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\deflang1045\pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs28\cf2 {\pntext\f1\'b7\tab}reset():TEXTWIDTH :=80 : 
\par \pard\ri4\plain\f3\fs24\cf1\b 
\par \plain\f3\fs36\cf1\b Grafika dla matematyka I \plain\f3\fs24\cf1\b 
\par 
\par 5.1 Kamera Wirtualna
\par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs28\cf2 {\pntext\f1\'b7\tab}f := (x,y) ->  x^2 + y^2:
\par \pard\li600\ri1\fi-300\plain\f4\fs28\cf2 g := (x,y) -> -x^2 + y^2:
\par h := (x,y) ->  x^2 - y^2:
\par p := (x,y) -> -x^2 - y^2:
\par \pard\ri4\plain\f3\fs24\cf1\b 
\par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs28\cf2 {\pntext\f1\'b7\tab}plotfunc3d(
\par \pard\li600\ri1\fi-300\plain\f4\fs28\cf2    f(x,y),g(x,y),h(x,y),p(x,y),
\par    x=-PI..PI, y=-PI..PI
\par )
\par \pard\ri4\plain\f3\fs24\cf1\b 
\par KOMENTARZ:  Wszystkie parametry grafiki mog\'b9 by\'e6 
\par                       modyfikowane w VCam.
\par KOMENTARZ: W Kamerze Wirtualnej nie mo\'bfemy utworzy\'e6 
\par                      nowych obiekt\'f3w graficznych, ale mo\'bfemy 
\par                      doda\'e6 nowe kamery i \'9cwiat\'b3a
\par 
\par 5.2 Struktura sceny graficznej MuPADa
\par 
\par 5.3 Galeria obiekt\'f3w matematycznych
\par 
\par KOMENTARZ: obiekt graficzny a klasa 
\par 
\par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs28\cf2 {\pntext\f1\'b7\tab}plot::Function3d::LineColor=RGB::Blue:
\par {\pntext\f1\'b7\tab}info(plot)
\par \pard\ri4\plain\f3\fs24\cf1\b 
\par 5.3.1 Function2d
\par 
\par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs28\cf2 {\pntext\f1\'b7\tab}G1 := plot::Function2d(sin(x), x=-5..5):
\par {\pntext\f1\'b7\tab}G2 := plot::Function2d(sin(x), x=-5..5,
\par \pard\li600\ri1\fi-300\plain\f4\fs28\cf2    LineColor=RGB::Blue,
\par    LineWidth=0.3*unit::mm
\par ):
\par 
\par G3 := plot::Function2d(sin(2*x), x=-3..3,
\par    LineColor=RGB::Red,
\par    LineWidth=0.6*unit::mm
\par ):
\par 
\par G4 := plot::Function2d(sin(3*x), x=-2..2,
\par    LineColor=RGB::Brown,
\par    LineWidth=0.8*unit::mm
\par ):
\par G5 := plot::Function2d(sin(4*x), x=-1..1,
\par    LineColor=[0.5, 0.5, 0.5],
\par    LineWidth=1*unit::mm
\par ):
\par  
\par plot(G1,G3,G4,G5)
\par \pard\ri4\plain\f3\fs24\cf1\b 
\par 5.3.2 Curve2d
\par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs28\cf2 {\pntext\f1\'b7\tab}C1 := plot::Curve2d(
\par \pard\li600\ri1\fi-300\plain\f4\fs28\cf2    [2*sin(3*t), 4*cos(5*t)], t=0..2*PI
\par ):
\par plot(C1)
\par \pard\ri4\plain\f3\fs24\cf1\b 
\par 5.3.3 Polar
\par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs28\cf2 {\pntext\f1\'b7\tab}P1 := plot::Polar(
\par \pard\li600\ri1\fi-300\plain\f4\fs28\cf2    [sin(5*alfa)+cos(3*alfa), alfa], alfa=0..6*PI,
\par    LineWidth=0.3
\par ):
\par plot(P1)
\par 
\par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs28\cf2 {\pntext\f1\'b7\tab}P1 := plot::Polar([1, alfa], alfa=0..2*PI,
\par \pard\li600\ri1\fi-300\plain\f4\fs28\cf2    LineWidth=0.3
\par ):
\par 
\par P2 := plot::Polar(
\par    [sin(2*alfa), alfa], alfa=0..2*PI,
\par    LineWidth=0.5
\par ):
\par 
\par P3 := plot::Polar(
\par    [exp(-1/u),u], u=0.1..4*PI,  
\par    LineWidth=1
\par ):
\par plot(P1, P2, P3)
\par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs28\cf2 {\pntext\f1\'b7\tab}a1 := plot::Polar([x,x], x=-2*PI..2*PI):
\par \pard\li600\ri1\fi-300\plain\f4\fs28\cf2 a2 := plot::Polar([x^2,x], x=-2*PI..2*PI):
\par a3 := plot::Polar([x^3,x], x=-2*PI..2*PI):
\par plot(a1,a2,a3)
\par \pard\ri4\plain\f3\fs24\cf1\b     
\par 5.3.4 Implicit2d
\par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs28\cf2 {\pntext\f1\'b7\tab}reset():
\par {\pntext\f1\'b7\tab}I1 := plot::Implicit2d(x^2+y^2=1, 
\par \pard\li600\ri1\fi-300\plain\f4\fs28\cf2    x=-2..2, y=-2..2,
\par    LineColor=RGB::Red
\par ):
\par plot(I1, Scaling=Constrained)
\par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs28\cf2 {\pntext\f1\'b7\tab}I1 := plot::Implicit2d(x^2+y^2=1, x=-2..2, y=-2..2,
\par \pard\li600\ri1\fi-300\plain\f4\fs28\cf2    LineColor=RGB::Red
\par ):
\par 
\par I2 := plot::Implicit2d(x^3+y^3=1, x=-2..2,y=-2..2,
\par    LineColor=RGB::Blue,
\par    LineWidth=0.5
\par ):
\par 
\par I3 := plot::Implicit2d(x^4+y^4=1, x=-1..1, y=-1..1,
\par    LineColor=RGB::Green,
\par    LineWidth=0.7
\par ):
\par 
\par I4 := plot::Implicit2d(x^11+y^11=1, x=-2..2,y=-2..2,
\par    LineColor=RGB::Brown,
\par    LineWidth=0.9
\par ):
\par 
\par plot(I1, I2, I3, I4, Scaling=Constrained)
\par \pard\ri4\plain\f3\fs24\cf1\b 
\par 5.3.5 Hatch
\par 
\par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs28\cf2 {\pntext\f1\'b7\tab}reset():     
\par {\pntext\f1\'b7\tab}F1 := plot::Function2d(x^2+1, x=-2..2):
\par \pard\li600\ri1\fi-300\plain\f4\fs28\cf2 F2 := plot::Function2d(0.5*x^2+1,x=-2..2):
\par F3 := plot::Function2d(x, x=-2..2, LineWidth=0.5):
\par 
\par H1 := plot::Hatch(F1,F2, -2..2,
\par    FillPattern=Solid, 
\par    FillColor=RGB::Gold
\par ):
\par 
\par H2 := plot::Hatch(F3, -2..2,
\par    FillPattern=VerticalLines,
\par    FillColor=[0.0, 0.0, 1]
\par ):
\par 
\par plot(H1,H2, F1, F2, F3)
\par \pard\ri4\plain\f3\fs24\cf1\b 
\par     
\par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs28\cf2 {\pntext\f1\'b7\tab}C1 := plot::Curve2d(
\par \pard\li600\ri1\fi-300\plain\f4\fs28\cf2    [cos(3*t), sin(5*t)], t=0..2*PI
\par ):
\par 
\par H4 := plot::Hatch(C1, -0.6..0.6,
\par    FillPattern=Solid
\par ):
\par 
\par plot(H4, C1, AxesInFront=TRUE)
\par \pard\ri4\plain\f3\fs24\cf1\b   
\par 5.3.6 Inequality
\par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs28\cf2 {\pntext\f1\'b7\tab}I1 := plot::Inequality(x^2-2*x+3*y>=0, 
\par \pard\li600\ri1\fi-300\plain\f4\fs28\cf2    x=-1..1, y=-1..1,
\par    XMesh=100, YMesh=100,   
\par    FillColorTrue=[1,0,0], 
\par    FillColorFalse=[0.8,0.8,0.8]
\par ):
\par plot(I1)
\par \pard\ri4\plain\f3\fs24\cf1\b 
\par 5.3.7 Histogram2d
\par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs28\cf2 {\pntext\f1\'b7\tab}dane := [frandom() $ k=1..100]:
\par {\pntext\f1\'b7\tab}H1 := plot::Histogram2d(dane, Cells=[50]):
\par \pard\li600\ri1\fi-300\plain\f4\fs28\cf2 plot(H1)
\par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs28\cf2 {\pntext\f1\'b7\tab}dane := [frandom() $ k=1..10000]:
\par {\pntext\f1\'b7\tab}H2 := plot::Histogram2d(dane, Cells=[50]):
\par \pard\li600\ri1\fi-300\plain\f4\fs28\cf2 plot(H2)
\par \pard\ri4\plain\f3\fs24\cf1\b 
\par 5.3.8 Boxplot
\par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs28\cf2 {\pntext\f1\'b7\tab}dane1 := [frandom() $ k=1..10]:
\par \pard\li600\ri1\fi-300\plain\f4\fs28\cf2 dane2 := [frandom() $ k=1..10]:
\par dane3 := [frandom() $ k=1..10]:
\par B1 := plot::Boxplot(dane1, dane2, dane3):
\par plot(B1)
\par \pard\ri4\plain\f3\fs24\cf1\b 
\par 5.3.9 Function3d
\par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs28\cf2 {\pntext\f1\'b7\tab}Kol := (x,y,z)->[abs(sin(x)),abs(sin(y)),abs(sin(z))]:
\par {\pntext\f1\'b7\tab}F1 := plot::Function3d(1.7*x*exp(-1/2*(x^2+y^2)),
\par \pard\li600\ri1\fi-300\plain\f4\fs28\cf2    x=-4..4, y=-4..4,
\par    FillColorFunction=Kol
\par ):
\par F2 := plot::Function3d(-1, x=-4..4, y=-4..4):
\par plot(F1, F2)
\par \pard\ri4\plain\f3\fs24\cf1\b KOMENTARZ: MuPAD u\'bfywa technologii OpenGL 
\par                      (om\'f3wi\'e6 konsekwencje)
\par 
\par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs28\cf2 {\pntext\f1\'b7\tab}Kol1 := (x,y,z)->[abs(sin(x)),abs(sin(y)),abs(sin(z)),0.8]:
\par {\pntext\f1\'b7\tab}F1 := plot::Function3d(1.7*x*exp(-1/2*(x^2+y^2)),
\par \pard\li600\ri1\fi-300\plain\f4\fs28\cf2    x=-4..4, y=-4..4,
\par    XMesh=50,
\par    YMesh=50,
\par    FillColorFunction=Kol1
\par ):
\par F2 := plot::Function3d(-1, x=-4..4, y=-4..4):
\par plot(F1, F2)
\par \pard\ri4\plain\f3\fs24\cf1\b 
\par 
\par 5.3.10 Surface
\par 
\par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs28\cf2 {\pntext\f1\'b7\tab}Kol2 := (u,v)->[u-trunc(u), v-trunc(v), 0 ]:
\par \pard\li600\ri1\fi-300\plain\f4\fs28\cf2 S1 := plot::Surface(
\par    [sin(u)*sin(v),
\par     sin(u)*cos(v),
\par     cos(u)*sin(v)],
\par    u=0..PI, v=0..PI,
\par    FillColorFunction=Kol2
\par ):
\par plot(S1)
\par \pard\ri4\plain\f3\fs24\cf1\b 
\par 5.3.11 Implicit3d
\par 
\par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs28\cf2 {\pntext\f1\'b7\tab}SteinerEq := (y^2*z^2 + z^2*x^2 + x^2*y^2 + 2*x*y*z = 0)
\par {\pntext\f1\'b7\tab}Steiner := plot::Implicit3d(
\par \pard\li600\ri1\fi-300\plain\f4\fs28\cf2    SteinerEq,
\par    x=-1..1, y=-1..1, z=-1..1,
\par    MeshVisible=TRUE,
\par    XMesh=25, YMesh=25, ZMesh=25
\par ):
\par plot(Steiner)
\par \pard\ri4\plain\f3\fs24\cf1\b 
\par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs28\cf2 {\pntext\f1\'b7\tab}Kol3 := (u,v,x,y,z)->[abs(x),abs(y),abs(z)]:
\par {\pntext\f1\'b7\tab}SteinerParam:=plot::Surface(    
\par \pard\li600\ri1\fi-300\plain\f4\fs28\cf2    [sin(2*u)*(cos(v))^2, 
\par     sin(u)*sin(2*v), 
\par     cos(u)*sin(2*v)],
\par     u=-PI/2..PI/2, 
\par     v=-PI/2..PI/2,
\par     FillColorFunction=Kol3,
\par     Scaling=Constrained,
\par     UMesh=50, 
\par     VMesh=50
\par ):
\par plot(SteinerParam)
\par \pard\ri4\plain\f3\fs24\cf1\b 
\par 
\par 5.3.12 Spherical
\par 
\par Przyk\'b3ad: r\'f3wnanie z=xy we wsp\'f3\'b3rz\'eadnych sferycznych
\par 
\par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs28\cf2 {\pntext\f1\'b7\tab}p := x -> abs(5*x - trunc(5*x)):
\par {\pntext\f1\'b7\tab}Kol4 := (u,v,x,y,z)->[p(x*y),p(y*z),p(z*x)]:
\par {\pntext\f1\'b7\tab}Shell := plot::Spherical(
\par \pard\li600\ri1\fi-300\plain\f4\fs28\cf2    [u*v,u,v],u=0..2*PI,v=0..PI,
\par    //[sin(3*u)+cos(5*v),u,v],u=0..2*PI,v=0..PI,
\par    FillColorFunction=Kol4
\par ):
\par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs28\cf2 {\pntext\f1\'b7\tab}plot(
\par \pard\li600\ri1\fi-300\plain\f4\fs28\cf2    Shell,
\par    Axes=Origin,
\par    AxesLineWidth=0.7,
\par    AxesTips=TRUE
\par )
\par \pard\ri4\plain\f3\fs24\cf1\b 
\par Animacja zakresu zmiennych
\par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs28\cf2 {\pntext\f1\'b7\tab}Shell := plot::Spherical(
\par \pard\li600\ri1\fi-300\plain\f4\fs28\cf2   [u*v,u,v], u=0..PI, v=0..a, a=0..PI,
\par   FillColorFunction=Kol4
\par ):
\par plot(Shell)
\par \pard\ri4\plain\f3\fs24\cf1\b 
\par 5.3.13 Cylindrical
\par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs28\cf2 {\pntext\f1\'b7\tab}reset():
\par \pard\ri4\plain\f3\fs24\cf1\b 
\par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs28\cf2 {\pntext\f1\'b7\tab}Kol5 := (u,z)->
\par \pard\li600\ri1\fi-300\plain\f4\fs28\cf2    [abs(1-z/PI),abs(1-u/PI),abs(u/PI)]:
\par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs28\cf2 {\pntext\f1\'b7\tab}CylSurf:=plot::Cylindrical(
\par \pard\li600\ri1\fi-300\plain\f4\fs28\cf2    [3*sin(2*z)+2*cos(3*u), u, z],
\par    u=0..PI, z=0..PI,
\par    Scaling=Unconstrained,
\par    FillColorFunction=Kol5
\par ):
\par plot(CylSurf)
\par \pard\ri4\plain\f3\fs24\cf1\b 
\par 
\par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs28\cf2 {\pntext\f1\'b7\tab}Kol6:= (u,z) ->  [abs(1-z/PI) ,abs(1-u/PI),abs(u/PI)]:
\par {\pntext\f1\'b7\tab}czapka := plot::Cylindrical(
\par \pard\li600\ri1\fi-300\plain\f4\fs28\cf2    [t*v, sin(t), sin(v)],  
\par    t=-2*PI..2*PI, v=0..2*PI,
\par    Scaling=Unconstrained,
\par    FillColorFunction=Kol6,
\par    UMesh=50,
\par    VMesh=50
\par ):
\par plot(czapka)
\par \pard\ri4\plain\f3\fs24\cf1\b 
\par 5.3.14 Curve3d i Tube
\par 
\par Wychodzimy od r\'f3wniania parametrycznego krzywej w R3
\par x=rsin atcos bt, 
\par y=rsin atsin bt, 
\par z=rcos at. 
\par 
\par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs28\cf2 {\pntext\f1\'b7\tab}a := 1: b := 2.5: r := 10:
\par \pard\li600\ri1\fi-300\plain\f4\fs28\cf2 //a := 8: b := 3.5: r := 3:
\par x := t -> r*sin(a*t)*cos(b*t):
\par y := t -> r*sin(a*t)*sin(b*t):
\par z := t -> r*cos(a*t):
\par C3D := plot::Curve3d([x(t),y(t),z(t)], t=0..4*PI,
\par    LineWidth=0.8,
\par    LineColorType=Dichromatic
\par ):
\par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs28\cf2 {\pntext\f1\'b7\tab}plot(C3D)
\par \pard\ri4\plain\f3\fs24\cf1\b 
\par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs28\cf2 {\pntext\f1\'b7\tab}a := 1:
\par \pard\li600\ri1\fi-300\plain\f4\fs28\cf2 b := 2.5:
\par r := 10:
\par 
\par x := t -> r*sin(a*t)*cos(b*t):
\par y := t -> r*sin(a*t)*sin(b*t):
\par z := t -> r*cos(a*t):
\par 
\par T1 := plot::Tube(
\par    [x(t),y(t),z(t)], 1, t=0..4*PI,    
\par    UMesh=121
\par ):
\par 
\par plot(T1)
\par \pard\ri4\plain\f3\fs24\cf1\b 
\par \pard\li300\ri5\fi-300{\*\pn\pnlvlblt\pnf1\pnindent300{\pntxtb\'b7}}\plain\f4\fs28\cf2 {\pntext\f1\'b7\tab}a := 1:
\par \pard\li600\ri1\fi-300\plain\f4\fs28\cf2 b := 2.5:
\par r := 10:
\par x := t -> r*sin(a*t)*cos(b*t):
\par y := t -> r*sin(a*t)*sin(b*t):
\par z := t -> r*cos(a*t):
\par T2 := plot::Tube(
\par    [x(t),y(t),z(t)], sin(5*b*t)+1, t=0..4*PI,  
\par    UMesh=221
\par ):
\par  plot(T2, Axes=None)
\par \pard\ri4\plain\f3\fs24\cf1\b 
\par 
\par }