Wizualizacja danych 2D i 3D - Gnuplot dr hab. Bożena Woźna-Szcześniak Akademia im. Jan Długosza bwozna@gmail.com Laboratorium 9
Plan Komenda set palette Kolorowe grafy
Aktualna paletę kolorów można zobaczyć wydajac polecenie: gnuplot> test palette
Komenda set palette set palette [ model [ RGB HSV ] ] [ defined ( {flt:v1} {clr:color1}, {flt:v2} {clr:color2}, {flt:v3} {clr:color3}) functions f1(gray), f2(gray), f3(gray) file "{str:filename}" [ using... ] ] [ positive negative ] [ maxcolors {int:n} ] Polecenie pozwala na zdefiniowanie własnej palety kolorów. Opcja model pozwala na ustalenie przestrzeni kolorów. Raz ustalony model pozostaje aktywny, do momentu ponownej zmiany opcja model. Opcja maxcolors ogranicza liczbę wyświetlanych kolorów.
Komenda set palete Opcja defined pozwala na wprowadzenie listy kolorów wraz z ich względnym położeniem wzdłuż widma. Na tej podstawie gnuplot wyznaczy pełne spektrum kolorów. set palette model RGB defined ( "red",.5 "yellow", 1 "green" ) set palette model RGB defined ( "red",.1 "yellow", 1 "green" )
Przykład zmiany palety gnuplot> set palette model RGB defined ( "red",.5 "yellow", 1 "green" ) gnuplot> test palette Stara Nowa
Przykład zmiany palety gnuplot> set palette model RGB defined ( "red",.1 "yellow", 1 "green" ) gnuplot> test palette Stara Nowa
Zmiany palety Następujace komendy sa równoważne: set palette model RGB defined ( "red", 1 "yellow", 2 "green" ) set palette model RGB defined ( "#FF",1 "#FFFF",2 "#FF" ) set palette model RGB defined ( 1, 1 1 1, 2 1 )
Predefiniowane kolory w palecie Następujace polecenie pozwala zobaczyć predefiniowane kolory w palecie: gnuplot> show palette colornames There are 112 predefined color names: white #ffffff = 255 255 255 black # = dark-grey #aaa = 16 16 16 red #ff = 255 web-green #c = 192 web-blue #8ff = 128 255 dark-magenta #cff = 192 255 dark-cyan #eeee = 238 238 dark-orange #c4 = 192 64 dark-yellow #c8c8 = 2 2 royalblue #4169e1 = 65 15 225 goldenrod #ffc2 = 255 192 32...
Predefiniowane kolory w palecie dark-spring-green #84 = 128 64 purple #c8ff = 192 128 255 steelblue #368 = 48 96 128 dark-red #8b = 139 dark-chartreuse #48 = 64 128 orchid #ff8ff = 255 128 255 aquamarine #7fffd4 = 127 255 212 brown #a52a2a = 165 42 42 yellow #ffff = 255 255 turquoise #4ed = 64 224 28 grey # = grey1 #1a1a1a = 26 26 26 grey2 #333333 = 51 51 51 grey3 #4d4d4d = 77 77 77 grey4 #666666 = 12 12 12...
Predefiniowane kolory w palecie grey5 #7f7f7f = 127 127 127 grey6 #999999 = 153 153 153 grey7 #b3b3b3 = 179 179 179 grey #ccc = 192 192 192 grey8 #cccccc = 24 24 24 grey9 #e5e5e5 = 229 229 229 grey1 #ffffff = 255 255 255 light-red #f3232 = 24 5 5 light-green #9ee9 = 144 238 144 light-blue #add8e6 = 173 216 23 light-magenta #f55f = 24 85 24 light-cyan #effff = 224 255 255 light-goldenrod #eedd82 = 238 221 13 light-pink #ffb6c1 = 255 182 193 light-turquoise #afeeee = 175 238 238...
Predefiniowane kolory w palecie gold #ffd7 = 255 215 green #ff = 255 dark-green #64 = 1 spring-green #ff7f = 255 127 forest-green #228b22 = 34 139 34 sea-green #2e8b57 = 46 139 87 blue #ff = 255 dark-blue #8b = 139 midnight-blue #19197 = 25 25 112 navy #8 = 128 medium-blue #cd = 25 skyblue #87ceeb = 135 26 235 cyan #ffff = 255 255 magenta #ffff = 255 255 dark-turquoise #ced1 = 26 29...
Predefiniowane kolory w palecie dark-pink #ff1493 = 255 2 147 coral #ff7f5 = 255 127 8 light-coral #f88 = 24 128 128 orange-red #ff45 = 255 69 salmon #fa872 = 25 128 114 dark-salmon #e9967a = 233 15 122 khaki #fe68c = 24 23 14 dark-khaki #bdb76b = 189 183 17 dark-goldenrod #b886b = 184 134 11 beige #f5f5dc = 245 245 22 olive #a82 = 16 128 32 orange #ffa5 = 255 165 violet #ee82ee = 238 13 238 dark-violet #94d3 = 148 211 plum #ddadd = 221 16 221 dark-plum #954 = 144 8 64...
Predefiniowane kolory w palecie dark-olivegreen #556b2f = 85 17 47 orangered4 #814 = 128 2 brown4 #81414 = 128 2 2 sienna4 #8414 = 128 64 2 orchid4 #848 = 128 64 128 mediumpurple3 #86c = 128 96 192 slateblue1 #86ff = 128 96 255 yellow4 #88 = 128 128 sienna1 #ff84 = 255 128 64 tan1 #ffa4 = 255 16 64 sandybrown #ffa6 = 255 16 96 light-salmon #ffa7 = 255 16 112 pink #ffcc = 255 192 192 khaki1 #ffff8 = 255 255 128 lemonchiffon #ffffc = 255 255 192...
Predefiniowane kolory w palecie bisque #cdb79e = 25 183 158 honeydew #ffff = 24 255 24 slategrey #ab6cd = 16 182 25 seagreen #c1ffc1 = 193 255 193 antiquewhite #cdcb = 25 192 176 chartreuse #7cff4 = 124 255 64 greenyellow #aff2 = 16 255 32 gray #bebebe = 19 19 19 light-gray #d3d3d3 = 211 211 211 light-grey #d3d3d3 = 211 211 211 dark-gray #aaa = 16 16 16 slategray #ab6cd = 16 182 25
Ustawienia palety przy pomocy funkcji W trybie HSV do definicji palety kolorów, zamiast polecenia set palette defined lepiej (nie znaczy to, że musimy!) jest użyć polecenia set palette functions. W definicjach funkcji używamy zamiast zmiennej x, zmiennej gray, np: set palette model HSV functions gray,1,1 Pierwsza funkcja jest postaci f(gray) = gray, pozostałe to funkcje stałe f(gray) = 1
Ustawienia palety przy pomocy funkcji gnuplot>set palette model HSV functions gray,1,1 gnuplot> test palette
Ustawienia palety przy pomocy danych pliku Dany jest plik "palette.txt" #Czerwony 255 255 255 #Zielony 255 255 255 #Niebieski 255 255 255 set palette model RGB file "palette.txt" using ($1/255):($2/255):($3/255)
Inne opcje polecenia set palette gnuplot> set palette model HSV functions gray,1,1 positive gnuplot> set palette model HSV functions gray,1,1 negative positive negative
Zapytania o paletę Informacje o palecie można uzyskać poleceniem: show palette [ palette {int:n} [ float int ] gradient colornames ] Polecenie jest zależne od wybranego terminala, np. dla wxt: gnuplot> set palette model HSV functions gray,1,1 negative gnuplot> show palette palette is COLOR color mapping is done by user defined functions A-formula: gray B-formula: 1 C-formula: 1 figure is NEGATIVE all color formulae ARE NOT written into output postscript file allocating ALL remaining color positions for discrete palette terminals Color-Model: HSV gamma is 1.5
Kolorowanie wykresów Kolorowanie wykresów kontrolujemy opcja pm3d: set pm3d [ at [b s t] ] [ implicit explicit ] [ hidden3d {idx:linestyle} nohidden3d ] [ interpolate {int:xsteps},{int:ysteps} ] [ corners2color [ mean geomean median min max c1 c2 c3 c4 ] ] [ scansautomatic scansforward scansbackward depthorder ]
Kolorowanie wykresów Kolorowe nieprzezroczyste powierzchnie moga być sporzadzone w trzech położeniach: na górze kreślonej powierzchni, na kreślonej powierzchni, na dole kreślonej powierzchni. Pozycja jest określona przez słowo kluczowe at wraz z kombinacja liter b (u dołu), s (powierzchnia), i t (u góry). Każda litera może pojawić się dwa razy.
Kolorowanie wykresów set hidden3d set isosamples 3 set pm3d at s splot [-2:2][-2:2] exp(-(x**2 + y**2))* cos(x/4) *sin(y)*cos(2*(x**2+y**2)) exp(-(x**2 + y**2))*cos(x/4) *sin(y)*cos(2*(x**2+y**2)).4.3.2.1 -.1 -.2 -.3 -.4-2 -1.5-1 -.5.5 1-1.5-1-.5 1.5 2-2.5 1 1.5 2.4.3.2.1 -.1 -.2 -.3 -.4
Kolorowanie wykresów set hidden3d set isosamples 3 set pm3d at t splot [-2:2][-2:2] exp(-(x**2 + y**2))* cos(x/4) *sin(y)*cos(2*(x**2+y**2)) exp(-(x**2 + y**2))*cos(x/4) *sin(y)*cos(2*(x**2+y**2)).4.3.2.1 -.1 -.2 -.3 -.4-2 -1.5-1 -.5.5 1-1.5-1-.5 1.5 2-2.5 1 1.5 2.4.3.2.1 -.1 -.2 -.3 -.4
Kolorowanie wykresów set hidden3d set isosamples 3 set pm3d at b splot [-2:2][-2:2] exp(-(x**2 + y**2))* cos(x/4) *sin(y)*cos(2*(x**2+y**2)) exp(-(x**2 + y**2))*cos(x/4) *sin(y)*cos(2*(x**2+y**2)).4.3.2.1 -.1 -.2 -.3 -.4-2 -1.5-1 -.5.5 1-1.5-1-.5 1.5 2-2.5 1 1.5 2.4.3.2.1 -.1 -.2 -.3 -.4
Kolorowanie wykresów set hidden3d set isosamples 3 set pm3d at b explicit splot [-2:2][-2:2] exp(-(x**2 + y**2))* cos(x/4) *sin(y)*cos(2*(x**2+y**2)) w pm3d exp(-(x**2 + y**2))*cos(x/4) *sin(y)*cos(2*(x**2+y**2)).4.3.2.1 -.1 -.2 -.3 -.4-2 -1.5-1 -.5.5 1-1.5-1-.5 1.5 2-2.5 1 1.5 2.4.3.2.1 -.1 -.2 -.3 -.4
Kolorowanie wykresów set hidden3d set isosamples 3 unset surface set pm3d at b splot [-2:2][-2:2] exp(-(x**2 + y**2))* cos(x/4) *sin(y)*cos(2*(x**2+y**2)) exp(-(x**2 + y**2))*cos(x/4) *sin(y)*cos(2*(x**2+y**2)) -2-1.5-1 -.5.5 1-1.5-1-.5 1.5 2-2.5 1 1.5 2.4.3.2.1 -.1 -.2 -.3 -.4
Kolorowanie wykresów set palette model HSV functions gray,1,1 set hidden3d set isosamples 3 set pm3d at s corners2color mean splot [-2:2][-2:2] exp(-(x**2 + y**2))* cos(x/4) *sin(y)*cos(2*(x**2+y**2)) exp(-(x**2 + y**2))*cos(x/4) *sin(y)*cos(2*(x**2+y**2)).4.3.2.1 -.1 -.2 -.3 -.4-2 -1.5-1 -.5.5 1-1.5-1-.5 1.5 2-2.5 1 1.5 2.4.3.2.1 -.1 -.2 -.3 -.4
Kolorowanie wykresów set palette model HSV functions gray,1,1 set hidden3d set isosamples 3 set pm3d at s corners2color geomean splot [-2:2][-2:2] exp(-(x**2 + y**2))* cos(x/4) *sin(y)*cos(2*(x**2+y**2)) exp(-(x**2 + y**2))*cos(x/4) *sin(y)*cos(2*(x**2+y**2)).4.3.2.1 -.1 -.2 -.3 -.4-2 -1.5-1 -.5.5 1-1.5-1-.5 1.5 2-2.5 1 1.5 2.4.3.2.1 -.1 -.2 -.3 -.4
Kolorowanie wykresów set palette model HSV functions gray,1,1 set hidden3d set isosamples 3 set pm3d at s corners2color median splot [-2:2][-2:2] exp(-(x**2 + y**2))* cos(x/4) *sin(y)*cos(2*(x**2+y**2)) exp(-(x**2 + y**2))*cos(x/4) *sin(y)*cos(2*(x**2+y**2)).4.3.2.1 -.1 -.2 -.3 -.4-2 -1.5-1 -.5.5 1-1.5-1-.5 1.5 2-2.5 1 1.5 2.4.3.2.1 -.1 -.2 -.3 -.4
Kolorowanie wykresów set palette model HSV functions gray,1,1 set hidden3d set isosamples 3 set pm3d at s corners2color min splot [-2:2][-2:2] exp(-(x**2 + y**2))* cos(x/4) *sin(y)*cos(2*(x**2+y**2)) exp(-(x**2 + y**2))*cos(x/4) *sin(y)*cos(2*(x**2+y**2)).4.3.2.1 -.1 -.2 -.3 -.4-2 -1.5-1 -.5.5 1-1.5-1-.5 1.5 2-2.5 1 1.5 2.4.3.2.1 -.1 -.2 -.3 -.4
Kolorowanie wykresów set palette model HSV functions gray,1,1 set hidden3d set isosamples 3 set pm3d at s corners2color max splot [-2:2][-2:2] exp(-(x**2 + y**2))* cos(x/4) *sin(y)*cos(2*(x**2+y**2)) exp(-(x**2 + y**2))*cos(x/4) *sin(y)*cos(2*(x**2+y**2)).4.3.2.1 -.1 -.2 -.3 -.4-2 -1.5-1 -.5.5 1-1.5-1-.5 1.5 2-2.5 1 1.5 2.4.3.2.1 -.1 -.2 -.3 -.4
Polecenie colorbox Polecenie colorbox jest odpowiednikiem polecenia key dla trybu pm3d. Składnia: set colorbox [ vertical horizontal ] [ noborder bdefault border {idx:linestyle} ] [ default user [ origin {pos:orig} ] [ size {pos:size} ] ] Wył aczenie następuje poprzez polecenie: unset colorbox
Przykład set terminal pdf set encoding utf8 set view 9, set isosamples 2,2 unset ytics set xtics offset,-2 set border 495 set xyplane set palette defined ( red,.25 red,.5 green,1.5 green, 1.75 red, 2 red ) set output "w9-1.pdf" splot sin(x)**3 +.3*sin(5*x) w l palette
Przykład - wykonanie sin(x)**3 +.3*sin(5*x) 1.5 1.5 -.5 1.5 1.5 -.5-1 -1.5-1 -1.5-1 -5 5 1
Przykład - wykonanie set view 6,65 1.5 1.5 -.5-1 -1.5 sin(x)**3 +.3*sin(5*x) 1.5 1.5 -.5-1 -1.5-1 -5 5 1
Przyklady Palet set hidden3d set isosamples 3 set palette model RGB defined ( black, 1 white ) set pm3d at s splot [-2:2][-2:2] exp(-(x**2 + y**2))* cos(x/4) *sin(y)*cos(2*(x**2+y**2)) set output "w9-12a.pdf" test palette
Wykonanie R,G,B profiles of the current color palette red green blue NTSC 1.9.8.7.6.5.4.3.2.1.1.2.3.4.5.6.7.8.9 1.4.3.2.1 -.1 -.2 -.3 -.4 exp(-(x**2 + y**2))*cos(x/4) *sin(y)*cos(2*(x**2+y**2)) -2-1.5-1 -.5.5 1-1.5-1-.5 1.5 2-2.5 1 1.5 2.4.3.2.1 -.1 -.2 -.3 -.4
Przyklady Palet set hidden3d set isosamples 3 set palette model HSV functions 1,,gray set pm3d at s splot [-2:2][-2:2] exp(-(x**2 + y**2))* cos(x/4) *sin(y)*cos(2*(x**2+y**2)) set output "xxx.pdf" test palette
Wykonanie R,G,B profiles of the current color palette red green blue NTSC 1.9.8.7.6.5.4.3.2.1.1.2.3.4.5.6.7.8.9 1.4.3.2.1 -.1 -.2 -.3 -.4 exp(-(x**2 + y**2))*cos(x/4) *sin(y)*cos(2*(x**2+y**2)) -2-1.5-1 -.5.5 1 1.5 2-2-1.5-1-.5.5 1 1.5 2.4.3.2.1 -.1 -.2 -.3 -.4
Przyklady Palet set hidden3d set isosamples 3 set palette model RGB defined ( red, 1 yellow, 2 white ) set pm3d at s splot [-2:2][-2:2] exp(-(x**2 + y**2))* cos(x/4) *sin(y)*cos(2*(x**2+y**2)) set output "xxx.pdf" test palette
Wykonanie R,G,B profiles of the current color palette red green blue NTSC 1.9.8.7.6.5.4.3.2.1.1.2.3.4.5.6.7.8.9 1.4.3.2.1 -.1 -.2 -.3 -.4 exp(-(x**2 + y**2))*cos(x/4) *sin(y)*cos(2*(x**2+y**2)) -2-1.5-1 -.5.5 1 1.5 2-2-1.5-1-.5.5 1 1.5 2.4.3.2.1 -.1 -.2 -.3 -.4
Przyklady Palet set hidden3d set isosamples 3 set palette model RGB defined ( -1 black, red, 1 yellow, 2 white ) set pm3d at s splot [-2:2][-2:2] exp(-(x**2 + y**2))* cos(x/4) *sin(y)*cos(2*(x**2+y**2)) set output "xxx.pdf" test palette
Wykonanie R,G,B profiles of the current color palette red green blue NTSC 1.9.8.7.6.5.4.3.2.1.1.2.3.4.5.6.7.8.9 1.4.3.2.1 -.1 -.2 -.3 -.4 exp(-(x**2 + y**2))*cos(x/4) *sin(y)*cos(2*(x**2+y**2)) -2-1.5-1 -.5.5 1 1.5 2-2-1.5-1-.5.5 1 1.5 2.4.3.2.1 -.1 -.2 -.3 -.4
Przyklady Palet set hidden3d set isosamples 3 set palette model HSV functions gray,1,1 set pm3d at s splot [-2:2][-2:2] exp(-(x**2 + y**2))* cos(x/4) *sin(y)*cos(2*(x**2+y**2)) set output "xxx.pdf" test palette
Wykonanie R,G,B profiles of the current color palette red green blue NTSC 1.9.8.7.6.5.4.3.2.1.1.2.3.4.5.6.7.8.9 1.4.3.2.1 -.1 -.2 -.3 -.4 exp(-(x**2 + y**2))*cos(x/4) *sin(y)*cos(2*(x**2+y**2)) -2-1.5-1 -.5.5 1 1.5 2-2-1.5-1-.5.5 1 1.5 2.4.3.2.1 -.1 -.2 -.3 -.4
Przyklady Palet set hidden3d set isosamples 3 set palette model RGB defined( #3366ff, 1 #99ffcc, 2 #3399, 3 #66ff33,4 #996633, 5 #ff99, 6 #ffff33 ) set pm3d at s splot [-2:2][-2:2] exp(-(x**2 + y**2))* cos(x/4) *sin(y)*cos(2*(x**2+y**2)) set output "xxx.pdf" test palette
Wykonanie R,G,B profiles of the current color palette red green blue NTSC 1.9.8.7.6.5.4.3.2.1.1.2.3.4.5.6.7.8.9 1.4.3.2.1 -.1 -.2 -.3 -.4 exp(-(x**2 + y**2))*cos(x/4) *sin(y)*cos(2*(x**2+y**2)) -2-1.5-1 -.5.5 1 1.5 2-2-1.5-1-.5.5 1 1.5 2.4.3.2.1 -.1 -.2 -.3 -.4
Przyklady Palet set hidden3d set isosamples 3 set palette model RGB defined ( -1 blue, white, 1 red ) set pm3d at s splot [-2:2][-2:2] exp(-(x**2 + y**2))* cos(x/4) *sin(y)*cos(2*(x**2+y**2)) set output "xxx.pdf" test palette
Wykonanie R,G,B profiles of the current color palette red green blue NTSC 1.9.8.7.6.5.4.3.2.1.1.2.3.4.5.6.7.8.9 1.4.3.2.1 -.1 -.2 -.3 -.4 exp(-(x**2 + y**2))*cos(x/4) *sin(y)*cos(2*(x**2+y**2)) -2-1.5-1 -.5.5 1 1.5 2-2-1.5-1-.5.5 1 1.5 2.4.3.2.1 -.1 -.2 -.3 -.4
Przyklady Palet set hidden3d set isosamples 3 hue(x) = x < 1./8. x > 7./8.? : (8*x-1)/6. sat(x) = x < 3./16. x > 15./16.? : (1+cos(8*2*pi*x))/2 lum(x) = x < 1./16.? : (1+cos(8*2*pi*x))/2 stp(x,y) = x < y? : 1 w =.99 set palette model HSV functions hue(gray), stp( sat(gray), w ), gray + (1-gray)*stp(lum(gray), w) set pm3d at s splot [-2:2][-2:2] exp(-(x**2 + y**2))* cos(x/4) *sin(y)*cos(2*(x**2+y**2)) set output "xxx.pdf" test palette
Wykonanie R,G,B profiles of the current color palette red green blue NTSC 1.9.8.7.6.5.4.3.2.1.1.2.3.4.5.6.7.8.9 1.4.3.2.1 -.1 -.2 -.3 -.4 exp(-(x**2 + y**2))*cos(x/4) *sin(y)*cos(2*(x**2+y**2)) -2-1.5-1 -.5.5 1 1.5 2-2-1.5-1-.5.5 1 1.5 2.4.3.2.1 -.1 -.2 -.3 -.4
Przyklady Palet f(x,y,n,m) = cos(n*x)*cos(m*y)+cos(m*x)*cos(n*y) set pm3d set view map set size square unset surface set isosamples 3 set palette model RGB defined ( black, 1 white ) set output "w2.pdf" splot [-6:6][-6:6] f(x,y,2,5)
Wykonanie 6 f(x,y,2,5) 4 2-2 -4-6 -6-4 -2 2 4 6 2 1.5 1.5 -.5-1 -1.5-2
Przyklady Palet f(x,y,n,m) = cos(n*x)*cos(m*y)+cos(m*x)*cos(n*y) set pm3d set view map set size square unset surface set isosamples 3 set palette defined ( magenta, 1 #66ff, 2 cyan, 3 #99, 4 green, 5 #996633, 6 orange, 7 yellow, 8 red ) set output "w21.pdf" splot [-6:6][-6:6] f(x,y,2,5)
Wykonanie 6 f(x,y,2,5) 4 2-2 -4-6 -6-4 -2 2 4 6 2 1.5 1.5 -.5-1 -1.5-2
Przyklady Palet f(x,y,n,m) = cos(n*x)*cos(m*y)+cos(m*x)*cos(n*y) set pm3d set view map set size square unset surface set isosamples 3 set palette defined ( magenta, 1 #3366ff, 2 #99ffcc, 3 #3399, 4 #66ff33, 5 #996633, 6 #ff99, 7 #ffff33, 8 red ) set output "w22.pdf" splot [-6:6][-6:6] f(x,y,2,5)
Wykonanie 6 f(x,y,2,5) 4 2-2 -4-6 -6-4 -2 2 4 6 2 1.5 1.5 -.5-1 -1.5-2
Przyklady Palet f(x,y,n,m) = cos(n*x)*cos(m*y)+cos(m*x)*cos(n*y) set pm3d set view map set size square unset surface set isosamples 3 set palette model RGB defined ( white, 1 white, 225 black, 15 white, 9999 white, 1 black ) set output "w23.pdf" splot [-6:6][-6:6] f(x,y,2,5)
Wykonanie 6 f(x,y,2,5) 4 2-2 -4-6 -6-4 -2 2 4 6 2 1.5 1.5 -.5-1 -1.5-2
Przyklady Palet f(x,y,n,m) = cos(n*x)*cos(m*y)+cos(m*x)*cos(n*y) set pm3d set view map set size square unset surface set isosamples 3 set logsc cb set palette model RGB defined ( log(15) white, log(2) #ff6666, log(35) #cc99cc, log(5) #3366ff, log(1) #99ffcc, log(133) #3399, log(167) #66ff33, log(2) #996633, log(25) #ff99, log(3) #ffff33, log(999) white, log(9999) white,log(1) black ) set output "w24.pdf" splot [-6:6][-6:6] f(x,y,2,5)
Wykonanie 6 4 2-2 -4 f(x,y,2,5) 1 1.1.1.1-6 -6-4 -2 2 4 6.1