{VERSION 2 3 "APPLE_68K_MAC" "2.3" }
{USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 
1 0 0 0 0 }{CSTYLE "" -1 256 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }
{CSTYLE "" -1 257 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 258 
"" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 259 "" 0 1 0 0 0 0 0 
1 0 0 0 0 0 0 0 }{CSTYLE "" -1 260 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }
{CSTYLE "" -1 261 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 262 
"" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 263 "" 0 1 0 0 0 0 0 
1 0 0 0 0 0 0 0 }{CSTYLE "" -1 264 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }
{CSTYLE "" -1 265 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 266 
"" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 267 "" 0 1 0 0 0 0 0 
1 0 0 0 0 0 0 0 }{CSTYLE "" -1 268 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }
{CSTYLE "" -1 269 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 270 
"" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 271 "" 0 1 0 0 0 0 0 
1 0 0 0 0 0 0 0 }{CSTYLE "" -1 272 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }
{CSTYLE "" -1 273 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 274 
"" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 275 "" 0 1 0 0 0 0 0 
1 0 0 0 0 0 0 0 }{CSTYLE "" -1 276 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }
{CSTYLE "" -1 277 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 278 
"" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" 
-1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 
0 }{PSTYLE "" 0 256 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 
0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 257 1 {CSTYLE "" -1 
-1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }
}
{SECT 0 {EXCHG {PARA 256 "" 0 "" {TEXT -1 27 "Virtual Reality -- Flatl
and" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 150 "T
he following cells define several Maple procedures for displaying and \+
manipulating images.  Each image is represented by a list of points of
 the form" }}{PARA 257 "" 0 "" {TEXT -1 2 "\n\n" }{TEXT 256 34 "[[x1, \+
y1], [x2, y2], ... [xn, yn]]" }{TEXT -1 2 "\n\n" }}{PARA 0 "" 0 "" 
{TEXT -1 89 "and is drawn by connecting the points by lines.\n\nYou wi
ll use the following procedures:\n\n" }{TEXT 257 18 "plotcurve(list, n
)" }{TEXT -1 118 " -- This procedure displays one image represented by
 a list of points as described above.  The x- and y-axes run from " }
{TEXT 258 2 "-n" }{TEXT -1 4 " to " }{TEXT 259 1 "n" }{TEXT -1 3 ".\n
\n" }{TEXT 260 27 "plotcurves(list1, list2, n)" }{TEXT -1 104 " -- Thi
s procedure displays two images represented by two lists of points.  t
he x- and y-axes run from  " }{TEXT 261 2 "-n" }{TEXT -1 5 "  to " }
{TEXT 262 1 "n" }{TEXT -1 84 ".  The first image is displayed in black
 and the second image is displayed in red.\n\n" }{TEXT 263 12 "mirror(
list)" }{TEXT -1 85 " -- This procedure computes the reflection in the
 x-axis of the image represented by " }{TEXT 264 5 "list\n" }{TEXT -1 
2 "\nt" }{TEXT 265 15 "rans(list, a, b" }{TEXT -1 54 ") -- This proced
ure translates the image represnted by" }{TEXT 266 6 " list " }{TEXT 
-1 3 "by " }{TEXT 267 2 "a " }{TEXT -1 23 "units horizontally and " }
{TEXT 268 1 "b" }{TEXT -1 20 " units vertically.\n\n" }{TEXT 269 16 "r
ot(list, theta)" }{TEXT -1 52 " -- This procedure rotates the image re
presented by " }{TEXT 270 5 "list " }{TEXT -1 3 "by " }{TEXT 271 5 "th
eta" }{TEXT -1 46 " radians counterclockwise around the origin.\n\n" }
{TEXT 272 15 "dilate(list, a)" }{TEXT -1 50 " -- This procedure dilate
s an image represented by" }{TEXT 273 5 " list" }{TEXT -1 15 " by the \+
factor " }{TEXT 274 1 "a" }{TEXT -1 3 ".\n\n" }{TEXT 275 12 "ident(lis
t) " }{TEXT -1 49 "-- This procedure leaves the image represented by" 
}{TEXT 276 5 " list" }{TEXT -1 9 " alone.\n\n" }{TEXT 277 26 "Evaluate
 the next cell now" }{TEXT -1 2 ".\n" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 839 "with('plots'):\n\n  plotcurve := proc(lst, n)\n     \+
plot(lst, -n..n, -n..n, scaling = CONSTRAINED)\n  end: \n\n  mirrorpt \+
:= x -> [x[1], -x[2]]:\n  transpt  := (x, a, b) -> [x[1] + a, x[2] + b
]:\n  rotpt    := (x, theta) -> [x[1] * cos(theta) - x[2] * sin(theta)
,\n                           x[1] * sin(theta) + x[2] * cos(theta)]:
\n  dilatept := (x, a) -> [x[1] * a, x[2] * a]:\n  identpt  := x -> x:
\n\n  mirror   := x -> [seq(mirrorpt(j), j=x)]:\n  trans    := (x, a, \+
b)  -> [seq(transpt(j, a, b), j=x)]:\n  rot      := (x, theta) -> [seq
(rotpt(j, theta), j=x)]:\n  dilate   := (x, a) -> [seq(dilatept(j, a),
 j=x)]:\n  ident    := x -> x:\n\n  plotcurves  := proc(x, y, n) local
 blk, rd;\n     blk := plot(x, -n..n, -n..n, scaling=CONSTRAINED, colo
r=black);\n     rd  := plot(y, -n..n, -n..n, scaling=CONSTRAINED, colo
r=red);\n     display([blk, rd]);\n  end:" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 78 "The next cell illustrates
 how these procedures are used to work with images.  " }{TEXT 278 16 "
Evaluate it now." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 114 "a := [[1,2], [2,1], [3,2]]:\n\n  plotcurve(a
, 3);\n\n  plotcurves(a, mirror(a), 3);\n\n  plotcurves(a, dilate(a, 2
), 8);" }}}}{MARK "0 0 0" 27 }{VIEWOPTS 1 1 0 1 1 1803 }