Quadriken

Vorbereitung der drei Rechtecke für die Hauptebenen

a=4; b=3; c=2;

Ebz=ContourPlot3D[{z==0},{x,-a,a},{y,-b,b},{z,-c,c}, Mesh->None,ContourStyle->Directive[RGBColor[1,0,1,0.2],Specularity[White,30]],BoxRatios->Automatic];

Eby=ContourPlot3D[{y==0},{x,-a,a},{y,-b,b},{z,-c,c}, Mesh->None,ContourStyle->Directive[RGBColor[0,1,0,0.2],Specularity[White,30]],
BoxRatios->Automatic];

Ebx=ContourPlot3D[x==0,{x,-a,a},{y,-b,b},{z,-c,c}, Mesh->None,ContourStyle->Directive[RGBColor[0,0.4,1,0.2],Specularity[White,100]],
BoxRatios->Automatic];

Show[Ebx,Eby,Ebz]

In diesem abc-Kasten sollen alle Quadriken dann dargestellt werden.

Erzeugung der Quadriken

Ellipsoid ((x^2)/(a^2))+((y^2)/(b^2))+((z^2)/(c^2))==1

quadrikElli=ContourPlot3D[{((x^2)/(a^2))+((y^2)/(b^2))+((z^2)/(c^2))==1},{x,-a,a},{y,-b,b},{z,-c,c}, Mesh->None,ContourStyle->Directive[Orange,Opacity[0.8],Specularity[White,10]],
Axes->None,BoxRatios->Automatic];

Dieser Code gilt mit der jeweils angegebenen Gleichung auch für die andernQuadriken.

Show[quadrikElli, Ebx,Eby, Ebz, Boxed->False]

Einschaliges Hyperboloid ((2(x^2))/(a^2))+((2(y^2))/(b^2))-((z^2)/(c^2))==1

quadrikHypEin=ContourPlot3D[{((2(x^2))/(a^2))+((2(y^2))/(b^2))-((z^2)/(c^2))==1},{x,((-a)/1),(a/1)},{y,((-b)/1),(b/1)},{z,-c,c}, Mesh->None,ContourStyle->Directive[Orange,Opacity[0.8],Specularity[White,10]],
Axes->None,BoxRatios->Automatic];

Show[quadrikHypEin, Ebx,Eby, Ebz, Boxed->False]

Zweischaliges Hyperboloid ((2(x^2))/(a^2))-((2(y^2))/(b^2))-((z^2)/(c^2))==1

quadrikHypZwei=ContourPlot3D[{((2(x^2))/(a^2))-((2(y^2))/(b^2))-((z^2)/(c^2))==1},{x,((-a)/1),(a/1)},{y,((-b)/1),(b/1)},{z,-c,c}, Mesh->None,ContourStyle->Directive[Orange,Opacity[0.8],Specularity[White,10]],
Axes->None,
BoxRatios->Automatic];

Show[quadrikHypZwei, Ebx,Eby, Ebz, Boxed->False]

Elliptisches Paraboloid ((2(x^2))/(a^2))+((2(y^2))/(b^2))-(z/c)==1

quadrikPara=ContourPlot3D[{((2(x^2))/(a^2))+((2(y^2))/(b^2))-(z/c)==1},{x,((-a)/1),(a/1)},{y,((-b)/1),(b/1)},{z,-c,c}, Mesh->None,ContourStyle->Directive[Orange,Opacity[0.8],Specularity[White,10]],
Axes->None,
BoxRatios->Automatic];

Show[quadrikPara, Ebx,Eby, Ebz, Boxed->False]

Hyperbolisches Paraboloid ((x^2)/(a^2))-((y^2)/(b^2))-(z/(c^2))==0

quadrikHypPara=ContourPlot3D[{((x^2)/(a^2))-((y^2)/(b^2))-(z/(c^2))==0},{x,((-a)/1),(a/1)},{y,((-b)/1),(b/1)},{z,-c,c}, Mesh->None,ContourStyle->Directive[Orange,Opacity[0.8],Specularity[White,10]],
Axes->None,BoxRatios->Automatic];

Show[quadrikHypPara, Ebx,Eby,Ebz, Boxed->False]

Elliptischer Kegel   ((x^2)/(a^2))+((y^2)/(b^2))-((z^2)/(c^2))==0

quadrikElliKegel=ContourPlot3D[{((x^2)/(a^2))+((y^2)/(b^2))-((z^2)/(c^2))==0},{x,((-a)/1),(a/1)},{y,((-b)/1),(b/1)},{z,-c,c}, Mesh->None,ContourStyle->Directive[Orange,Opacity[0.8],Specularity[White,10]],
Axes->None,BoxRatios->Automatic];

Show[quadrikElliKegel, Ebx,Eby,Ebz, Boxed->False]

Parabelrinne, xy- bzw  xz- bzw. yz-Ebene ((2(x^2))/(a^2))+((3y)/(b^2))-((2z)/(c^2))==0

quadrikParaRinne=ContourPlot3D[{((2(x^2))/(a^2))+((3y)/(b^2))-((2z)/(c^2))==0},{x,((-a)/1),(a/1)},{y,((-b)/1),(b/1)},{z,-c,c}, Mesh->None,ContourStyle->Directive[Orange,Opacity[0.8],Specularity[White,10]],
Axes->None,BoxRatios->Automatic];

Show[quadrikParaRinne, Ebz, Boxed->False]

Show[quadrikParaRinne, Eby, Boxed->False]

Show[quadrikParaRinne, Ebx, Boxed->False]

Elliptischer Zylinder    ((x^2)/(a^2))+((y^2)/(b^2))==1

quadrikElliZyl=ContourPlot3D[{((x^2)/(a^2))+((y^2)/(b^2))==1},{x,((-a)/1),(a/1)},{y,((-b)/1),(b/1)},{z,-c,c}, Mesh->None,ContourStyle->Directive[Orange,Opacity[0.8],Specularity[White,10]],
Axes->None,BoxRatios->Automatic];

Show[quadrikElliZyl, Ebx,Eby,Ebz, Boxed->False]

Hyperbolischer Zylinder   ((4(x^2))/(a^2))-3((y^2)/(b^2))==1

quadrikHypZyl=ContourPlot3D[{((4(x^2))/(a^2))-3((y^2)/(b^2))==1},{x,((-a)/1),(a/1)},{y,((-b)/1),(b/1)},{z,-c,c}, Mesh->None,ContourStyle->Directive[Orange,Opacity[0.8],Specularity[White,10]],
Axes->None,BoxRatios->Automatic];

Show[quadrikHypZyl, Ebx,Eby,Ebz, Boxed->False]

Parabolischer Zylinder  ((2(x^2))/(a^2))+((3y)/(b^2))==1

quadrikParaZyl=ContourPlot3D[{((2(x^2))/(a^2))+((3y)/(b^2))==1},{x,((-a)/1),(a/1)},{y,((-b)/1),(b/1)},{z,-c,c}, Mesh->None,ContourStyle->Directive[Orange,Opacity[0.8],Specularity[White,10]],
Axes->None,BoxRatios->Automatic];

Show[quadrikParaZyl, Ebx,Eby,Ebz, Boxed->False]