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56ED09ACA92BFD8B0181DF6D4EEBFE64CB9DEA9AD0BBFED27FAA6A6196B-%&STYLEG6# %-PATCHCONTOURG-%*AXESSTYLEG6#%$BOXG-%(SCALINGG6#%,CONSTRAINEDG" 1 4 0 1 10 0 2 1 1 2 1 1.000000 37.000000 61.000000 0 0 "Curve 1" }}}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 43 "Se vsemi options se muzeme seznami t pomoci " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "?plot3d,option s" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 7 "Style: " }}{PARA 0 "" 0 "" {TEXT -1 18 "style=displaystyle" }}{PARA 0 "" 0 "" {TEXT -1 34 "point \+ - pouze kresli pocitane body" }}{PARA 0 "" 0 "" {TEXT -1 33 "line - sp ojuje tyto body useckami" }}{PARA 0 "" 0 "" {TEXT -1 40 "hidden - resi i vitelnost, drateny model" }}{PARA 0 "" 0 "" {TEXT -1 50 "wireframe \+ - drateny model, neuvazuje se vidtelnost" }}{PARA 0 "" 0 "" {TEXT -1 55 "patch - povrch je kreslen barevne nebo v odstinech sedi" }}{PARA 0 "" 0 "" {TEXT -1 47 "patchnogrid - povrch, ale nezobrazuje se mrizka " }}{PARA 0 "" 0 "" {TEXT -1 26 "contour - pouze vrstevnice" }}{PARA 0 "" 0 "" {TEXT -1 38 "patchcontour - povrch i s vrstevnicemi" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 8 "Shading:" }}{PARA 0 "" 0 "" {TEXT -1 14 "shading=option" }}{PARA 0 "" 0 "" {TEXT -1 65 "z - barevne sche ma je voleno podle z-tove souradnice bodu povrchu" }}{PARA 0 "" 0 "" {TEXT -1 46 "xy, xyz - kazda z os ma vlastni barevny rozsah" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 5 "Axes:" }}{PARA 0 "" 0 "" {TEXT -1 32 "axes=none, normal, boxed, framed" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 27 "Orientation and projection:" }}{PARA 0 "" 0 "" {TEXT -1 37 "Uhe l pohledu je nastavovan parametrem" }}{PARA 0 "" 0 "" {TEXT -1 161 "or ientation=[theta, fi]. Zvetsovanim uhlu theta rotujeme obrazek proti s meru hodinovych rucicek. Uhle fi urcuje, kde nad (pod) plochou je umis ten pozorovaci bod." }}{PARA 0 "" 0 "" {TEXT -1 83 "projection=r, kde \+ r je z [0,1], specifikuje vzdalenost pozorovaciho bodu od povrchu" }} {PARA 0 "" 0 "" {TEXT -1 64 "(0 znamena na povrchu, 1 nekonecne vzdale ny, \"normalni\" je 1/2)." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "a:=array(1..2,1..2):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 92 "a[1,1]:=plot3d(x^3-3*x*y^2, x=-1..1, y=-1..1, style=patch, axes=boxed , orientation=[45,45]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 91 " a[1,2]:=plot3d(x^3-3*x*y^2, x=-1..1, y=-1..1, style=patch, axes=boxed, orientation=[5,45]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 91 "a[ 2,1]:=plot3d(x^3-3*x*y^2, x=-1..1, y=-1..1, style=patch, axes=boxed, o rientation=[5,80]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 93 "a[2, 2]:=plot3d(x^3-3*x*y^2, x=-1..1, y=-1..1, style=patch, axes=boxed, ori entation=[-60,60]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "plot s[display](a);\n" }}{PARA 13 "" 1 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"Curve 19" "Curve 20" "Curve 21" "Curve 22" "Curve 23" "Curve 24" "C urve 25" "Curve 26" "Curve 27" "Curve 28" "Curve 29" "Curve 30" "Curve 31" "Curve 32" "Curve 33" "Curve 34" "Curve 35" "Curve 36" "Curve 37 " "Curve 38" "Curve 39" "Curve 40" "Curve 41" "Curve 42" "Curve 43" "C urve 44" "Curve 45" "Curve 46" "Curve 47" "Curve 48" "Curve 49" "Curve 50" "Curve 51" "Curve 52" "Curve 53" "Curve 54" "Curve 55" "Curve 56 " "Curve 57" "Curve 58" "Curve 59" "Curve 60" "Curve 61" "Curve 62" "C urve 63" "Curve 64" "Curve 65" "Curve 66" "Curve 67" "Curve 68" "Curve 69" "Curve 70" "Curve 71" "Curve 72" }}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 182 "Zmena stylu osbetlovani nebo zmena pozorovaciho bodu nez pusobi prepocitani grafickeho objektu, obrazek se pouze znovu prekresl i na obrazovku. Toto vsak neplati pro nasledujici volbu." }}{PARA 0 " " 0 "" {TEXT -1 5 "Grid:" }}{PARA 0 "" 0 "" {TEXT -1 180 "V 3D nema Ma ple zjemnovaci algoritmus. Implicitne se pouzije mrizka s 25 equidista tnimi body pro oba smery. Toto nastaveni menime parametrem grid=[m,n], m pro osu x a n pro osu y. " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 89 "P ro porovnani vzhledu a vypocetni narocnosti vyzkousejte nasledujici po sloupnost prikazu:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 78 "pp:=( n,m)->plot3d(-y/(1+x^2)/(1+y^2),x=-5..5,y=-3..3,grid=[n,m],style=patch ):\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "t0:=time():" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "pp(20,20);\n" }}{PARA 13 "" 1 "" {GLPLOT3D 479 479 479 {PLOTDATA 3 "6%-%%GRIDG6%;$!\"&\"\"!$\"\"&F );$!\"$F)$\"\"$F)X,%)anythingG6\"6\"[gl'!%\"!!#[dl\"5\"53F87A17A17A17A 183F89C4D47AE9FE7D3F8C39E7AB5ABC8A3F8F038962C128003F9107CBA1CD888C3F92 893B5DB128943F93981664ABE0C53F932796140742323F8E795C94A0BF063F7844F9EE C1843BBF7844F9EEC18464BF8E795C94A0BF10BF93279614074234BF93981664ABE0C5 BF92893B5DB12893BF9107CBA1CD888ABF8F038962C127FDBF8C39E7AB5ABC88BF89C4 D47AE9FE7ABF87A17A17A17A163F8D3CE4576AA6ED3F8FE21EDB6FCEC03F91763B1F64 B64F3F932FB6373016363F951248C1A6058C3F96EF2D3D8627583F983E4CF9F5CCCE3F 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LEG6#%$BOXG-%+AXESLABELSG6%%\"xG%\"yGQ!F/-%%VIEWG6%%(DEFAULTGF=;$F)F)$ \"\"'F)" 1 2 0 1 10 0 2 1 1 2 2 1.000000 45.000000 45.000000 0 0 "Curv e 1" }}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 78 "Nastaveni voleb globalne \+ (pro celou session) se provede prikazem setoptions3d." }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 22 "Struktura grafiky v 3D" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 314 "Vytvareni grafiky v 3D probiha opet ve dvou fazi ch (jako v 2D). Nejdrive se pocitaji funkcni hodnoty v referencnich bo dech, pak je obrazek vykreslovan na obrazovce. 3D graficky objekt v Ma plu predstavuje funkce PLOT3D s argumenty popisujicimi osy, funkci, sp ocitany soradnicemi bodu, parametry mrizky, barvami atd." }}{PARA 0 " " 0 "" {TEXT -1 89 "Nasledujici objekt popisuje ctyrsten s vrcholy (1, 1,1), (-1,-1,1), (-1,1,-1) a (1,-1,-1)." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 203 "PLOT3D(POLYGONS([ [1,1,1], [-1,-1,1], [-1,1,-1]], [[ 1,1,1], [-1,-1,1],[1,-1,-1]], [ [-1,1,-1], [1,-1,-1], [-1,-1,1]], [ [- 1,1,-1], [1,-1,-1], [1,1,1]]), STYLE(LINE), AXESSTYLE(BOX), ORIENTATIO N(30,60));\n" }}{PARA 13 "" 1 "" {GLPLOT3D 479 479 479 {PLOTDATA 3 "6& -%)POLYGONSG6&7%7%\"\"\"F(F(7%!\"\"F*F(7%F*F(F*7%F'F)7%F(F*F*7%F+F-F)7 %F+F-F'-%&STYLEG6#%%LINEG-%*AXESSTYLEG6#%$BOXG-%+PROJECTIONG6%\"#I\"#g F(" 1 6 0 1 10 0 2 1 1 2 2 1.000000 60.000000 30.000000 1 0 "Curve 1" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 221 "P:=plots[polygonplot3d] ([ [ [1,1,1], [-1,-1,1], [-1,1,-1]], [[1,1,1], [-1,-1,1],[1,-1,-1]], \+ [ [-1,1,-1], [1,-1,-1], [-1,-1,1]], [ [-1,1,-1], [1,-1,-1], [1,1,1]]], style=line, axes=boxed, orientation=[30,60], color=red);\n" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%\"PG-%1INTERFACE_PLOT3DG6'-%)POLYGONSG6&7% 7%$\"\"\"\"\"!F-F-7%$!\"\"F/F1F-7%F1F-F17%F,F07%F-F1F17%F3F5F07%F3F5F, -%&STYLEG6#%%LINEG-%*AXESSTYLEG6#%$BOXG-%'COLOURG6&%$RGBG$\"*++++\"!\" )$F/F/FG-%+PROJECTIONG6%$\"#IF/$\"#gF/F." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "P;\n" }}{PARA 13 "" 1 "" {GLPLOT3D 479 479 479 {PLOTDATA 3 "6'-%)POLYGONSG6&7%7%$\"\"\"\"\"!F(F(7%$!\"\"F*F,F(7%F,F(F ,7%F'F+7%F(F,F,7%F.F0F+7%F.F0F'-%&STYLEG6#%%LINEG-%*AXESSTYLEG6#%$BOXG -%'COLOURG6&%$RGBG$\"*++++\"!\")$F*F*FB-%+PROJECTIONG6%$\"#IF*$\"#gF*F )" 1 6 0 1 10 0 2 6 1 2 2 1.000000 60.000000 30.000000 1 0 "Curve 1" } }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 39 "Obecnejsi priklad (graf funkce \+ z=x*y^2:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 106 "P:=plot3d(x*y^ 2, x=-1..1, y=-1..1, grid=[5,5], axes=boxed, orientation=[30,30], sty le=line, color=black):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "l print(P);" }}{PARA 6 "" 1 "" {TEXT -1 620 "PLOT3D(GRID(-1. .. 1.,-1. . . 1.,Array(1 .. 5,1 .. 5,\{(1, 1) = -1., (1, 2) = -.250000000000000000 , (1, 4) = -.250000000000000000, (1, 5) = -1., (2, 1) = -.500000000000 000000, (2, 2) = -.125000000000000000, (2, 4) = -.125000000000000000, \+ (2, 5) = -.500000000000000000, (4, 1) = .500000000000000000, (4, 2) = \+ .125000000000000000, (4, 4) = .125000000000000000, (4, 5) = .500000000 000000000, (5, 1) = 1., (5, 2) = .250000000000000000, (5, 4) = .250000 000000000000, (5, 5) = 1.\},datatype = float[8],storage = rectangular, order = C_order),COLOR(RGB,0.,0.,0.)),ORIENTATION(30.,30.),STYLE(LINE) ,AXESSTYLE(BOX),AXESLABELS(x,y,\"\"))" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "P;\n" }}{PARA 13 "" 1 "" {GLPLOT3D 479 479 479 {PLOTDATA 3 "6'-%%GRIDG6&;$!\"\"\"\"!$\"\"\"F)F&X,%)anythingG6\"6\"[gl '!%\"!!#:\"&\"&BFF0000000000000BFD00000000000008000000000000000BFD0000 000000000BFF0000000000000BFE0000000000000BFC00000000000008000000000000 000BFC0000000000000BFE000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000003FE00000000000003FC000000 000000000000000000000003FC00000000000003FE00000000000003FF000000000000 03FD000000000000000000000000000003FD00000000000003FF0000000000000-%&CO LORG6&%$RGBG$F)F)F4F4-%&STYLEG6#%%LINEG-%*AXESSTYLEG6#%$BOXG-%+AXESLAB ELSG6%%\"xG%\"yGQ!F/-%+PROJECTIONG6%$\"#IF)FFF+" 1 6 0 1 10 0 2 1 1 2 2 1.000000 30.000000 30.000000 1 0 "Curve 1" }}}}{EXCHG {PARA 0 "" 0 " " {TEXT -1 254 "Maple spojuje s funkci dvou promennych na pravouhle si ti graficky objekt. Tento objekt je pouzivan pro primkovou interpolaci mezi prilehlymi body obrazku. Funkcni hodnoty pro body site jsou poci tany numericky. V 3D neexistuje automaticke zjemnovani site." }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 24 "Grafy nespojitych funkci" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "f:=(x^2*y)/(x^2+y^2);\n" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fG*(%\"xG\"\"#%\"yG\"\"\",&*$)F&F' F)F)*$)F(F'F)F)!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 64 "plo t3d(f, x=-3..3, y=-3..3, orientation=[-57,38], axes=framed);\n" }} {PARA 13 "" 1 "" {GLPLOT3D 511 511 511 {PLOTDATA 3 "6&-%%GRIDG6%;$!\"$ \"\"!$\"\"$F)F&7;7;$!3++++++++:!#<$!3K4:kA'RV\\\"F0$!3'Qdlg$)4aZ\"F0$! 3&*************R9F0$!3e%Q:YQ:YQ\"F0$!3&\\Gl=[*p08F0$!3'**************> \"F0$!3\")\\kRd()3l5F0$!3C+++++++!*!#=$!3;l\"F0$\"3&\\Gl=[ *p08F0$\"3e%Q:YQ:YQ\"F0$\"3&*************R9F0$\"3'Qdlg$)4aZ\"F0$\"3K4: kA'RV\\\"F0$\"3++++++++:F07;$!3!pra2K6)p8F0$!3+++++++v8F0$!3W')Ha!Gy(o 8F0$!3vAxAxAxZ8F0$!323\"3\"3\"3\"38F0$!3n3&zCFAFH$\"3X68s'>3&zCFA$\"3')************R[FA$\"3RI#p2Bp2)pFA$\" 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setrovana funkce neni spojita je pri teto hustote site totozny s uzlov ym bodem a program v nem nemuze spocitat funkcni hodnotu." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 88 "Zmenime hustotu uzlovych bodu tak, aby bo d [0,0] (bod nespojitosti) nebyl uzlovym bodem." }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 78 "plot3d(f, x=-3..3, y=-3..3, orientation=[-57,3 8], axes=framed, grid=[30,30]);\n" }}{PARA 13 "" 1 "" {GLPLOT3D 511 511 511 {PLOTDATA 3 "6&-%%GRIDG6%;$!\"$\"\"!$\"\"$F)F&X,%)anythingG6\" 6\"[gl'!%\"!!#_cn\"?\"?BFF8000000000000BFF7F058B403E9D2BFF7BCF1AE468C6 6BFF75E8D4464285DBFF6CD477D0132B9BFF600DA17006D0CBFF4F10C3BCF10C4BFF39 6557E51A6ABBFF1EAB57B2F2502BFEFD56C0AA4FD57BFEB2CFB008E291ABFE5E5897DF C8C61BFE012EB4EA1FED5BFD3A6DA0D4073ADBFBA7388D12D9B2C3FBA7388D12D9AF23 FD3A6DA0D4073A03FE012EB4EA1FECE3FE5E5897DFC8C5B3FEB2CFB008E29153FEFD56 C0AA4FD543FF1EAB57B2F25013FF396557E51A6A93FF4F10C3BCF10C33FF600DA17006 D0B3FF6CD477D0132B83FF75E8D4464285C3FF7BCF1AE468C653FF7F058B403E9D33FF 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4F\\is7$$\"3wka8\"4U-X\"F4Fais7$$\"3f-(4tb(GR9F4Ffis7$$\"3x<$z=_'oH9F4 F[js7$$\"3mB>79nO?9F4F`js7$$\"3alQ)ewVLT\"F4Fejs7$$\"3,Z')f++R29F4Fjjs 7$$\"3^!GSI^iMS\"F4F_[t7$$\"32;$p+eP3S\"F4Fd[t7$$\"3'Rw!Qn/++9F4Fi[t7$ $\"3g_\"\\:eK3S\"F4F^\\t7$$\"38:`q.#>LS\"F4Fc\\t7$$\"3%HHy!G#\\wS\"F4F h\\t7$$\"3zRW*Q_;MT\"F4F]]t7$$\"3\\5:3F>$3U\"F4Fb]t7$$\"3L9TRzFdH9F4Fg ]t7$$\"3)oq#[9;pQ9F4F\\^t7$$\"3#=?u-tW-X\"F4Fa^t7$$\"36GHB9.Sh9F4Ff^t7 $$\"3S\\Kgh\"[RZ\"F4F[_t7$$\"3AI&QpK!R'[\"F4F`_t7$$\"3ST?3++++:F4Fe`sF [[lFc[lFc[mFg[mF`\\mFd\\mFc[mF`\\m" 1 2 0 1 10 0 2 9 1 1 1 1.000000 44.000000 44.000000 0 0 "Curve 1" "Curve 2" }}}}{SECT 0 {PARA 4 "" 0 " " {TEXT -1 25 "Slozitejsi ukazka animace" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1849 " restart:\n with(plots):\n body := [[1,1,1],[-1,1,1 ],[-1,-1,1],[1,-1,1]],[[1,1,-1],[-1,1,-1],[-1,-1,-1],[1,-1,-1]],\n \+ [[1,1,1],[1,-1,1],[1,-1,-1],[1,1,-1]],[[-1,1,1],[-1,-1,1],[- 1,-1,-1],[-1,1,-1]]:\n tail:=[[-1,-.5,.5],[-4,-.8,.8],[-4,.8,.8],[-1,. 5,.5]],[[-1,-.5,-.5],[-4,-.8,-.8],[-4,.8,-.8],[-1,.5,-.5]]:\n lwing01: =[[-1,1,1],[1,1,1],[.5,6,4],[-1,6,4]],[[-1,1,-1],[1,1,-1],[.5,6,3.5],[ -1,6,3.5]],\n [[.5,6,3.5],[-1,6,3.5],[-.4,11,3],[-.4,11 ,3]],[[.5,6,4],[-1,6,4],[-.4,11,3],[-.4,11,3]]:\n lwing02:=[[-1,1,1],[ 1,1,1],[.5,6,-2],[-1,6,-2]],[[-1,1,-1],[1,1,-1],[.5,6,-2.5],[-1,6,-2.5 ]],\n [[.5,6,-2.5],[-1,6,-2.5],[-.4,11,-5],[-.4,11,-5]] ,[[.5,6,-2],[-1,6,-2],[-.4,11,-5],[-.4,11,-5]]:\n rwing01:=[[-1,-1,1], [1,-1,1],[.5,-6,4],[-1,-6,4]],[[-1,-1,-1],[1,-1,-1],[.5,-6,3.5],[-1,-6 ,3.5]],\n [[.5,-6,3.5],[-1,-6,3.5],[-.4,-11,3],[-.4,-11 ,3]],[[.5,-6,4],[-1,-6,4],[-.4,-11,3],[-.4,-11,3]]:\n rwing02:=[[-1,-1 ,1],[1,-1,1],[.5,-6,-2],[-1,-6,-2]],[[-1,-1,-1],[1,-1,-1],[.5,-6,-2.5] ,[-1,-6,-2.5]],\n [[.5,-6,-2.5],[-1,-6,-2.5],[-.4,-11,- 5],[-.4,-11,-5]],[[.5,-6,-2],[-1,-6,-2],[-.4,-11,-5],[-.4,-11,-5]]:\n \+ head:=[[1,.5,1],[1,-.5,1],[2,-.3,1.5],[2,.3,1.5]],[[1,.5,0],[1,-.5,0], [2,-.3,1],[2,.3,1]],\n [[2,-.3,1],[2,.3,1],[3,0,1],[3,0,1]] ,[[2,-.3,1.5],[2,.3,1.5],[3,0,1],[3,0,1]]:\n bird01:=[body,tail,lwing0 1,rwing01, head]:\n bird02:=[body,tail,lwing02,rwing02, head]:\n polyg onplot3d(bird01, axes = boxed, labels = [x,y,z], scaling=constrained); \n polygonplot3d(bird02, axes = boxed, labels = [x,y,z], scaling=const rained);\n morph3d:=proc(first,last,t)\n local k,j;\n [seq([seq([(1-t) *op(1,op(j,op(k,first))) + t*op(1,op(j,op(k,last))),\n (1-t)*op(2,op( j,op(k,first))) + t*op(2,op(j,op(k,last))),(1-t)*\n op(3,op(j,op(k,fir st))) + t*op(3,op(j,op(k,last)))],j=1..4)], k=1..nops(first))]:\n end: \n\n" }}{PARA 7 "" 1 "" {TEXT -1 50 "Warning, the name changecoords ha s been redefined\n" }}{PARA 13 "" 1 "" {GLPLOT3D 501 501 501 {PLOTDATA 3 "6&-%)POLYGONSG647&7%$\"\"\"\"\"!F(F(7%$!\"\"F*F(F(7%F,F,F (7%F(F,F(7&7%F(F(F,7%F,F(F,7%F,F,F,7%F(F,F,7&F'F/F4F17&F+F.F3F27&7%F,$ !\"&F-$\"\"&F-7%$!\"%F*$!\")F-$\"\")F-7%F>FBFB7%F,F;F;7&7%F,F9F97%F>F@ F@7%F>FBF@7%F,F;F97&F+F'7%F;$\"\"'F*$\"\"%F*7%F,FMFO7&F2F17%F;FM$\"#NF 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