{VERSION 2 3 "APPLE_68K_MAC" "2.3" }
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{CSTYLE "" -1 257 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 }{CSTYLE "" -1 258 
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{SECT 0 {EXCHG {PARA 256 "" 0 "" {TEXT -1 61 "Looking a a Three Dimens
ional World with Two Dimensional Eyes" }}{PARA 0 "" 0 "" {TEXT -1 0 "
" }}{PARA 0 "" 0 "" {TEXT -1 117 "The following cell illustrates how M
aple works with vectors, scalar multiplication, the dot product, and m
agnitude.  " }{TEXT 256 16 "Evaluate it now." }}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "with(linalg):" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "u := [1, 2, 3]:" }}{PARA 0 "> " 0 "
" {MPLTEXT 1 0 15 "v := [6, 3, 1]:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 
13 "evalm(4 * u);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "dotprod(u, v);
" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "magnitude := x -> sqrt(dotprod(
x, x)):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "magnitude(u);" }}{PARA 
0 "> " 0 "" {MPLTEXT 1 0 27 "magnitude([1, 2, 3, 4, 5]);" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 169 "The foll
owing cell illustrates how Maple can be used to find the point where t
wo lines \"intersect\" even when they don't exactly intersect because \+
of measurement error.  " }{TEXT 257 16 "Evaluate it now." }}{PARA 0 "
" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "View
   := [0, 0, 105]:          # Viewpoint" }}{PARA 0 "> " 0 "" {MPLTEXT 
1 0 61 "Ground := [3.20, 4.20, 0]:      # Apparent location on ground
" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "Light  := [-105, 0, 105]:      \+
 # Light source" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "Shadow := [8.3, \+
4.3, 0]:        # Shadow" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "# The next lines define the functio
n  f(s, t)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 131 "P := (s, t) -> evalm(t * Light) + evalm((1 - t) * Sh
adow) -\n(evalm(s * View) + evalm((1 - s) * Ground)):                 \+
          " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 42 "F  := (s, t) -> dotprod(P(s, t), P(s, t)):" }}{PARA 
0 "> " 0 "" {MPLTEXT 1 0 33 "Ft := (s, t) -> diff(F(s, t), t):" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "Fs := (s, t) -> diff(F(s, t), s):" 
}}{PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "fsolve(\{Ft(s, t) = 0, Fs(s, t) =
 0\}, \{s, t\}):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 135 "subs(\", evalm
(0.5 * (t * Light + (1 - t) * Shadow +\n                     s * View \+
+ (1 - s) * Ground)));                               " }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 168 "The next
 cell defines the points and rods for the pyramid used as an example i
n this module.  Then it draws the picture taken by a camera from a par
ticular viewpoint.  " }{TEXT 258 245 "Evaluate the next cell now and t
hen look at this pyramid from various different points-of-view.   Then
 use the same ideas to draw pictures taken by a camera looking at your
 TinkerToy house from various points-of-view.  Use your own measuremen
ts." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 16 "with(plottools):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 
13 "with(plots):\n" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "theta  := Pi/
8:          # Angle from x-axis to viewpoint" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 61 "radius := 100:           # Distance along ground to v
iewpoint" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "height := 75:          \+
  # Height of viewpoint" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "# The three parameters above define
 the direction of the viewpoint" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "
" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "aa := [-1,  0, 0]:" }}{PARA 0 "
> " 0 "" {MPLTEXT 1 0 18 "bb := [ 1,  0, 0]:" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 18 "cc := [ 0,  1, 0]:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 
18 "dd := [ 0, -1, 0]:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "tt := [ 0
,  0, 1]:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 32 "Points := \{aa, bb, cc, dd, tt\}: " }}{PARA 0 "> " 0 
"" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 103 "Rods   := \+
\{\{aa, cc\}, \{cc, bb\}, \{bb, dd\}, \{dd, aa\},\n           \{aa, tt
\}, \{bb, tt\}, \{cc, tt\}, \{dd, tt\}\}: " }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "u := [-sin(thet
a), cos(theta), 0]:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 149 "v := [-heig
ht * cos(theta)/sqrt(height^2 + radius^2),\n      -height * sin(theta)
/sqrt(height^2 + radius^2),\n      radius/sqrt(height^2 + radius^2)]:
\n" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "linelist := \{\}:" }}{PARA 0 
"> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 284 "for \+
i from 1 to nops(Rods) do\n    linelist := linelist union \{line([dotp
rod(u, Rods[i][1]),\n                                      dotprod(v, \+
Rods[i][1])],\n                                     [dotprod(u, Rods[i
][2]),\n                                      dotprod(v, Rods[i][2])])
\}\nod:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 63 "display(linelist, color=black, scaling=CONSTRAINED, a
xes=NONE);" }}}}{MARK "2 1 0" 36 }{VIEWOPTS 1 1 0 1 1 1803 }