Εντολές Γραφικών Παραστάσεων

Plot

Plot[(x^(1/2)), {x,-2,4}]

Plot[Sin[x]+Sin[3x]/2, {x, 0, 4Pi}]

Plot[(x-1)(x-3)(x-4)(x-5), {x, 0, 6}]

Plot[1/(3^(x^2)),{x,-3,5}]

Επιλογές - Options

Options[Plot];

Plot[expr, {var, min, max},
 	optionName1 -> optionValue1,
 	optionName2 -> optionValue2]

ParametricPlot

?ParametricPlot

parfun={3p^2+E^p+2p,(4p^E+5E^p-7p)/2}

ParametricPlot[parfun,{p,0,1.5}]

ParametricPlot[parfun,{p,0,1.5},AxesOrigin->{0,0}]

ParametricPlot[parfun,{p,0,1.5},AxesOrigin->{0,0}, 
	PlotRange->{{0,6},{0,4}}]

Plot[Sin[Pi x]/(Pi x), {x, -4, 4}]

Plot[Sin[Pi x]/(Pi x), {x, -4, 4},
	PlotRange-> {-.1, 1} ]

Plot[Sin[Pi x]/(Pi x), {x, -4, 4},
	PlotRange-> All ]

Plot[(x-1)(x-3)(x-4)(x-5), {x, 0, 10}]

Plot[(x-1)(x-3)(x-4)(x-5), 
	{x, 0, 10}, PlotRange->All]

a

Manipulate[Plot[a Sin[9x],{x,-Pi/2,Pi/2}],{a,1,3}]

Manipulate[Plot[a Sin[9x],{x,-Pi/2,Pi/2},PlotRange->{-3,3}],{a,1,3}]

Plot[Sec[x] Sin[9x],{x,-Pi/2,Pi/2}]

Plot[Sec[x] Sin[9x],{x,-Pi/2,Pi/2},PlotRange->All]

Integrate[(y+1),x]

(∫_0^1)(∫_(y^2)^(2y-y^2))(y+1)\[DifferentialD]x\[DifferentialD]y

Show

parab = Plot[{x^(1/2),-x^(1/2), (1-x)^(1/2)+1,(1-x)^(1/2)+1,-(1-x)^(1/2)+1}, {x, -2, 5}]

a = 3; 
expfun = Plot[a(Exp[x/a] + Exp[-x/a])/2 - a,  {x, -2, 2}]

Show[parab, expfun]

?abs

Εμφάνιση γραφήματος πάντα

Plot[(x+1)(x-3), {x,-2,4}];

Plot[(x+1)(x-3), {x,-2,4},DisplayFunction->(Print[#];&)];

ShowPlotAlways=(Print[#];&)

Plot[(x+1)(x-3), {x,-2,4},DisplayFunction->ShowPlotAlways];

w=Integrate[x,{x,0,1}];
Print["w=",w];
Plot[x,{x, 0, 1}, DisplayFunction -> (Print[#]; &)];
z=Integrate[x,{x,0,1}]

w

p1=Plot[x,{x, 0, 1}];

p1

w=10;Print[p1];y=5

??Plot

q=10;s=20

Παράδειγματα

Plot[{x^2/4, Exp[x/2]+Exp[-x/2]-2}, 
	{x, -2, 2},
	PlotStyle -> {
		{Thickness[.01], Dashing[{.05,.02}]},
		{Thickness[.005], RGBColor[1,0,1]} 
	}
]

Needs["PlotLegends`"];
 Plot[{((x^2)/4),(E^(x/2))+(E^(-(x/2)))-2},{x,-2,2},PlotStyle->{Thick,Dashed},PlotLegend->{((x^2)/4),(E^(x/2))+(E^(-(x/2)))-2}]

?PlotLegend

(* από παλαιότερη έκδοση -  Needs["Graphics`Colors`"]*) 
Plot[{x^2/4, Exp[x/2] + Exp[-x/2] - 2}, {x, -2, 2},
	PlotStyle -> {{Dashed, Blue},{Thick, Green } },
	PlotLegend -> {x^2/4, Exp[x/2]+Exp[-x/2]-2}]

Plot[{x^2/4, Exp[x/2]+Exp[-x/2]-2}, {x, -2, 2},
	PlotStyle -> {
		{ Thickness[.01], Dashing[{.05,.02}] },
		{ Thickness[.005], RGBColor[1,0,1] } },
	LegendSize -> {1.5, 0.6}, 
	LegendPosition->{1, -0.5},
	PlotLegend -> {x^2/4,Exp[x/2] + Exp[-x/2] - 2}]

Plot[{x^2/4, Exp[x/2]+Exp[-x/2]-2}, {x, -2, 2},
	PlotStyle -> {
		{ Thickness[.01], Dashing[{.05,.02}] },
		{ Thickness[.005], RGBColor[1,0,1] } },
	LegendSize -> Automatic, LegendPosition->{1, -0.5},
	PlotLegend -> {x^2/4,Exp[x/2] + Exp[-x/2] - 2}]

Επιλογή AspectRatio

Plot[x^2-x+2, {x, -2, 2}]

??AspectRatio

Plot[x^2-x+2, {x, -2, 2}, AspectRatio->0.5 ]

??Plot

Set AspectRatio to 1 to draw the graph in which the height = the width.

Plot[x^2-x+2, {x, -2, 2}, AspectRatio->1]

Plot[x^2-x+2, {x, -2, 2}]

Plot[x^2-x+2, {x, -2, 2}, ImageSize -> Scaled[.25] ]

ParametricPlot[{Cos[7t]Cos[11t],Cos[7t]Sin[11t]},{t, 0, 2Pi}]

ParametricPlot[{Cos[11t]Cos[17t],Cos[11t]Sin[17t]},{t,0,2Pi},
	Axes->None]

ParametricPlot[{Cos[theta], Sin[theta]}, {theta,0,2Pi}]

ContourPlot[Cos[x]+Cos[y],{x,0,4Pi},{y,0,4Pi}]

ContourPlot[x^2+y^2,{x,-1,1},{y,-1,1}]

ContourPlot[x^2+y^2==1,{x,-1,1},{y,-1,1}]

ParametricPlot[{Cos[theta], Sin[theta]}, {theta,0,2Pi},AspectRatio->1,ImageSize -> Scaled[.25]]

circle=x^2+y^2-1

Solve[circle==0,y]

sol=y/.%

sol

Plot[{sol[[1]],sol[[2]]},{x,-1.5,1.5}, AspectRatio->Automatic, PlotStyle->{Blue,Blue}]

PlotCircle[x_, y_,x0_, y0_, r_]:=Module[{sol},
sol=Solve[(x-x0)^2+(y-y0)^2==r^2, y];
Print[sol];
sol=y/.sol;
Print[sol];
Plot[{sol[[1]],sol[[2]]},{x,x0-r,x0+r}, AspectRatio->Automatic,AxesOrigin->{x0,y0}, PlotStyle->{Blue,Blue}]]

PlotCircle[x,y,1,1,3]

?Circle

Ορισμός επιλογών

Plot[x,{x,0,10}]

SetOptions[Plot,
	PlotStyle->Thickness[0.05]]

Plot[x,{x,0,24}]

SetOptions[Plot,
	PlotStyle->Automatic] ;

Plot[x,{x,0,24}]

Εσωτερική μορφή γραφήματος

samples=
Plot[(2x-1)(x-2)(x-3),{x,0,4}]

Short[FullForm[samples], 20]

samples

smallsamples=First[Rest[First[Rest[Rest[First[First[samples]]]]]]][[1]];

Length[%]

smallsamples=Drop[smallsamples,{1,430,2}];

Length[%]

smallsamples=Drop[smallsamples,{1,215,2}];

Length[%]

smallsamples=Drop[smallsamples,{1,107,2}];

Length[%]

smallsamples

Show[Graphics[{Thickness[0.001],Line[smallsamples]}], Axes->Automatic,
AspectRatio -> 1/2, AxesOrigin->{0,0}]

p1=Plot[x,{x, 0, 1}];

FullForm[p1]

Γραφήματα 3D

Plot3D[Sin[x*y], {x, 0, Pi}, {y, 0, 2Pi},AxesLabel -> {"x","y","z"} ]

Show[%, ViewPoint->{0.723, 0.664, 1.199}]

Show[%, ViewPoint->{0, 0, 2}]

Show[%,ViewPoint->{0,0,10}]

?Color*

Plot3D[Log[x1]+Log[x2],{x1,1,10},{x2,1,10},ColorFunction->Function[{x,y,z},Hue[z]]]

Plot3D[Log[x1]+Log[x2],{x1,1,10},{x2,1,10},ColorFunction->"AlpineColors"]

Plot3D[{f,s},{x,xmin,xmax},{y,ymin,ymax}]

Plot3D[Log[x1]+Log[x2],{x1,1,10},{x2,1,10},ColorFunction->(Hue[(1/3) (Log[x1]+Log[x2])]/.{x1->#1,x2->#2}&),ColorFunctionScaling->False]

Plot3D[Sin[x y],{x,0,π},{y,0,2 π},ColorFunction->(Hue[((x y+1)/(5 π))]/.{x->#1,y->#2}&),ColorFunctionScaling->False,AxesLabel->{"X","Y","Z"}]

Υψομετρικά

ContourPlot[Log[x1] + Log[x2], {x1, 1, 10}, {x2, 1, 10}]

ContourPlot[Log[x1] + Log[x2],{x1, 1, 10}, {x2, 1, 10},
	ContourShading -> False]

ContourPlot[Log[x1] + Log[x2],{x1, 1, 10}, {x2, 1, 10},
	ContourShading -> False,Contours -> 5]

DensityPlot[Log[x1]+Log[x2],{x1,1,10},{x2,1,10}]

DensityPlot[Sin[x1 x2],{x1,1,10},{x2,1,10},PlotPoints->50]

DensityPlot[Sin[x y],{x,-2,2},{y,-2,2},PlotPoints->25]

Γραφήματα σημείων λίστας

nlist = {{1900, 1263}, {1930, 16185}, {1960, 284093}, {1990, 3233313}}

ListPlot[nlist]

g1=ListPlot[nlist,PlotStyle->PointSize[0.02]]

g2=ListPlot[nlist,Joined->True]

g3 = ListPlot[nlist, PlotStyle -> {PointSize[0.02],
		RGBColor[1,0,0]}, Joined -> True]

g3 = ListPlot[nlist, Joined -> True, PlotMarkers->Automatic,PlotStyle -> {Red}]

Show[g1,g2]

g4=ListPlot[nlist,PlotStyle->RGBColor[1,0,0],Joined->True]

Show[g1,g2]

??ListPlot

f1 = Fit[nlist, {1, x}, x]

f2 = Fit[nlist, {1,x,x^2,x^3}, x ]

Plot[{f1, f2}, {x, 1900, 2000}]

Show[g1, %]

BarCharts

slist = {5, 6, 4, 5, 5, 5, 3, 
  5, 5, 4, 2, 4, 1,6, 6, 6, 5, 5, 4, 
  2, 5, 2, 6, 5, 1, 4, 6, 5, 6, 5, 1, 
  5, 5, 5, 5, 6, 0, 6, 5, 5, 5, 5, 5, 
  6, 6, 2, 6}

slistbars = 
	Table[Count[slist,i],{i,6}]

Needs["BarCharts`"]
Needs["Histograms`"]
Needs["PieCharts`"]
 BarChart[slistbars]

BarChart[slistbars,
	PlotRange -> All]

Options[BarChart]

SetOptions[BarChart,
	BarOrientation -> Horizontal]

BarChart[slistbars,
	PlotRange -> All,
	Frame -> True]

SetOptions[BarChart, 
	BarOrientation -> Vertical]

Παραδείγματα

Plot[Sin[x], {x, 0, 2Pi}]

Plot[Sin[x], {x, 0, 2Pi},
  PlotStyle -> {{Thickness[0.02], GrayLevel[0.5]}}]

Plot[BesselJ[2, x], {x, 0, 10},
  PlotStyle -> {{Thickness[0.02], GrayLevel[0.5]}}]

Plot[Sin[x], {x, 0, 2Pi}, AxesLabel->{"X","Y"},PlotLabel->"SIN[X]",
	Ticks->{{0,Pi/2,Pi,3Pi/2,2Pi}, {-1,-.5,0,.5,1}}]

Διάφορα

Needs["VectorFieldPlots`"] ;
Needs["VectorFieldPlots`"];
VectorFieldPlots`VectorFieldPlot[{Cos[x],Sin[x]},{x,0,π},{y,0,π}]

Needs["VectorFieldPlots`"] ;
Needs["VectorFieldPlots`"];
VectorFieldPlots`VectorFieldPlot3D[{-(y/z),((x+y)/z),0},{x,-1,1},{y,-1,1},{z,1,3},VectorHeads->True]

Plot[Cos[x],{x,0,2 π},Filling->Axis]

Plot[{Cos[x],Sin[x],(x/10)},{x,0,2 π},Filling->{1->{2},2->{3}}]

Plot[{((Sin[x])/x),If[Abs[x]<2,0,((Sin[x])/x)]},{x,-2 π,2 π},Filling->{1->{2}}]

Needs["WorldPlot`"]
WorldPlot["Finland"]

WorldPlot[ {Europe, RandomGrays},
	WorldProjection -> Mollweide]

WorldPlot[{World, RandomColors}]

Κίνηση

(* για παλαιότερες εκδόσεις *)
Table[Plot[Sin[Exp[x + t]],
		{x, 0, 4}, PlotPoints -> 70 ],
	{t, 0, 1, .25} ]

Animate[Plot[Sin[Exp[x + t]],
		{x, 0, 4}, PlotPoints -> 70 ],
	{t, 0, 1, .25} ]

Manipulate[Plot[Sin[Exp[x + t]],
		{x, 0, 4}, PlotPoints -> 70 ],
	{t, 0, 1, .25} ]

coversheetAnimation =
	Table[
		Plot3D[
			Sin[x y],
			{x, 0, t/2},
			{y, 0, t},
			PlotPoints -> 20,
			Ticks -> None
		],
		{t, 1, 8, 3/4} ]

GraphicsGrid[{Take[coversheetAnimation, 5],Drop[coversheetAnimation, 5]},Frame->All]

Manipulate[
		Plot3D[
			Sin[x y],
			{x, 0, t/2},
			{y, 0, t},
			PlotPoints -> 10,
			Ticks -> None
		],
		{t, 1, 6, 1/4} ]

Παραδείγματα 1

p1=Plot3D[Sin[x] (E^(Cos[y])),{x,0,2 π},{y,0,4 π},PlotPoints->30,Ticks->None]

p1=Plot3D[Sin[x] (E^(Cos[y])),{x,0,2 π},{y,0,4 π},PlotPoints->30,Ticks->None,DisplayFunction->(PopupWindow[Button["Click here"],#]&)]

p2=Plot3D[Sin[x] (E^(Cos[y])),{x,0,2 π},{y,0,4 π},PlotPoints->30,Ticks->None,DisplayFunction->Identity,ColorFunction->(White&)]

p3=Plot3D[Sin[x] (E^(Cos[y])),{x,0,2 π},{y,0,4 π},ColorFunction->(RGBColor[1,0,0]/.{x->#1,y->#2}&),ColorFunctionScaling->False,PlotPoints->30,Ticks->None,DisplayFunction->Identity]

p4=Plot3D[Sin[x] (E^(Cos[y])),{x,0,2 π},{y,0,4 π},ColorFunction->(RGBColor[0,Abs[Sin[x] Cos[y]],0]/.{x->#1,y->#2}&),ColorFunctionScaling->False,PlotPoints->30,Ticks->None,DisplayFunction->Identity]

Show[GraphicsGrid[{{p1,p2},{p3,p4}}]]

??ContourPlot

Παραδείγματα 2

Clear[g]
g[x_,y_]=x Sin[y]+y Sin[x] 
ContourPlot[g[x,y],{x,0,5π},{y,0,5π},PlotPoints->60]

ContourPlot[g[x,y],{x,0,5π},{y,0,5π},Contours->20,ContourShading->False,Axes->Automatic,Frame->False,AxesOrigin->{0,0},PlotPoints->120]

Παραδείγματα 3

Clear[f]
f[x_,y_]=(x^2)-4x+(y^2)-2y+5 
ContourPlot[f[x,y],{x,-2,6},{y,-3,5},ContourShading->False,PlotPoints->60]

ContourPlot[f[x,y],{x,-2,6},{y,-3,5},Contours->{9},Frame->False,Axes->Automatic,AxesOrigin->{0,0},ContourShading->False,PlotPoints->120]

Παραδείγματα 4

Clear[h]
h[x_,y_]=(((x^2)-(y^2))/((x^2)+(y^2)))
ploth=Plot3D[h[x,y],{x,-2,2},{y,-2,2},PlotPoints->30,DisplayFunction->Identity,ColorFunction->(White&)]
cph=ContourPlot[h[x,y],{x,-2,2},{y,-2,2},Frame->False,Axes->Automatic,AxesOrigin->{0,0},PlotPoints->60,PlotRange->{-1,1},ContourShading->False,DisplayFunction->Identity]
Show[GraphicsRow[{ploth,cph}]]

??ParametricPlot3D

Παραδείγματα 5

pp1=ParametricPlot3D[{Cos[2 t],Sin[2 t],(t/5)},{t,0,8 π},PlotPoints->120,Ticks->None,DisplayFunction->Identity]
pp2=ParametricPlot3D[{t Cos[2 t],t Sin[2 t],(t/5)},{t,0,8 π},PlotPoints->120,Ticks->None,DisplayFunction->Identity]
Show[GraphicsRow[{pp1,pp2}]]

Παραδείγματα 6

Clear[g]
g[x_,y_]=Cos[x+Sin[y]] 
Plot3D[g[x,y],{x,0,4π},{y,0,4π},PlotPoints->30]

pp1=ParametricPlot3D[{5,t,0},{t,0,4π},DisplayFunction->Identity] 
pp2=ParametricPlot3D[{5,t,g[5,t]},{t,0,4π},DisplayFunction->Identity] 
pp3=ParametricPlot3D[{t,5,0},{t,0,4π},DisplayFunction->Identity] 
pp4=ParametricPlot3D[{t,6,g[t,6]},{t,0,4π},DisplayFunction->Identity] 
Show[pp1,pp2,pp3,pp4,DisplayFunction->$DisplayFunction]

pp5=ParametricPlot3D[{t,t,0},{t,0,4π},DisplayFunction->Identity] 
pp6=ParametricPlot3D[{t,t,g[t,t]},{t,0,4π},DisplayFunction->Identity] 
pp7=ParametricPlot3D[{t,4π-t,0},{t,0,4π},DisplayFunction->Identity] 
pp8=ParametricPlot3D[{t,4π-t,g[t,4π-t]},{t,0,4π},DisplayFunction->Identity] 
Show[pp5,pp6,pp7,pp8,DisplayFunction->$DisplayFunction]

Παραδείγματα 7

Clear[f]
f[x_,y_]=(x^3) Sin[4 y]+(y^2) Cos[3 x]
pp3=ParametricPlot3D[{Cos[t],Sin[t],0},{t,0,2 π},DisplayFunction->Identity]
pp4=ParametricPlot3D[{Cos[t],Sin[t],f[Cos[t],Sin[t]]},{t,0,2 π},DisplayFunction->Identity]
pp5=Show[pp3,pp4]
pp6=Plot3D[f[x,y],{x,-1.5`,1.5`},{y,-1.5`,1.5`},PlotPoints->30,DisplayFunction->Identity]
Show[GraphicsRow[{pp5,pp6}]]

Παραδείγματα 8

Clear[x,y,z]
x[t_,r_]=4 Cos[t] Cos[r] 
y[t_,r_]=2 Cos[t] Sin[r] 
z[t_,r_]=Sin[t] 
ParametricPlot3D[{x[t,r],y[t,r],z[t,r]},{t,-(π/2),(π/2)},{r,-π,π}]

Clear[x,y,z]
x[t_,r_]=4 Sec[t] Cos[r] 
y[t_,r_]=2 Sec[t] Sin[r] 
z[t_,r_]=Tan[t] 
ParametricPlot3D[{x[t,r],y[t,r],z[t,r]},{t,-(π/3),(π/3)},{r,-π,π}]