COMMENT ⊗   VALID 00012 PAGES
C REC  PAGE   DESCRIPTION
C00001 00001
C00002 00002	TITLE PAGE - GEOMED MANUAL.
C00005 00003	CONTENTS
C00006 00004	INTRODUCTION.
C00008 00005	GEOMED COMMAND SUMMARY:
C00010 00006	GEOMED COMMAND SUMMARY:
C00012 00007	GEOMED COMMAND SUMMARY:
C00014 00008	PRIMER:	INSTANT CUBE, TRANSLATION.
C00018 00009	PRIMER: CONTROL, META, AND META-CONTROL.
C00022 00010	PRIMER:	ROTATION.
C00026 00011	PRIMER:	DRAWING A CUBE.
C00029 00012	PRIMER:	DRAWING A TORUS.
C00034 ENDMK
C⊗;
TITLE PAGE - GEOMED MANUAL.

SAILON NUMBER 68.			                GEOMED MANUAL

STANFORD ARTIFICIAL INTELLIGENCE LABORATORY                MARCH 1974
OPERATING NOTE NUMBER 68.2



                     GEOMED  -  GEOMETRIC EDITOR.

                          Bruce g. Baumgart





ABSTRACT: 

	GEOMED is  a package of  subroutines for doing  3-D geometric
modeling.  Used from  a keyboard,  GEOMED  is an  interactive drawing
program; used as  a package of SAIL  or LISP accessible  subroutines,
GEOMED is a  graphics language. With GEOMED,  arbitrary polyhedra can
be  contructed; moved  about  and viewed  in perspective  with hidden
lines eliminated.  In addition to polyhedra; camera  and image models
are provided so that  simulators relevant to computer vision, problem
solving,  and animation can be constructed.















---------------------------------------------------------------------
This  research  was  supported  in  part  by  the  Advanced  Research
Projects  Agency of  the  Office of  the Secretary  of  Defense under
Contract DAHC15-73-C-0435

The views and  conclusions contained  in this document  are those  of
the author and should not  be interpreted as necessarily representing
the  official policies, either expressed or  implied, of the Advanced
Research Project Agency or the United States Government.
---------------------------------------------------------------------
CONTENTS

SECTION							PAGE

INTRODUCTION.

	This SAILON  consists of  two parts:  part one, explains  the
external  keyboard commands of GEOMED  for use as  a drawing program;
and  part  two,  explains  the  internal  SAIL  and  LISP  accessible
subroutines of GEOMED for use as a language for geometric modeling.

	The command summary  comes at the beginning of  this document
rather than at the end so that the program itself can always find the
summary on pages 4,  5 and 6 of this file GEOMED.BGB[S,DOC].
This document  can be accessed while  using GEOMED by typing  the "H"
help command.
GEOMED COMMAND SUMMARY:

α CONTROL KEY PREFIX.
β META KEY PREFIX.
ε META-CONTROL PREFIX.

:  EUCLIDEAN TRANSFORMATION +X.			  TRANSLATION.
;  EUCLIDEAN TRANSFORMATION -X.			α ROTATION.
)  EUCLIDEAN TRANSFORMATION +Y.			β DILATION.
(  EUCLIDEAN TRANSFORMATION -Y.			ε REFLECTION.
*  EUCLIDEAN TRANSFORMATION +Z.
-  EUCLIDEAN TRANSFORMATION -Z.

/  HALVE STRENGTH.
\  DOUBLE STRENGTH.

!  TRANSLATION DEFAULT SWITCH.
@  ROTATION DEFAULT SWITCH.

π  ACCEPT ROTATION STRENGTH.
λ  ACCEPT TRANSLATION STRENGTH.
%  ACCEPT DILATION RATIO.

∂  FLIP NODE DISPLAY SWITCH.         α∂ FLIP NODE DISPLAY FORMAT.
∀  ENABLE ALL BODY MOTIONS.
   DISABLE:   α∀ FRAME MOTION.   β∀ VERTEX MOTION.   ε∀ PARTS MOTION.
_  STICKY DISPLAY MODE SWITCH.

↓  COPY PUSH.   α↓ ROTATE PUSH.
↑  PADPDL POP.  α↑ ROTATE POP.
↔  SWAP STACK 1ST ↔ 2ND   1ST α↔ 3RD   1ST β↔ LAST    2ND ε↔ 3RD

∩  FETCH DAD LINK,
∪  FETCH SON LINK,
⊂  FETCH BRO LINK.
⊃  FETCH SIS LINK.

<  FETCH NFACE LINK.
>  FETCH PFACE LINK.
≥  FETCH PED LINK.
≤  FETCH NED LINK.
∧  FETCH PVT LINK
∨  FETCH NVT LINK.
,  CLOCKWISE LINK.
.  COUNTER CLOCKWISE LINK.
⊗  FETCH UNIVERSE NODE.
←  FETCH ALT LINK.
→  FETCH ALT2 LINK.
+  OTHER LINK.
GEOMED COMMAND SUMMARY:

α∩ BODY INTERSECTION.
α∪ BODY UNION.
α¬ BODY SUBTRACTION.

¬  BODY EVERT.
$  MAKE CONVEX.
|  INVERT EDGE PARITY.

0-9  SET-DIGIT COMMAND.
?  INFORMATION PREFIX.
#  TWENTY CRLF'S.
∞  INSTANT CUBE. α∞ INSTANT TORUS.

A  ATTACH, βAXECNT.
B  BODY RETRIEVAL.
C  COPY, αC NOW CAMERA.
D  DETACH, αDARKEN, βDUAL, εUNDARKEN.
E  SWEEP WIRE. εE EXIT.
F  FRAME STEP SWITCH. αF SET FOCAL LENGTH. β UNSTEP FRAME SWITCH.

G  GLUE COMMAND.
H  HELP. αH UNHELP.
I  INPUT B3D. αI INPUT CAMERA. βI INPUT CRE.
J  JOIN VERTEX-VERTEX.
K  KILL COMMAND.
L  LABEL LIGHTS SWITCH.

M  MIDPOINT COMMAND.
N  NAME BODY
O  OUTPUT COMMANDS.
P  OUTPUT PLOT FILE
Q  FRAME ORIGIN SWITCH.
R  ROTATION COMPLETION.

S  SWEEP COMMANDS.
T  CREATE/EDIT TEXT LABEL.
U
V  MAKE VERTEX BODY.

W  MAKE: W WORLD. αW WINDOW. βW CAMERA. εW IMAGE.
X  EXIT GEOMED.
Y
Z  EXECUTE MACRO, αZ CREATE/EDIT MACRO, βZ INPUT COMMAND FILE.

ALT  OCCULT. αALT FRONT FACE. βALT ALL EDGES.
GEOMED COMMAND SUMMARY:

TEXT EDIT COMMANDS:

System line  edit commands, enter line edit mode.

<CR>	Forward 1 line
<VT>	Backward 1 line
αε>	Forward 4 lines
αε<	Backward 4 lines
αε≥	Forward 16 lines
αε≤	Backward 16 lines

εD	Delete a line
εI	Enter line insert mode
αZ	Concatenate next line with current line

αεE	Return to GEOMED
αεV	Update display
αM	Invoke a macro
αN	Take commands from text file





----------------------------------------------------------------------
X EXTEND COMMANDS:

X CUBIC DX DY DZ		MAKE CUBIC PRISM.
X BALL  RADIUS M N		MAKE SPHERE M LONGITUDES, N LATITUDES.
X CYLN  RADIUS N DZ		MAKE CYLINDER OF N-SIDES, HEIGHT DZ.

X COLOR 99R 99B 99G 99A		COLOR RED, BLUE, GREEN, ALBEDO.
X NSHARP			MARK ALL EDGES NOT SHARP
PRIMER:	INSTANT CUBE, TRANSLATION.

	This  section  is  literally an  operating  manual;  you  are
supposed  to be operating  GEOMED as you  read. I will  tell you what
keys to type and you will type them to see for yourself what happens;
although  an  explanation  is  given  later  for  each  command,  the
complexity  of  individual commands  tends  to obscure  their  use in
sequences. The system copy of GEOMED is started by  typing "R GEOMED"
carriage  return at a  III display  console.   GEOMED will  display a
rectangle,  type  an asterisk  and await  single character  commands.
Typing carriage returns will yield more asterisks showing that GEOMED
is alive and listening.

INSTANT CUBE.

	Type the character "∞" to get a drawing of a cube.
	Adjust the pots on the III so that the cube looks right.

TRANSLATION.

   Type the character ":" to move the cube right (positive x axis).
   Type the character ";" to move the cube left (negative x axis).
   Type the character ")" to move the cube up (positive y axis).
   Type the character "(" to move the cube down (negative y axis).
   Type the character "*" to move the cube nearer (positive z axis).
   Type the character "-" to move the cube away (negative z axis).

	Clearly  these command  characters  are not  mnemonics,  they
were  chosen  because  they  do  not  require  the  TOP key  and  are
conveniently grouped in pairs under one's right hand.

STRENGTH OF TRANSLATION.

	The distance the cube is moved by a  translation  command  is
called  the  strength  of  translation  or TDEL. The value of TDEL is
displayed in the upper right corner of the screen  and  is  initially
one foot. The strength of translation is halved by typing the command
character "/" or doubled by typing "\".

WORLD FRAME OF REFERENCE.

	The direction the  cube moved was  with respect to  the world
frame  of reference which is  a right handed coordinate  system,  the
initial camera is  positioned looking down  the Z  axis at the  world
origin. The  world origin is  in the center  of the display  screen a
simulated sixteen feet away; and the positive world X axis is to your
right; and the positive world Y axis is upwards.
PRIMER: CONTROL, META, AND META-CONTROL.

	Notice that the Stanford A.I. keyboard  has four "shift" keys
labeled SHIFT, TOP,  META & CONTROL. SHIFT only determines whether an
alphabetic letters is upper or lower case; GEOMED converts lower case
letters into upper so  that the SHIFT key has no  effect. The TOP key
allows  two ASCII character  codes to  be on each  physical key, this
doubling up on  the physical  keys is not  important to GEOMED  since
"TOP-E"  can always  be  referred to  as  "@".   Finally,   of  great
importance, the CONTROL and META keys add two extra bits to the 7-bit
ASCII code,   so that a 9-bit character  is sent to GEOMED.   In this
document  the characters  "α",  "β"  and "ε"  will be used  as prefix
abbreviations  for CONTROL,    META  and  META-CONTROL  keying  of  a
character. Furthermore,   the command scanner  accepts the characters
"α",  "β" and "ε" as  prefix modifiers that  will add the appropriate
control and  meta bits  to the  next  character.   The question  mark
character,   explained immediately  below, is  the only  other prefix
modifier character.

QUESTION MARK "?".

	Typing  the  question  mark  charcter  "?"  followed  by  any
character will type a one line reminder  of what commands are invoked
by that character.

EXTENDED COMMAND SCANNER.

	x-commands are executed  by typing "X" followed by  the first
three letters of a mnemonic (further letters are ignored) followed by
any necessary arguments,  the command is terminated by a  RETURN. The
arguments  may  be separated  by  any  reasonible delimiters:  space,
comma,   tab,  etc.  The following three extend commands provide easy
creation of simple polyhedra.

	X CUBIC DELTAX,DELTAY,DELTAZ
	X BALL  RADIUS,M-LONGUTUDES,N-LATITUDES
	X CYLN	RADIUS,N-SIDES,DZ-HEIGHT

	The CUBIC command makes a right  rectangular prism with width
height  and depth  as  given in  three distance  arguments.  The BALL
command make a polyhedron that approximates a sphere. The CYLN make a
right prism that approximates a circular cylinder.

EXAMPLES:
	X CUB 2 3 4
	X CYL 4 10 10
	X BALL 1 6 10
PRIMER:	ROTATION.

ROTATION.

	The  rotation  command  characters  are  the  same   as   for
translation  except  you must hold the CONTROL key down or prefix the
command with an "α". Try rotating the instant cube about  the  X-axis
with  "α:".  The positive direction of rotation is counter-clockwise.
The negative direction of rotation is clockwise.

STRENGTH OF ROTATION.

	The strength of rotation is named RDEL,  the value of RDEL is
displayed  in three  formats in  the upper right  hand corner  of the
screen: as a  pi fraction  and in  degrees,  minutes,   seconds.  The
initial value of  RDEL is π/4, 45 degrees.  Analogous to translation,
the  strength  of rotation  is  halved or  doubled by  "α/"  and "α\"
respectively.

ROTATION DEFAULT.

	Since a sequence of rotations is quite common, there is a way
to  make the CTRL key  be sticky. The  usual Euclidean transformation
default is translation world frame; but after typing the  "@" command
character, the Euclidean default is rotation world frame. Translation
default  is  restored by  typing  "!".   The state  of  the Euclidean
transformation default is also  displayed in the status in  the upper
right hand corner of the screen. (The "≡" command disables the status
display, "≡" toggles).

THE STACK AND THE FEV RINGS.

	GEOMED commands  take their  arguments from  and leave  their
results in a push  down stack of bodies,  faces,  edges and vertices.
The contents of the stack are displayed on the left hand side  of the
III screen.   Having made a  cube, you will  have a B1 in  the stack;
making  a second cube will  push a B2 into the  stack. To retrieve B1
use the  "↑" stack  pop or  the "α↑" stack  rotate up  or "α↓"  stack
rotate down  or "↔" the  swap top of  stack command. The  "↓" command
pushs the stack down and  places in the new  top the entity that  was
previously  top  of  stack.  A  polyhedron consists  of  three  rings
(circular double linked lists):

	Face ring	 "<" NFACE,PFACE ">"
	Edge ring	 "≤"   NED,PED   "≥"
	Vertex ring	 "∨"   NVT,PVT   "∧"

The rings can be  traveled using the command characters  "<>≤≥∨∧" for
fetching the NFACE,  PFACE, NED, PED, NVT and PVT link of the current
top of stack  which is  replaced. Notice  that when a  face, edge  or
vertex node  is in the top  of the stack the  corresponding entity is
intensified in the drawing. 
PRIMER:	DRAWING A CUBE.

	After "∞" and  "X CUBE", a third way  to draw a cube  will be
used to  illustrate the primitive topology  commands. Starting with a
fresh copy of GEOMED,  type the command letters in the  second column
to get the advertised results:

1.	V	Vertex body creation.
2.	:)	Position the vertex into the first quadrant.
3.	S;;	Make an edge and vertex and move left.
4.	S((	Edge vertex down.
5.	S::	Edge vertex right.
6.	J↑	Join the first and last vertices of the wire.
7.	*	Pull the face lamina towards you.
8.	S	Sweep the square face into a very thin solid.
9.	--↑	Move the face away from you giving the cube depth.
10.	@/):!	Rotate the cube to a more familiar position.

Three commands that have not been mentioned yet are:

	"V"	Vertex Body Creation.
	"S"	Sweep.
	"J"	Join two vertices with a new edge.

	The "V"  command takes  no arguments  and pushs  a brand  new
body,    face and  vertex  into  the stack.    This  degenerate point
polyhedron satisfies  the  Euler equation  F-E+V=2 (1-0+1=2)  and  is
always placed at the world origin.  The first three sweep commands in
the  example, sweep  a vertex  polyhedron into  a wire  polyhedron by
adding a new vertex  and a new edge; incidentally  preserving Euler's
equation  as do all  GEOMED commands.  The wire-sweep takes  a Vertex
argument, and returns  the new vertex.  The new vertex  has the  same
locus as the argument vertex. After three sides of a square have been
formed,   the "J" command creates  a new face and  a new edge between
the first and last  vertex of the wire face.   The wire-join case  of
the "J" command takes a vertex  argument and identifies it as the end
of  a wire and knows enough  to fetch the other  end of that wire, as
its second argument.
PRIMER:	DRAWING A TORUS.

1.	V:@		First Vertex.
2.	S*S*S*		Seven more vertices.
	S*S*S*S*
3.	J↑		Form Lamina.
4.	!//:		Position the lamina.
5.	@S)S)S)S)	Sweep the face around the Y-axis.
	S)S)S)S)
6.	↓>G↑		Glue the ends of the torus together.

EXERCISES.

	1. DRAW THE SOMA CUBES AS IN FIGURE.
	2. DRAW A JACK AS IN FIGURE.

HIDDEN LINE ELIMINATION

	Hit the ALT-MODE key in order to see your drawing with its
hidden lines eliminated.

FRAMES OF REFERENCE

	In addition to the world frame of reference, each body and camera
has a reference frame. The current frame of reference is  determined by
a four state switch and the contents of the top of the stack.

PARTS TREE STRUCTURE

DILATION and REFLECTION