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  • Beitrag zuletzt geändert am:09.05.2020
  • Beitrags-Kategorie:Mathematik
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Title:			 Koordinatensysteme - 3d-Kartesisch
% Author:      Tobias Krähling
% Needs:       pstricks, pst-3dplot
% DesignScale: unit=15mm
% Size:			   3.9 x 3.85
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
{\sbPSTDefault\sffamily
	\psset{unit=15mm}
	\begin{pspicture}(-0.8,-1.35)(3.1,2.5)
		\psset{Alpha=80}
		\pstThreeDDot[drawCoor=true,linecolor=sblinemed,linewidth=1pt](2,2,2)
		\pstThreeDLine[linecolor=sblinemed
                  ,linestyle=dashed
                  ,linewidth=1pt
                  ](0,0,2)(2,2,2)
		\pstThreeDLine[linecolor=sblinemed
                  ,linestyle=dashed
                  ,linewidth=1pt
                  ](0,0,0)(2,2,0)
		\pstThreeDLine[linecolor=sblinehighlight
                  ,linestyle=solid
                  ,arrows=->
                  ,linewidth=1pt
                  ](0,0,0)(1.95,1.95,1.95)
		\pstThreeDCoor[xMin=0,xMax=2.5
                  ,yMin=0,yMax=2.5
                  ,zMin=0,zMax=2.5
                  ,linecolor=black,linewidth=1pt]
		\pstThreeDPut( 0.0,-0.2,2.0){$z_1$}
		\pstThreeDPut(-0.2, 2.0,0.2){$y_1$}
		\pstThreeDPut( 2.2,-0.2,0.2){$x_1$}
		\pstThreeDPut( 1.1, 0.7,0.0){$r_p$}
		\pstThreeDPut( 1.0, 1.0,1.3){$r$}
		\pstThreeDPut( 2.2, 2.2,2.3){\rput[l]{U}{$P_1(x_1,y_1,z_1)$}}
	\end{pspicture}
}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Title:			 Koordinatensysteme - 3d-Kartesisch
% Author:      Tobias Krähling
% Needs:       pstricks, pst-3dplot
% DesignScale: unit=15mm
% Size:			   3.6 x 3.85
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
{\sbPSTDefault\sffamily
	\psset{unit=15mm}
	\begin{pspicture}(-0.8,-1.35)(2.8,2.5)
		\psset{Alpha=80}
		\pstThreeDDot[drawCoor=true,linecolor=sblinemed,linewidth=1pt](2,2,2)
		\pstThreeDLine[linecolor=sblinemed
                  ,linestyle=dashed
                  ,linewidth=1pt
                  ](0,0,2)(2,2,2)
		\pstThreeDLine[linecolor=sblinemed
                  ,linestyle=dashed
                  ,linewidth=1pt
                  ](0,0,0)(2,2,0)
		\pstThreeDLine[linecolor=sblinehighlight
                  ,linestyle=solid
                  ,arrows=->
                  ,linewidth=1pt
                  ](0,0,0)(1.95,1.95,1.95)
		\pstThreeDCoor[xMin=0,xMax=2.5
                  ,yMin=0,yMax=2.5
                  ,zMin=0,zMax=2.5
                  ,linecolor=black,linewidth=1pt]
		\pstThreeDPut( 0.0,-0.2,2.0){$z$}
		\pstThreeDPut(-0.2, 2.0,0.2){$y$}
		\pstThreeDPut( 2.2,-0.2,0.2){$x$}
		\pstThreeDPut( 1.0, 1.0,1.3){$\Vec{r}$}
		\pstThreeDPut( 2.2, 2.2,2.3){\rput[l]{U}{$P(x,y,z)$}}
	\end{pspicture}
}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Title:			 Koordinatensystem - Zylinderkoordinaten
% Author:      Tobias Krähling
% Needs:       pstricks, pst-3dplot
% DesignScale: unit=15mm
% Size:			   3.6 x 4.0
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
{\sbPSTDefault\sffamily
	\psset{unit=15mm}
	\begin{pspicture}(-0.8,-1.5)(2.8,2.5)
		\psset{Alpha=80}
		\pstThreeDDot[drawCoor=true,linecolor=sblinemed,linewidth=1pt
                 ](2,2,2)
		\pstThreeDLine[linecolor=sblinemed,linestyle=dashed,linewidth=1pt
                  ](0,0,2)(2,2,2)
		\pstThreeDLine[linecolor=sblinemed,linestyle=dashed,linewidth=1pt
                  ](0,0,0)(2,2,0)
		\pstThreeDLine[linecolor=sblinehighlight,linestyle=solid,linewidth=1pt
                  ,arrows=->
                  ](0,0,0)(1.95,1.95,1.95)
		\pstThreeDEllipse[beginAngle=0,endAngle=45,arrows=->
                     ,linewidth=1pt,linecolor=sblinemed
                     ](0,0,0)(0.8,0,0)(0,0.8,0)
		\pstThreeDCoor[xMin=0,xMax=2.5,yMin=0,yMax=2.5,zMin=0,zMax=2.5
                  ,linecolor=black,linewidth=1pt]
		\pstThreeDPut( 0.0,-0.2,2.0){$z_1$}
		\pstThreeDPut(-0.2, 2.0,0.2){$y_1$}
		\pstThreeDPut( 2.2,-0.2,0.2){$x_1$}
		\pstThreeDPut( 1.1, 0.7,0.0){$\varrho$}
		\pstThreeDPut( 1.0, 1.0,1.3){$r$}
		\pstThreeDPut( 2.2, 2.2,2.3){\rput[l]{U}{$P_1(\varrho,\varphi,z)$}}
		\pstThreeDPut( 2.2, 2.2,0.0){$P'_1$}
		\pstThreeDPut( 0.5, 0.2,0.0){$\varphi$}
	\end{pspicture}
}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Title:			 Koordinatensystem - Zylinderkoordinaten
% Author:      Tobias Krähling
% Needs:       pstricks, pst-3dplot
% DesignScale: unit=15mm
% Size:			   4.5 x 4
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
{\sbPSTDefault\sffamily
	\psset{unit=15mm}
	\begin{pspicture}(-1,-1.5)(3.5,2.5)
		\psset{Alpha=80}
		\pstThreeDSquare[fillcolor=sbfilllight!30,fillstyle=solid
                    ,linestyle=none
                    ](0,-2.8,0)(0,5.62,0)(0,0,2.3)
		\pstThreeDEllipse[fillcolor=sbfilllight!30,fillstyle=solid
                     ,linestyle=none
                     ](0,0,0)(2.8,0,0)(0,2.8,0)
		\pstThreeDLine[linecolor=sbfillmed](0,2.835,0.1)(0,2.835,2.3)
		\pstThreeDEllipse[linecolor=sbfillmed
                     ,beginAngle=-90,endAngle=90
                     ](0,0,0)(2.8,0,0)(0,2.8,0)
		\pstThreeDEllipse[fillcolor=sbfilllight!30,fillstyle=solid
                     ,linecolor=sbfillmed
                     ](0,0,2)(2.8,0,0)(0,2.8,0)
		\pstThreeDEllipse[linecolor=sbfillmed,linestyle=dashed
                     ,beginAngle=90,endAngle=270
                     ](0,0,0)(2.8,0,0)(0,2.8,0)
		\pstThreeDEllipse[linestyle=dotted,linecolor=sbfillmed
                     ](0,0,0.5)(2.8,0,0)(0,2.8,0)
		\pstThreeDEllipse[linestyle=dotted,linecolor=sbfillmed
                     ](0,0,1)(2.8,0,0)(0,2.8,0)
		\pstThreeDEllipse[linestyle=dotted,linecolor=sbfillmed
                     ](0,0,1.5)(2.8,0,0)(0,2.8,0)
		%\pstThreeDEllipse[fillcolor=lightblue,fillstyle=solid](0,0,0)(2,0,2)(0,2,2)
		\pstThreeDDot[drawCoor=true
                 ,linecolor=sblinemed,linewidth=1pt
                 ](2,2,2)
		\pstThreeDLine[linecolor=sblinemed,linestyle=dashed,linewidth=1pt
                  ](0,0,2)(2,2,2)
		\pstThreeDLine[linecolor=sblinemed,linestyle=dashed,linewidth=1pt
                  ](0,0,0)(2,2,0)
		\pstThreeDLine[linecolor=sblinehighlight,linestyle=solid,linewidth=1pt
                  ,arrows=->
                  ](0,0,0)(1.95,1.95,1.95)
		\pstThreeDEllipse[beginAngle=0,endAngle=45
                     ,arrows=->
                     ,linewidth=1pt,linecolor=sblinemed
                     ](0,0,0)(0.8,0,0)(0,0.8,0)
		\pstThreeDCoor[xMin=0,xMax=2.5,yMin=0,yMax=2.5,zMin=0,zMax=2.5
                  ,linecolor=black,linewidth=1pt]
		\pstThreeDPut( 0.0,-0.2,2.0){$z$}
		\pstThreeDPut(-0.2, 2.0,0.2){$y$}
		\pstThreeDPut( 2.2,-0.2,0.2){$x$}
		\pstThreeDPut( 1.1, 0.7,0.0){$\varrho$}
		\pstThreeDPut( 1.0, 1.0,1.3){$r$}
		\pstThreeDPut( 2.2, 2.2,2.3){\rput[l]{U}{$P(\varrho,\varphi,z)$}}
		\pstThreeDPut( 0.5, 0.2,0.0){$\varphi$}
	\end{pspicture}
}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Title:			 Koordinatensysteme - Kugelkoordinaten
% Author:      Tobias Krähling
% Needs:       pstricks, pst-grad, pst-3d, pst-3dplot
% DesignScale: unit=15mm
% Size:			   3.9 x 4.0	
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
{\sbPSTDefault\sffamily
	\psset{unit=15mm}
	\begin{pspicture}(-1.0,-1.5)(2.9,2.5)
		\psset{Alpha=80}
		\pstThreeDSphere[linecolor=sbfilllight
                    ,linestyle=none
                    ,SegmentColor={sbfilllight!30!white}
                    ](0,0,0){2}
		\pstThreeDDot[drawCoor=true
                 ,linecolor=sblinemed
                 ,linewidth=1pt
                 ](2,2,2)
		\pstThreeDLine[linecolor=sblinemed
                  ,linestyle=dashed
                  ](0,0,2)(2,2,2)
		\pstThreeDLine[linecolor=sblinemed
                  ,linestyle=dashed
                  ](0,0,0)(2,2,0)
		\pstThreeDLine[linecolor=sblinehighlight
                  ,linestyle=solid
                  ,arrows=->
                  ,linewidth=1pt
                  ](0,0,0)(1.95,1.95,1.95)
		\pstThreeDEllipse[beginAngle=0,endAngle=44
                     ,arrows=->
                     ,linewidth=1pt
                     ,linecolor=sblinemed
                     ](0,0,0)(0.8,0,0)(0,0.8,0)
		\pstThreeDEllipse[beginAngle=0,endAngle=70
                     ,arrows=->
                     ,linewidth=1pt
                     ,linecolor=sblinemed
                     ](0,0,0)(0,0,0.5)(0.8,0.8,0.4)
		\pstThreeDCoor[xMin=0,xMax=2.5
                  ,yMin=0,yMax=2.5
                  ,zMin=0,zMax=2.5
                  ,linecolor=black
                  ,linewidth=1pt]
		\pstThreeDPut(1.0,1.0,1.3){$r$}
		\pstThreeDPut(2.2,2.2,2.3){\rput[l]{U}{$P_1(r,\vartheta,\varphi)$}}
		\pstThreeDPut(0.5,0.2,0.0){$\varphi$}
		\pstThreeDPut(0.5,0.25,0.55){$\vartheta$}
	\end{pspicture}
}