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{SECT 0 {EXCHG {PARA 215 "" 0 "" {TEXT 224 23 "Euclidean motions in 3D
" }{TEXT 224 0 "" }}}{EXCHG {PARA 216 "> " 0 "" {MPLTEXT 1 225 8 "rest
art;" }{MPLTEXT 1 225 0 "" }}}{EXCHG {PARA 216 "> " 0 "" {MPLTEXT 1 
225 30 "with(plottools): with(plots): " }{MPLTEXT 1 225 0 "" }}}
{EXCHG {PARA 217 "" 0 "" {TEXT 226 53 "Construct a 3D \"molecule\" con
sisting of colored lines" }{TEXT 226 0 "" }}}{EXCHG {PARA 218 "> " 0 "
" {MPLTEXT 1 0 11 "thick := 4:" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 
219 "> " 0 "" {MPLTEXT 1 227 62 "a3 := line([1,-1,0], [1,1,0], thickne
ss = thick, color = red):" }{MPLTEXT 1 227 0 "" }{MPLTEXT 1 227 67 "\n
b3 := line([-1,-1,0], [-1,1,0], thickness = thick, color = green):" }
{MPLTEXT 1 227 0 "" }{MPLTEXT 1 227 65 "\nc3 := line([0,0,0], [0,0,1],
 thickness = thick, color = orange):" }{MPLTEXT 1 227 0 "" }{MPLTEXT 
1 227 69 "\nd3 := line([0,0,0], [0,0,-1], thickness = thick +2, color \+
= yellow):" }{MPLTEXT 1 227 0 "" }{MPLTEXT 1 227 62 "\ne3 := line([1,1
,0], [0,0,1], thickness = thick, color = red):" }{MPLTEXT 1 227 0 "" }
{MPLTEXT 1 227 63 "\nf3 := line([1,-1,0], [0,0,1], thickness = thick, \+
color = red):" }{MPLTEXT 1 227 0 "" }{MPLTEXT 1 227 66 "\ng3 := line([
-1,-1,0], [0,0,1], thickness = thick, color = green):" }{MPLTEXT 1 
227 0 "" }{MPLTEXT 1 227 65 "\nh3 := line([-1,1,0], [0,0,1], thickness
 = thick, color = green):" }{MPLTEXT 1 227 0 "" }{MPLTEXT 1 227 62 "\n
mol := map(x->scale(x,.3,.3,.3),\{a3,b3,c3,d3, e3, f3,g3,h3\}):" }
{MPLTEXT 1 227 0 "" }}}{EXCHG {PARA 219 "> " 0 "" {MPLTEXT 1 227 55 "d
isplay3d(mol, scaling = unconstrained, axes = framed);" }{MPLTEXT 1 
227 0 "" }}}{EXCHG {PARA 220 "" 0 "" {TEXT 228 87 "T1 transforms a set
 of 3D plot structure by translating by (2,0,1).  You must use the  " 
}{TEXT 229 4 "map " }{TEXT 228 15 "command since  " }{TEXT 229 3 "mol"
 }{TEXT 228 58 "  is not a plot structure but a set of graphics object
s.  " }{TEXT 228 0 "" }}}{EXCHG {PARA 219 "> " 0 "" {MPLTEXT 1 227 43 
"T1 := x ->  map(y -> translate(y,2,0,1),x):" }{MPLTEXT 1 227 0 "" }
{MPLTEXT 1 227 63 "\ndisplay3d(mol, T1(mol), scaling = constrained, ax
es = framed);" }{MPLTEXT 1 227 0 "" }}}{EXCHG {PARA 220 "" 0 "" {TEXT 
228 48 "Rotations on plot structures are defined by the " }{TEXT 230 
7 "rotate " }{TEXT 228 141 "command.  The last three arguments give an
gles about the x, y and z axes respectively.  T2 rotates an anlge of 1
80 degress about the x axis. " }{TEXT 228 0 "" }}}{EXCHG {PARA 219 "> \+
" 0 "" {MPLTEXT 1 227 40 "T2 := x -> map(y -> rotate(y,Pi,0,0),x):" }
{MPLTEXT 1 227 0 "" }}}{EXCHG {PARA 221 "> " 0 "" {MPLTEXT 1 231 24 "d
isplay3d(mol, T2(mol));" }{MPLTEXT 1 231 0 "" }}}{EXCHG {PARA 217 "" 0
 "" {TEXT 226 86 "T3 is a compositon of a rotation and a translation a
nd is therefore a screw rotation. " }{TEXT 226 0 "" }}}{EXCHG {PARA 
219 "> " 0 "" {MPLTEXT 1 227 21 "T3 := x -> T1(T2(x)):" }{MPLTEXT 1 
227 0 "" }}}{EXCHG {PARA 219 "> " 0 "" {MPLTEXT 1 227 75 "display3d(se
q((T3@@k)(mol), k = 1..4), scaling = constrained, axes = none);" }
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