
1478 mged> {\em p 45 0 0} \\
1479 mged>
1480 }
1481
1482 The torus is rotated 45 degrees counter-clockwise about the positive X axis.
1483 The
1484 coordinates of the points I and H are transformed using the following matrix:
1485 \begin{verbatim}
1486     [x'] [1   0      0   ] [x]
1487     [y']=[0  .7071 -.7071] [y]
1488     [z'] [0  .7071  .7071] [z]
1489 \end{verbatim}
1490 See Figure \ref{est-xrot}.
1491
1492 \noindent{\tt
1493 mged> {\em p 0 45 0} \\
1494 mged>
1495 }
1496
1497 The torus is rotated 45 degrees counter-clockwise about the positive Y axis.
1498 See Figure \ref{est-yrot}.
1499
1500 \noindent{\tt
1501 mged> {\em p 0 0 45} \\
1502 mged>
1503 }
1504
1505 The torus is rotated 45 degrees counter-clockwise about the positive Z axis.
1506 See Figure \ref{est-zrot}.
1507 The original orientation is restored by entering
1508
1509 \noindent{\tt
1510 mged> {\em p 0 0 0} \\
1511 mged>
1512 }
1513
1514 \subsection{Scale Operation}
1515
1516 \begin{figure}
1517 \centering \includegraphics{est-scale.ps}
1518 \caption{Torus Scale Increased.}
1519 \label{est-scale}
1520 \end{figure}
1521
1522 \noindent{\tt
1523 mged> {\em Select the Scale'' entry in the solid edit menu} \\
1524 mged> {\em p 1.5} \\
1525 mged>
1526 }
1527
1528 The vertex remains the same and all distances from the vertex are
1529 multiplied by 1.5, the value entered with p.  See Figure \ref{est-scale}.
1530 To return to the original scale, enter
1531
1532 \noindent{\tt
1533 mged> {\em p 1} \\
1534 mged>
1535 }
1536
1537 \subsection{Scale Radius 1 Command}
1538
1539 \begin{figure}
1540 \centering \includegraphics{est-sr1.ps}
1541 \caption{Scale Torus Radius 1.}
1542 \label{est-sr1}
1543 \end{figure}
1544
1545 \noindent{\tt
1546 mged> {\em Select the edit menu'' entry in the solid edit menu} \\
1547 mged> {\em Select the scale radius 1'' entry in the TORUS menu} \\
1548 mged> {\em p 1.5} \\
1549 mged>
1550 }
1551
1552 The distance from the vertex to the center of the cross-section of the
1553 ring is set equal to the values given with {\em p}, e.g., 1.5.
1554 See Figure \ref{est-sr1}.
1555 The original scale can be restored with
1556
1557 \noindent{\tt
1558 mged> {\em p 1} \\
1559 mged>
1560 }
1561
1562 \subsection{Scale Radius 2 Command}
1563
1564 \begin{figure}
1565 \centering \includegraphics{est-sr2.ps}
1566 \caption{Scale Torus Radius 2.}
1567 \label{est-sr2}
1568 \end{figure}
1569
1570 \noindent{\tt
1571 mged> {\em Select the edit menu'' entry in the solid edit menu} \\
1572 mged> {\em Select the scale radius 2'' entry in the TORUS menu} \\
1573 mged> {\em p 0.5} \\
1574 mged>
1575 }
1576
1577 The distance from the center of the cross-section of the ring is set equal
1578 to the value given with {\em p}, e.g. 0.5.
1579 This value must remain less than the value for r1.
1580 See Figure \ref{est-sr2}.
1581 The command
1582
1583 \noindent{\tt
1584 mged> {\em p 0.2} \\
1585 mged>
1586 }
1587
1588 will restore the original shape.
1589
1590 To return control to the VIEWING state, select the REJECT Edit''
1591 item on the button menu, press the reject'' button on the button box,
1592 or enter the command {\em press reject} on the keyboard.
1593 Then, enter
1594
1595 \noindent{\tt
1596 mged> {\em d tor} \\
1597 mged>
1598 }
1599
1600 to drop the torus from view.