GSP4TQThat document was created with a newer version of Sketchpad and cannot be opened.|This document was created with a newer version of Sketchpad. Some information may be lost. The document will open as a copy.$"uLGraph Template` a b c d e f g h i j k l m n o p q _ ,#GSP4_M_0554/Mar 2 20040#H GenevaJ Charcoal Arial       '''$'$'$' @ $'$' $' $'$'$'$' $' $' %'&'8'8'8'9':' nQ\aAD a@Y@ nQ\aAA3#y@`nm@ <#?Ġ_X<@?J`?  @     a h$@Scale 4гZ@W?? @  $rϥwg) V@ @   ['&8ʿE{KRXY@ $rϥwg) V@  E   4гZ@W??  $rϥwg) V@ @   @    $rϥwg) V@ @   @   @ / @   @    E/ @   - CT@ @  @  - ST@ -  $rϥwg) V@ @  aa>>Q??R+?0?0R@ O` `<0>t ea @0?YY@?? nQ\aA=x[min]`d O^ <0>t ea >0?YY@?? nQ\aA=x[max] O` `<0>t ea @0?YY@?? nQ\aA=y[min]`d) O^ <0>t ea >0?YY@?? nQ\aA=y[max]) O^ a0<0>t ea >0?YY@?? nQ\aA=z[min]a0e> O` 0<0>t ea @0?YY@?? nQ\aA=z[max]0> %mIgtJHUZ -4гZ@W?? @ -. E// @ - - 1CF 2$rϥwg) V@CF@ @ 3 3/ @ - - 6SF@ @ 7. @ 8 - 9  : -CT*SF 5; 5; @ ; ; @ =? ; A3 @ AB @ <A. @  8 - E F -ST*SF 5G H;$ =grid_unitZ @ I= @ H5 <G AG M3$ =grid_unitX @ G G P3 Q;$ =grid_unitY P3 @ 5S S; @ =U P; @ ?W @ PW P; Z3 @ ZP Z3xyi @ N] @ R] G @ M` `; @ `b `3 d;& =grid_origin @ eN"  ?+xi @ IeDݚ?+zi @ eRq?+yi5ReN].#>  -   S nQ\aAXY view $,L7߁ə%??igin>  -k   R nQ\aAXZ view P` s<0>t ea @0bX<@T*J%@bX<@?nQ\aAt[7]e s km$;f;f?F@igin>  k-n   R nQ\aAYZ View>  - D>@ ף9FA ף9F   S"nQ\aA Spin Axes4C>> 4Cs> 4 "#$%&'()*+,q   J*nQ\aAShow Graph Bounds> ,  -/0   R5.nQ\aAShow Axes ControllerllY>>>n0.,|> ,|ySQThat document was created with a newer version of Sketchpad and cannot be opened.|This document was created with a newer version of Sketchpad. Some information may be lost. The document will open as a copy.>$"[LPlotting Points` a b c d e f g h i j k l m n o p q _ ,#GSP4_M_0554/Mar 2 20040#H GenevaJ Charcoal`Arial HelveticaApple Chancery       '''$'$'$' @ $'$' $' $'$'$'$' $' $' %'&'8'8'8'9':' nQ\aAD a@Y@ nQ\aAA3#y@`nm@ <#?Ġ_X<@??  @     %K @Scale 4гZ@W?? @  $rϥwg) V@ @   f!KO?4Y?XY@ $rϥwg) V@  E   4гZ@W??  $rϥwg) V@ @   @    $rϥwg) V@ @   @   @ / @   @    E/ @   - CT@ @  @  - ST@ -  $rϥwg) V@ @  aa>>Q??R+?0?0R@ O` `<0>t ea @0?YY@?? nQ\aA=x[min]` O^ <0>t ea >0?YY@?? nQ\aA=x[max] O` `<0>t ea @0?YY@?? nQ\aA=y[min]`) O^ <0>t ea >0?YY@?? nQ\aA=y[max]) O` a0<0>t ea @0?YY@?? nQ\aA=z[min]a0> O^ 0<0>t ea >0?YY@?? nQ\aA=z[max]0> ųeO?YzUlֿZ -4гZ@W?? @ -. E// @ - - 1CF 2$rϥwg) V@CF@ @ 3 3/ @ - - 6SF@ @ 7. @ 8 - 9  : -CT*SF 5; 5; @ ; ; @ =? ; A3 @ AB @ <A. @  8 - E F -ST*SF 5G H;$ =grid_unitZ @ I= @ H5 <G AG M3$ =grid_unitX @ G G P3 Q;$ =grid_unitY P3 @ 5S S; @ =U P; @ ?W @ PW P; Z3 @ ZP Z3xyi @ N] @ R] G @ M` `; @ `b `3 d;& =grid_origin @ eN"  ?+xi @ IeDݚ?+zi @ eRq?+yi5ReN].#>  -   S nQ\aAXY view $,L7߁ə%??igin>  -k   R nQ\aAXZ view P` s<0>t ea @0bX<@T*J%@bX<@?nQ\aAt[7]e s km$;f;f?F@igin>  k-n   R nQ\aAYZ View>  - D>@ ף9FA ף9F   S"nQ\aA Spin Axes4C>> 4Cs> 4 "#$%&'()*+,q   J*nQ\aAHide Graph Bounds> ,  -/0   R5.nQ\aAShow Axes Controller0.,|> ,|y O^ <0>s  3 >0?YY@??nQ\aA1 0 3u'(r 9<0>#AAx R0 LP"aHDb `sl# ``  ``  ! Nev. wh0 3u'(r 9<0>#AAx R0 LP"aHDb `sl# ``  ``  ! Ney. zh O^ <0>s  3 >0?YY@??nQ\aA0 ' O` (<0>s  3 @0?YY@??nQ\aA-1w (80 3u'(r 9<0>#AAx R0 LP"aHDb `sl# ``  ``  ! Ne~. h0 3|)*r 9<0>#AAx R0 LP"aHDb `sl# ``  ``  ! Re. f - 0 3|+,r 9<0>#AAx R0 LP"aHDb `sl# ``  ``  ! Iee"(1,0, 0)  0 3}'(r 9<0>#AAx R0 LP"aHDb `sl# ``  ``  ! Ne. h0 3|)*r 9<0>#AAx R0 LP"aHDb `sl# ``  ``  ! Re. f - 0 3|+,r 9<0>#AAx R0 LP"aHDb `sl# ``  ``  ! Iee" (-1,0, 0) 0 3|'(r 9<0>#AAx R0 LP"aHDb `sl# ``  ``  ! Ne. h0 3u)*r 9<0>#AAx R0 LP"aHDb `sl# ``  ``  ! Re. f - 0 3|+,r 9<0>#AAx R0 LP"aHDb `sl# ``  ``  ! Iee"(0,1, 0) 0 3|'(r 9<0>#AAx R0 LP"aHDb `sl# ``  ``  ! Ne. h0 3})*r 9<0>#AAx R0 LP"aHDb `sl# ``  ``  ! Re. f - 0 3|+,r 9<0>#AAx R0 LP"aHDb `sl# ``  ``  ! Iee" (0,-1, 0) 0 3|'(r 9<0>#AAx R0 LP"aHDb `sl# ``  ``  ! Ne. h0 3|)*r 9<0>#AAx R0 LP"aHDb `sl# ``  ``  ! Re. f - 0 3u+,r 9<0>#AAx R0 LP"aHDb `sl# ``  ``  ! Iee"(0,0, 1) 0 3|'(r 9<0>#AAx R0 LP"aHDb `sl# ``  ``  ! Ne. h0 3|)*r 9<0>#AAx R0 LP"aHDb `sl# ``  ``  ! Re. f - 0 3}+,r 9<0>#AAx R0 LP"aHDb `sl# ``  ``  ! Iee" (0,0, -1)             5C >>>>>C H((GN>>>>>>>GNC>    )m:nQ\aA What about that blue dropshadow? 0QThat document was created with a newer version of Sketchpad and cannot be opened.|This document was created with a newer version of Sketchpad. Some information may be lost. The document will open as a copy.>$ LPlot Points Yourself` a b c d e f g h i j k l m n o p q _ ,#GSP4_M_0554/Mar 2 20040#H GenevaJ Charcoal`Arial Helvetica       $$$'''$'$'$' @ $'$' $' $'$'$'$' $' $' %'&'8'8'8'9':' nQ\aAD a@Y@ nQ\aAA3#$z@`Nj@ <#?Ġ_X<@?dow??  @     x>! @Scale 4гZ@W?? @  $rϥwg) V@ @   !ΉP1߰XY@ $rϥwg) V@  E   4гZ@W??  $rϥwg) V@ @   @    $rϥwg) V@ @   @   @ / @   @    E/ @   - CT@ @  @  - ST@ -  $rϥwg) V@ @  aa>>Q??R+?0?0R@ O` `<0>t ea @0?YY@?? nQ\aA=x[min]`d O^ <0>t ea >0?YY@?? nQ\aA=x[max] O` `<0>t ea @0?YY@?? nQ\aA=y[min]`d) O^ <0>t ea >0?YY@?? nQ\aA=y[max]) O` a0<0>t ea @0?YY@?? nQ\aA=z[min]a0e> O^ 0<0>t ea >0?YY@?? nQ\aA=z[max]0> ie1p?wW?Z -4гZ@W?? @ -. E// @ - - 1CF 2$rϥwg) V@CF@ @ 3 3/ @ - - 6SF@ @ 7. @ 8 - 9  : -CT*SF 5; 5; @ ; ; @ =? ; A3 @ AB @ <A. @  8 - E F -ST*SF 5G H;$ =grid_unitZ @ I= @ H5 <G AG M3$ =grid_unitX @ G G P3 Q;$ =grid_unitY P3 @ 5S S; @ =U P; @ ?W @ PW P; Z3 @ ZP Z3xyi @ N] @ R] G @ M` `; @ `b `3 d;& =grid_origin @ eN"  ?+xi @ IeDݚ?+zi @ eRq?+yi5ReN].#>  -   S nQ\aAXY view $,L7߁ə%??igin>  -k   R nQ\aAXZ view P` s<0>t ea @0bX<@T*J%@bX<@?nQ\aAt[7]e s km$;f;f?F@igin>  k-n   R nQ\aAYZ View>  - D>@ ף9FA ף9F   S"nQ\aA Spin Axes4C>> 4Cs0.TY> TYg O^ h<0>s  3 >0?YY@??nQ\aA0 h O^ h<0>s  3 >0?YY@??nQ\aA0 h O^ Qh<0>s  3 >0?YY@??nQ\aA1 Qhi(&#>>>><0>>a#LDD9T0>9T f0 3s'(r 1<0>#AAx R0 LP"aHDb `sl# ``  ``  ! Nex. yh0 3t)*r 1<0>#AAx R0 LP"aHDb `sl# ``  ``  ! Re{. |f - z}0 3t+,r 1<0>#AAx R0 LP"aHDb `sl# ``  ``  ! Ie0 3u'(r 1<0>#AAx R0 LP"aHDb `sl# ``  ``  ! Ne. h0 3t)*r 1<0>#AAx R0 LP"aHDb `sl# ``  ``  ! Re. f - 0 3t+,r 1<0>#AAx R0 LP"aHDb `sl# ``  ``  ! Ie0 3t'(r 1<0>#AAx R0 LP"aHDb `sl# ``  ``  ! Ne. h0 3s)*r 1<0>#AAx R0 LP"aHDb `sl# ``  ``  ! Re. f - 0 3t+,r 1<0>#AAx R0 LP"aHDb `sl# ``  ``  ! Ie0 3t'(r 1<0>#AAx R0 LP"aHDb `sl# ``  ``  ! Ne. h0 3u)*r 1<0>#AAx R0 LP"aHDb `sl# ``  ``  ! Re. f - 0 3t+,r 1<0>#AAx R0 LP"aHDb `sl# ``  ``  ! Ie0 3t'(r 1<0>#AAx R0 LP"aHDb `sl# ``  ``  ! Ne. h0 3t)*r 1<0>#AAx R0 LP"aHDb `sl# ``  ``  ! Re. f - 0 3s+,r 1<0>#AAx R0 LP"aHDb `sl# ``  ``  ! Ie0 3t'(r 1<0>#AAx R0 LP"aHDb `sl# ``  ``  ! Ne. h0 3t)*r 1<0>#AAx R0 LP"aHDb `sl# ``  ``  ! Re. f - 0 3u+,r 1<0>#AAx R0 LP"aHDb `sl# ``  ``  ! Ie 0f >0fD f >f  > 1 >1E O` D<0>s  3 @0?YY@??nQ\aA-1n Dh O^ <0>s  3 >0?YY@??nQ\aA0  O^ <0>s  3 >0?YY@??nQ\aA0   > / >/C O^ P<0>s  3 >0?YY@??nQ\aA0 Ph O^ <0>s  3 >0?YY@??nQ\aA1  O^ <0>s  3 >0?YY@??nQ\aA0   >  / >/C  O^ P<0>s  3 >0?YY@??nQ\aA0 Ph  O` <0>s  3 @0?YY@??nQ\aA-1n  O^ <0>s  3 >0?YY@??nQ\aA0   ! >!N 0! >0!DN O^ Q#<0>s  3 >0?YY@??nQ\aA0 Q#iN O^ #<0>s  3 >0?YY@??nQ\aA0 #N O^ #<0>s  3 >0?YY@??nQ\aA1 #N R >R 0R >0RD O^ QT<0>s  3 >0?YY@??nQ\aA0 QTi O^ T<0>s  3 >0?YY@??nQ\aA0 T O` T<0>s  3 @0?YY@??nQ\aA-1n T0QThat document was created with a newer version of Sketchpad and cannot be opened.|This document was created with a newer version of Sketchpad. Some information may be lost. The document will open as a copy.>$"xLPlotting Curves` a b c d e f g h i j k l m n o p q _ ,#GSP4_M_0554/Mar 2 20040#H GenevaJ Charcoal ArialApple Chancery Helvetica        '''$'$'$' @ $'$' $' $'$'$'$' $' $' %'&'8'8'8'9':' nQ\aAD a@Y@ nQ\aAA3#ty@`k@ <#?Ġ_X<@?F?  @     a h$@Scale 4гZ@W?? @  $rϥwg) V@ @   D ?XY@ $rϥwg) V@  E   4гZ@W??  $rϥwg) V@ @   @    $rϥwg) V@ @   @   @ / @   @    E/ @   - CT@ @  @  - ST@ -  $rϥwg) V@ @  b>b>>:>>:QJ?O>?OR_?d>?dRt O` `;<0>t ea @0?YY@?? nQ\aA=x[min]`;dI O^ ;<0>t ea >0?YY@?? nQ\aA=x[max];I O` `O<0>t ea @0?YY@?? nQ\aA=y[min]`Od] O^ O<0>t ea >0?YY@?? nQ\aA=y[max]O] O` ad<0>t ea @0?YY@?? nQ\aA=z[min]ader O^ d<0>t ea >0?YY@?? nQ\aA=z[max]dr [A{?OZ?Z -4гZ@W?? @ -. E// @ - - 1CF 2$rϥwg) V@CF@ @ 3 3/ @ - - 6SF@ @ 7. @ 8 - 9  : -CT*SF 5; 5; @ ; ; @ =? ; A3 @ AB @ <A. @  8 - E F -ST*SF 5G H;$ =grid_unitZ @ I= @ H5 <G AG M3$ =grid_unitX @ G G P3 Q;$ =grid_unitY P3 @ 5S S; @ =U P; @ ?W @ PW P; Z3 @ ZP Z3xyi @ N] @ R] G @ M` `; @ `b `3 d;& =grid_origin @ eN"  ?+xi @ IeDݚ?+zi @ eRq?+yi5ReN].#>  -   S nQ\aAXY view $,L7߁ə%??igin>  -k   R nQ\aAXZ view P` s<0>t ea @0bX<@T*J%@bX<@?nQ\aAt[7]e s km$;f;f?F@igin>  k-n   R nQ\aAYZ View>  - D>@ ף9FA ף9F   S"nQ\aA Spin Axes<>> <%> 4 "#$%&'()*+,q   d*nQ\aAShow Graph Bounds (>>>(J0.,|> ,|yH ^@ a@G f@ a@ @ uv vu wܵ)?#?t uy)1vuy  G<0>dnQ\aAt 9f Jg<0>xCat F0La4b `sl  xJg{ 9b J|<0>xCat B0La4b `sl  yJ|G 9 |}j J<0>xCat J0La4b `slp p z0 3 |{b I<0>xCat B0La4b `slp` nQ\aAm[7]G0 3 }{b I<0>xCat B0La4b `slp` nQ\aAm[8]G0 3 ~{b I<0>xCat B0La4b `slp` nQ\aAm[7]G0 3'(r v<0>#AAx R0 LP"aHDb `sl# ``  `` ! Ne. h0 3)*r v<0>#AAx R0 LP"aHDb `sl# ``  `` ! Re. f - 0 3+,r v<0>#AAx R0 LP"aHDb `sl# ``  `` ! Iee,(x(t), y(t), z(t))#* Hwy{  (-DT!@0QThat document was created with a newer version of Sketchpad and cannot be opened.|This document was created with a newer version of Sketchpad. Some information may be lost. The document will open as a copy.$HLCredits` a b c d e f g h i j k l m n o p q _ ,#GSP4_M_0554/Mar 2 20040#H GenevaJ '''$'mtr$'nme$' fj$'ms$'$'$'$'$'$' $' $' %'&'8'8'8'9':'0.!%<0><0><0><0><0>>!%$$>iDB".>sנ"  h  h Lhttp://www.keypress.com/sketchpad/general_resources/advanced_sketch_gallery/0nQ\aAAdvanced Sketch Gallery <  < !http://www.keypress.com/sketchpad2nQ\aASketchpad Resource Center{A tool in this document was created with a newer version of Sketchpad and cannot be read. The document will open as a copy.aA tool in this document was created with a newer version of Sketchpad and may not work correctly.$LPlot Point (XYZ)Apple Chancery HelveticaBaskerville Genevai$$nQ\aA =grid_unitZ Ӄ&nQ\aA =grid_originoԌfunem$nQ\aA =grid_unitYL$nQ\aA =grid_unitXsW !^  <0>cuil >0p*b_ҌTNp#$p nQ\aA=z[max]  !^  <0>cuil >0p*b_ҌTNp#$p nQ\aA=z[min]  !^  <0>cuil >0p*b_ҌTNp#$p nQ\aA=y[max]  !^  <0>cuil >0p*b_ҌTNp#$p nQ\aA=y[min]  !^  <0>cuil >0p*b_ҌTNp#$p nQ\aA=x[max]  !^  <0>cuil >0p*b_ҌTNp#$p nQ\aA=x[min]  !^  <0>cuil >0p*b_ҌTNp#$pnQ\aAz  !^  <0>cuil >0p*b_ҌTNp#$pnQ\aAy  !^  <0>cuil >0p*b_ҌTNp#$pnQ\aAx  @ nQ\aAj @ nQ\aAk0 ! r /<0>b R0 LP"aHDb `sl# ``  `` ! 0 ! r <0>b R0 LP"aHDb `sl# ``  `` ! 0 ! r <0>b R0 LP"aHDb `sl# ``  `` ! . nQ\aAl. nQ\aAm - nQ\aAA,=({11},{12}, {13})C8  H/#This tool plots a point on the 3D Graph Template's coordinate system given their (x, y, z) coordinates. The construction scales each coordinate to a vector along the relevant axis, given the min and max values for that axis, and then translates the origin by these three vectors to locate the point in 3-space. - N. Jackiw 20020{A tool in this document was created with a newer version of Sketchpad and cannot be read. The document will open as a copy.aA tool in this document was created with a newer version of Sketchpad and may not work correctly.$' LPlot Segment (X1Y1Z to X2Y2Z2) HelveticaApple ChanceryBaskerville Genevai$ !^  <0>cuil >0p*b_GTNp#$pnQ\aAz[2])  !^  <0>cuil >0p*b_GTNp#$pnQ\aAy[2])  !^  <0>cuil >0p*b_GTNp#$pnQ\aAx[2])  !^  <0>cuil >0p*b_GTNp#$pnQ\aAz[1])  !^  <0>cuil >0p*b_GTNp#$pnQ\aAy[1])  !^  <0>cuil >0p*b_GTNp#$pnQ\aAx[1])  !^  <0>cuil >0p*b_GTNp#$p nQ\aA=z[max]  !^  <0>cuil >0p*b_GTNp#$p nQ\aA=z[min]  !^  <0>cuil >0p*b_GTNp#$p nQ\aA=y[max]  !^  <0>cuil >0p*b_GTNp#$p nQ\aA=y[min]  !^  <0>cuil >0p*b_GTNp#$p nQ\aA=x[max]  !^  <0>cuil >0p*b_GTNp#$p nQ\aA=x[min] $nQ\aA =grid_unitX##$nQ\aA =grid_unitYA&nQ\aA =grid_originp$nQ\aA =grid_unitZ @  nQ\aAj @ nQ\aAk0 ! r c<0>b R0 LP"aHDb `sl# ``  `` !  . nQ\aAn0 ! r c<0>b R0 LP"aHDb `sl# ``  `` ! . nQ\aAo - nQ\aAB0 !r c<0>b R0 LP"aHDb `sl# ``  `` ! & (x1, y1, z1)p0 ! r c<0>b R0 LP"aHDb `sl# ``  `` !  . nQ\aAl0 ! r c<0>b R0 LP"aHDb `sl# ``  `` !  . !nQ\aAm - "nQ\aAA0 !r c<0>b R0 LP"aHDb `sl# ``  `` ! $#%& (x2, y2, z2)p &D 4/#This tool constructs a segment on the 3D Graph Template's coordinate system, given two pairs of (x, y, z) coordinates determining the endpoints of those segments. It works by first applying the "Plot Point (XYZ)" construction twice, and then connecting the two image points with a segment. - N. Jackiw 2002c