Intersection of a line with a plane, where is wrong in third way?












3















Let SABCD be a pyramid, SA perpendicular to the plane ABC, the base of pyramid is a rectangle,SA=h, AB=a, AD=b. A plane P passing A and perpendicular to the line SC cut the lines SB, SD, SC respectively at E, F, K.
I tried it in three ways.



First way 



documentclass[border=3.14mm,12pt,tikz]{standalone}

usepackage{tikz,tikz-3dplot} 

usepackage{tkz-euclide}

usetkzobj{all}

usetikzlibrary{intersections,calc,backgrounds}

begin{document}

    tdplotsetmaincoords{60}{120}

    begin{tikzpicture}[tdplot_main_coords,scale=1.5]

    pgfmathsetmacroa{3}

    pgfmathsetmacrob{4}

    pgfmathsetmacroh{5}



    % definitions

    path 

    coordinate(A) at (0,0,0)

    coordinate (B) at (a,0,0)

    coordinate (C) at (a,b,0) 

    coordinate (D) at (0,b,0)                            

    coordinate (S) at (0,0,h)

    coordinate (E) at ({a*h^2/(a^2+h^2)}, 0, {a^2*h/(a^2+h^2)})

    coordinate (F) at (0, {b*h^2/(b^2+h^2)}, {b^2*h/(b^2+h^2)})

    coordinate (K) at ({a*h^2/(a^2+b^2+h^2)}, {b*h^2/(a^2+b^2+h^2)}, {(a^2+b^2)*h/(a^2+b^2+h^2)});              



begin{scope}

draw [dashed, thick, name path=B--D] (B) -- (D);

draw [dashed, thick, name path=C--A] (C) -- (A);

path [name intersections={of=B--D and C--A,by=O}];

end{scope}



begin{scope}

draw [dashed, thick, name path=S--O] (S) -- (O);

draw [dashed, thick, name path=E--F] (E) -- (F);

path [name intersections={of=S--O and E--F,by=I}];

end{scope}



    begin{scope}

    draw[dashed, thick]

    (A) -- (B)   (D)--(A) (S)--(A);

    draw[dashed, thick]

    (E) --(A)  -- (F);

    draw[ultra thick]

    (S) -- (B) -- (C) -- (D)--cycle (S)--(C) (E) -- (K) --(F);

    draw [thick, dashed] (A) -- (K)  (E) -- (F) ;

    tkzMarkRightAngle(S,A,D)

    tkzMarkRightAngle(S,A,B)

    tkzMarkRightAngle(A,B,C)

    tkzMarkRightAngle(B,A,D)

    tkzMarkRightAngle(A,F,D)

    tkzMarkRightAngle(A,E,B)

    tkzMarkRightAngle(A,K,C)

    end{scope}



    foreach point/position in {A/left,B/below,C/below,S/above,D/right,E/left,D/right,F/right,K/above right,O/below,I/below}

    {

        fill (point) circle (1.5pt);

        node[position=3pt] at (point) {$point$};

    }

    end{tikzpicture}



end{document}


Second way



documentclass[border=3mm,12pt]{standalone}

usepackage{fouriernc}

usepackage{tikz,tikz-3dplot} 

usepackage{tkz-euclide}

usetkzobj{all}



newcounter{smuggle}

DeclareRobustCommandsmuggleone[1]{%

    stepcounter{smuggle}%

    expandafterglobalexpandafterletcsname smuggle@arabic{smuggle}endcsname#1%

    aftergroupletaftergroup#1expandafteraftergroupcsname smuggle@arabic{smuggle}endcsname

}

DeclareRobustCommandsmuggle[2][1]{%

    smuggleone{#2}%

    ifnum#1>1

    aftergroupsmuggleaftergroup[expandafteraftergroupthenumexpr#1-1aftergroup]aftergroup#2%

    fi

}



usetikzlibrary{intersections,calc,backgrounds}

tikzset{projection of point/.style args={(#1,#2,#3) on line through (#4,#5,#6)

        and (#7,#8,#9)}{%

        /utils/exec=pgfmathsetmacro{myprefactor}{((#1-#4)*(#7-#4)+(#2-#5)*(#8-#5)+(#3-#6)*(#9-#6))/((#7-#4)*(#7-#4)+(#8-#5)*(#8-#5)+(#9-#6)*(#9-#6))},

        insert path={%

            ({#4+myprefactor*(#7-#4)},{#5+myprefactor*(#8-#5)},{#6+myprefactor*(#9-#6)})}

}}



 begin{document}



    tdplotsetmaincoords{60}{120}

 begin{tikzpicture}[tdplot_main_coords,scale=1.5]

 pgfmathsetmacroa{3}

 pgfmathsetmacrob{4}

 pgfmathsetmacroh{5}



 % definitions

 path 

 coordinate(A) at (0,0,0)

 coordinate (B) at (a,0,0)

 coordinate (C) at (a,b,0) 

 coordinate (D) at (0,b,0)                            

 coordinate (S) at (0,0,h);   



 path[projection of point={(0,0,0) on line through (a,0,0) and  (0,0,h)}]

 coordinate (E)

 [projection of point={(0,0,0) on line through (0,0,h) and (0,b,0) }]

 coordinate (F)

 [projection of point={(0,0,0) on line through (0,0,h) and (a,b,0) }]

 coordinate (K);           



 begin{scope}

 draw [dashed, thick, name path=B--D] (B) -- (D);

 draw [dashed, thick, name path=C--A] (C) -- (A);

 path [name intersections={of=B--D and C--A,by=O}];

 end{scope}



 begin{scope}

 draw [dashed, thick, name path=S--O] (S) -- (O);

 draw [dashed, thick, name path=E--F] (E) -- (F);

 path [name intersections={of=S--O and E--F,by=I}];

 end{scope}





 begin{scope}

 draw[dashed, thick]

 (A) -- (B)   (D)--(A) (S)--(A);

 draw[dashed, thick]

 (E) --(A)  -- (F);

 draw[ultra thick]

 (S) -- (B) -- (C) -- (D)--cycle (S)--(C) (E) -- (K) --(F);

  draw [thick, dashed] (A) -- (K)  (E) -- (F) ;



 tkzMarkRightAngle(S,A,D)

 tkzMarkRightAngle(S,A,B)

 tkzMarkRightAngle(A,B,C)

 tkzMarkRightAngle(B,A,D)

 tkzMarkRightAngle(A,F,D)

 tkzMarkRightAngle(A,E,B)

 tkzMarkRightAngle(A,K,C)

 end{scope}



  foreach point/position in {A/left,B/below,C/below,S/above,D/right,E/left,D/right,F/right,K/above right,O/below,I/below}

 {

    fill (point) circle (1.5pt);

    node[position=3pt] at (point) {$point$};

 }



 end{tikzpicture}

 end{document}


enter image description here



Third way
Base on the answer Is there a command to find coordinates of projection of a point on a plane?



I defined command defVecMinus(#1,#2,#3)-(#4,#5,#6){(#1-#4,#2-#5,#3-#6)} and tried



documentclass[border=3.14mm,12pt,tikz]{standalone}

usepackage{tikz,tikz-3dplot} 

%% smuggling from https://tex.stackexchange.com/a/470979/121799

newcounter{smuggle}

DeclareRobustCommandsmuggleone[1]{%

    stepcounter{smuggle}%

    expandafterglobalexpandafterletcsname smuggle@arabic{smuggle}endcsname#1%

    aftergroupletaftergroup#1expandafteraftergroupcsname smuggle@arabic{smuggle}endcsname

}

DeclareRobustCommandsmuggle[2][1]{%

    smuggleone{#2}%

    ifnum#1>1

    aftergroupsmuggleaftergroup[expandafteraftergroupthenumexpr#1-1aftergroup]aftergroup#2%

    fi

}



defparsecoord(#1,#2,#3)>(#4,#5,#6){%

    def#4{#1}%

    def#5{#2}%

    def#6{#3}%

    smuggle{#4}%

    smuggle{#5}%

    smuggle{#6}%

}

defSPTD(#1,#2,#3).(#4,#5,#6){#1*#4+#2*#5+#3*#6}

defVPTD(#1,#2,#3)x(#4,#5,#6){(#2*#6-#3*#5,#3*#4-#1*#6,#1*#5-#2*#4)}

defVecMinus(#1,#2,#3)-(#4,#5,#6){(#1-#4,#2-#5,#3-#6)}

defVecAdd(#1,#2,#3)+(#4,#5,#6){(#1+#4,#2+#5,#3+#6)}

tikzset{intersection of line trough/.style args={#1 and #2 with plane

        containing #3 and normal #4}{%

        /utils/exec={pgfmathsetmacro{ltest}{abs(SPTD#2.#4-SPTD#1.#4)}

            parsecoord#1>(myAx,myAy,myAz)

            parsecoord#2>(myBx,myBy,myBz)

            ifdimltest pt<0.01pt

            typeout{Planespace andspace linespace arespace parallel!ltest}

            pgfmathsetmacro{myd}{0}

            else

            pgfmathsetmacro{myd}{(SPTD#3.#4-SPTD#1.#4)/(SPTD#2.#4-SPTD#1.#4)}

            fi

            %typeout{({myAx+myd*(myBx-myAx)},{myAy+myd*(myBy-myAy)},{myAz+myd*(myBz-myAz)})}

            defmyP{({myAx+myd*(myBx-myAx)},{myAy+myd*(myBy-myAy)},{myAz+myd*(myBz-myAz)})}

            smugglemyP},

        insert path={%

            myP}

}}



begin{document}

    tdplotsetmaincoords{75}{110}

    begin{tikzpicture}[tdplot_main_coords,scale=1.5]

    pgfmathsetmacroa{3}

    pgfmathsetmacrob{4}

    pgfmathsetmacroh{5}



    % definitions

    path 

    coordinate(A) at (0,0,0)

    coordinate (B) at (a,0,0)

    coordinate (C) at (a,b,0) 

    coordinate (D) at (0,b,0)                            

    coordinate (S) at (0,0,h);                

    defmynormal{VecMinus(a,b,0)-(0,0,h)}

    typeout{mynormal:(a,b,-h)}

    path[intersection of line trough={(0,0,h) and (a,0,0) with plane containing (0,0,0) and normal (a,b,-h)}]  coordinate (E)

    [intersection of line trough={(0,0,h) and  (0,b,0) with plane containing (0,0,0) and normal (a,b,-h)}]  coordinate (F)

    [intersection of line trough={(0,0,h) and  (a,b,0) with plane containing (0,0,0) and normal (a,b,-h)}]  coordinate (K);





    draw[dashed, thick]

    (A) -- (B)   (D)--(A) (S)--(A);

    draw[dashed, thick]

    (E) --(A)  -- (F);

    draw[ultra thick]

    (S) -- (B) -- (C) -- (D)--cycle (S)--(C);



    draw [thick, dashed] (A) -- (K) (A) -- (C) (B) -- (D) (E) -- (F) ;

    draw [thick] (E) -- (K) -- (F) ;



    foreach point/position in {A/left,B/below,C/below,S/above,D/right,E/left,D/right,F/right,K/above right}

    {

        fill (point) circle (1.5pt);

        node[position=3pt] at (point) {$point$};

    }



    end{tikzpicture}

        end{document}


I got
enter image description here






tikz-pgf tikz-3dplot







share|improve this question


















  • 2





    This was a really stupid error that I made. Sorry for this!

    – marmot
    Jan 28 at 6:01
















3















Let SABCD be a pyramid, SA perpendicular to the plane ABC, the base of pyramid is a rectangle,SA=h, AB=a, AD=b. A plane P passing A and perpendicular to the line SC cut the lines SB, SD, SC respectively at E, F, K.
I tried it in three ways.



First way 



documentclass[border=3.14mm,12pt,tikz]{standalone}

usepackage{tikz,tikz-3dplot} 

usepackage{tkz-euclide}

usetkzobj{all}

usetikzlibrary{intersections,calc,backgrounds}

begin{document}

    tdplotsetmaincoords{60}{120}

    begin{tikzpicture}[tdplot_main_coords,scale=1.5]

    pgfmathsetmacroa{3}

    pgfmathsetmacrob{4}

    pgfmathsetmacroh{5}



    % definitions

    path 

    coordinate(A) at (0,0,0)

    coordinate (B) at (a,0,0)

    coordinate (C) at (a,b,0) 

    coordinate (D) at (0,b,0)                            

    coordinate (S) at (0,0,h)

    coordinate (E) at ({a*h^2/(a^2+h^2)}, 0, {a^2*h/(a^2+h^2)})

    coordinate (F) at (0, {b*h^2/(b^2+h^2)}, {b^2*h/(b^2+h^2)})

    coordinate (K) at ({a*h^2/(a^2+b^2+h^2)}, {b*h^2/(a^2+b^2+h^2)}, {(a^2+b^2)*h/(a^2+b^2+h^2)});              



begin{scope}

draw [dashed, thick, name path=B--D] (B) -- (D);

draw [dashed, thick, name path=C--A] (C) -- (A);

path [name intersections={of=B--D and C--A,by=O}];

end{scope}



begin{scope}

draw [dashed, thick, name path=S--O] (S) -- (O);

draw [dashed, thick, name path=E--F] (E) -- (F);

path [name intersections={of=S--O and E--F,by=I}];

end{scope}



    begin{scope}

    draw[dashed, thick]

    (A) -- (B)   (D)--(A) (S)--(A);

    draw[dashed, thick]

    (E) --(A)  -- (F);

    draw[ultra thick]

    (S) -- (B) -- (C) -- (D)--cycle (S)--(C) (E) -- (K) --(F);

    draw [thick, dashed] (A) -- (K)  (E) -- (F) ;

    tkzMarkRightAngle(S,A,D)

    tkzMarkRightAngle(S,A,B)

    tkzMarkRightAngle(A,B,C)

    tkzMarkRightAngle(B,A,D)

    tkzMarkRightAngle(A,F,D)

    tkzMarkRightAngle(A,E,B)

    tkzMarkRightAngle(A,K,C)

    end{scope}



    foreach point/position in {A/left,B/below,C/below,S/above,D/right,E/left,D/right,F/right,K/above right,O/below,I/below}

    {

        fill (point) circle (1.5pt);

        node[position=3pt] at (point) {$point$};

    }

    end{tikzpicture}



end{document}


Second way



documentclass[border=3mm,12pt]{standalone}

usepackage{fouriernc}

usepackage{tikz,tikz-3dplot} 

usepackage{tkz-euclide}

usetkzobj{all}



newcounter{smuggle}

DeclareRobustCommandsmuggleone[1]{%

    stepcounter{smuggle}%

    expandafterglobalexpandafterletcsname smuggle@arabic{smuggle}endcsname#1%

    aftergroupletaftergroup#1expandafteraftergroupcsname smuggle@arabic{smuggle}endcsname

}

DeclareRobustCommandsmuggle[2][1]{%

    smuggleone{#2}%

    ifnum#1>1

    aftergroupsmuggleaftergroup[expandafteraftergroupthenumexpr#1-1aftergroup]aftergroup#2%

    fi

}



usetikzlibrary{intersections,calc,backgrounds}

tikzset{projection of point/.style args={(#1,#2,#3) on line through (#4,#5,#6)

        and (#7,#8,#9)}{%

        /utils/exec=pgfmathsetmacro{myprefactor}{((#1-#4)*(#7-#4)+(#2-#5)*(#8-#5)+(#3-#6)*(#9-#6))/((#7-#4)*(#7-#4)+(#8-#5)*(#8-#5)+(#9-#6)*(#9-#6))},

        insert path={%

            ({#4+myprefactor*(#7-#4)},{#5+myprefactor*(#8-#5)},{#6+myprefactor*(#9-#6)})}

}}



 begin{document}



    tdplotsetmaincoords{60}{120}

 begin{tikzpicture}[tdplot_main_coords,scale=1.5]

 pgfmathsetmacroa{3}

 pgfmathsetmacrob{4}

 pgfmathsetmacroh{5}



 % definitions

 path 

 coordinate(A) at (0,0,0)

 coordinate (B) at (a,0,0)

 coordinate (C) at (a,b,0) 

 coordinate (D) at (0,b,0)                            

 coordinate (S) at (0,0,h);   



 path[projection of point={(0,0,0) on line through (a,0,0) and  (0,0,h)}]

 coordinate (E)

 [projection of point={(0,0,0) on line through (0,0,h) and (0,b,0) }]

 coordinate (F)

 [projection of point={(0,0,0) on line through (0,0,h) and (a,b,0) }]

 coordinate (K);           



 begin{scope}

 draw [dashed, thick, name path=B--D] (B) -- (D);

 draw [dashed, thick, name path=C--A] (C) -- (A);

 path [name intersections={of=B--D and C--A,by=O}];

 end{scope}



 begin{scope}

 draw [dashed, thick, name path=S--O] (S) -- (O);

 draw [dashed, thick, name path=E--F] (E) -- (F);

 path [name intersections={of=S--O and E--F,by=I}];

 end{scope}





 begin{scope}

 draw[dashed, thick]

 (A) -- (B)   (D)--(A) (S)--(A);

 draw[dashed, thick]

 (E) --(A)  -- (F);

 draw[ultra thick]

 (S) -- (B) -- (C) -- (D)--cycle (S)--(C) (E) -- (K) --(F);

  draw [thick, dashed] (A) -- (K)  (E) -- (F) ;



 tkzMarkRightAngle(S,A,D)

 tkzMarkRightAngle(S,A,B)

 tkzMarkRightAngle(A,B,C)

 tkzMarkRightAngle(B,A,D)

 tkzMarkRightAngle(A,F,D)

 tkzMarkRightAngle(A,E,B)

 tkzMarkRightAngle(A,K,C)

 end{scope}



  foreach point/position in {A/left,B/below,C/below,S/above,D/right,E/left,D/right,F/right,K/above right,O/below,I/below}

 {

    fill (point) circle (1.5pt);

    node[position=3pt] at (point) {$point$};

 }



 end{tikzpicture}

 end{document}


enter image description here



Third way
Base on the answer Is there a command to find coordinates of projection of a point on a plane?



I defined command defVecMinus(#1,#2,#3)-(#4,#5,#6){(#1-#4,#2-#5,#3-#6)} and tried



documentclass[border=3.14mm,12pt,tikz]{standalone}

usepackage{tikz,tikz-3dplot} 

%% smuggling from https://tex.stackexchange.com/a/470979/121799

newcounter{smuggle}

DeclareRobustCommandsmuggleone[1]{%

    stepcounter{smuggle}%

    expandafterglobalexpandafterletcsname smuggle@arabic{smuggle}endcsname#1%

    aftergroupletaftergroup#1expandafteraftergroupcsname smuggle@arabic{smuggle}endcsname

}

DeclareRobustCommandsmuggle[2][1]{%

    smuggleone{#2}%

    ifnum#1>1

    aftergroupsmuggleaftergroup[expandafteraftergroupthenumexpr#1-1aftergroup]aftergroup#2%

    fi

}



defparsecoord(#1,#2,#3)>(#4,#5,#6){%

    def#4{#1}%

    def#5{#2}%

    def#6{#3}%

    smuggle{#4}%

    smuggle{#5}%

    smuggle{#6}%

}

defSPTD(#1,#2,#3).(#4,#5,#6){#1*#4+#2*#5+#3*#6}

defVPTD(#1,#2,#3)x(#4,#5,#6){(#2*#6-#3*#5,#3*#4-#1*#6,#1*#5-#2*#4)}

defVecMinus(#1,#2,#3)-(#4,#5,#6){(#1-#4,#2-#5,#3-#6)}

defVecAdd(#1,#2,#3)+(#4,#5,#6){(#1+#4,#2+#5,#3+#6)}

tikzset{intersection of line trough/.style args={#1 and #2 with plane

        containing #3 and normal #4}{%

        /utils/exec={pgfmathsetmacro{ltest}{abs(SPTD#2.#4-SPTD#1.#4)}

            parsecoord#1>(myAx,myAy,myAz)

            parsecoord#2>(myBx,myBy,myBz)

            ifdimltest pt<0.01pt

            typeout{Planespace andspace linespace arespace parallel!ltest}

            pgfmathsetmacro{myd}{0}

            else

            pgfmathsetmacro{myd}{(SPTD#3.#4-SPTD#1.#4)/(SPTD#2.#4-SPTD#1.#4)}

            fi

            %typeout{({myAx+myd*(myBx-myAx)},{myAy+myd*(myBy-myAy)},{myAz+myd*(myBz-myAz)})}

            defmyP{({myAx+myd*(myBx-myAx)},{myAy+myd*(myBy-myAy)},{myAz+myd*(myBz-myAz)})}

            smugglemyP},

        insert path={%

            myP}

}}



begin{document}

    tdplotsetmaincoords{75}{110}

    begin{tikzpicture}[tdplot_main_coords,scale=1.5]

    pgfmathsetmacroa{3}

    pgfmathsetmacrob{4}

    pgfmathsetmacroh{5}



    % definitions

    path 

    coordinate(A) at (0,0,0)

    coordinate (B) at (a,0,0)

    coordinate (C) at (a,b,0) 

    coordinate (D) at (0,b,0)                            

    coordinate (S) at (0,0,h);                

    defmynormal{VecMinus(a,b,0)-(0,0,h)}

    typeout{mynormal:(a,b,-h)}

    path[intersection of line trough={(0,0,h) and (a,0,0) with plane containing (0,0,0) and normal (a,b,-h)}]  coordinate (E)

    [intersection of line trough={(0,0,h) and  (0,b,0) with plane containing (0,0,0) and normal (a,b,-h)}]  coordinate (F)

    [intersection of line trough={(0,0,h) and  (a,b,0) with plane containing (0,0,0) and normal (a,b,-h)}]  coordinate (K);





    draw[dashed, thick]

    (A) -- (B)   (D)--(A) (S)--(A);

    draw[dashed, thick]

    (E) --(A)  -- (F);

    draw[ultra thick]

    (S) -- (B) -- (C) -- (D)--cycle (S)--(C);



    draw [thick, dashed] (A) -- (K) (A) -- (C) (B) -- (D) (E) -- (F) ;

    draw [thick] (E) -- (K) -- (F) ;



    foreach point/position in {A/left,B/below,C/below,S/above,D/right,E/left,D/right,F/right,K/above right}

    {

        fill (point) circle (1.5pt);

        node[position=3pt] at (point) {$point$};

    }



    end{tikzpicture}

        end{document}


I got
enter image description here






tikz-pgf tikz-3dplot







share|improve this question


















  • 2





    This was a really stupid error that I made. Sorry for this!

    – marmot
    Jan 28 at 6:01














3












3








3








Let SABCD be a pyramid, SA perpendicular to the plane ABC, the base of pyramid is a rectangle,SA=h, AB=a, AD=b. A plane P passing A and perpendicular to the line SC cut the lines SB, SD, SC respectively at E, F, K.
I tried it in three ways.



First way 



documentclass[border=3.14mm,12pt,tikz]{standalone}

usepackage{tikz,tikz-3dplot} 

usepackage{tkz-euclide}

usetkzobj{all}

usetikzlibrary{intersections,calc,backgrounds}

begin{document}

    tdplotsetmaincoords{60}{120}

    begin{tikzpicture}[tdplot_main_coords,scale=1.5]

    pgfmathsetmacroa{3}

    pgfmathsetmacrob{4}

    pgfmathsetmacroh{5}



    % definitions

    path 

    coordinate(A) at (0,0,0)

    coordinate (B) at (a,0,0)

    coordinate (C) at (a,b,0) 

    coordinate (D) at (0,b,0)                            

    coordinate (S) at (0,0,h)

    coordinate (E) at ({a*h^2/(a^2+h^2)}, 0, {a^2*h/(a^2+h^2)})

    coordinate (F) at (0, {b*h^2/(b^2+h^2)}, {b^2*h/(b^2+h^2)})

    coordinate (K) at ({a*h^2/(a^2+b^2+h^2)}, {b*h^2/(a^2+b^2+h^2)}, {(a^2+b^2)*h/(a^2+b^2+h^2)});              



begin{scope}

draw [dashed, thick, name path=B--D] (B) -- (D);

draw [dashed, thick, name path=C--A] (C) -- (A);

path [name intersections={of=B--D and C--A,by=O}];

end{scope}



begin{scope}

draw [dashed, thick, name path=S--O] (S) -- (O);

draw [dashed, thick, name path=E--F] (E) -- (F);

path [name intersections={of=S--O and E--F,by=I}];

end{scope}



    begin{scope}

    draw[dashed, thick]

    (A) -- (B)   (D)--(A) (S)--(A);

    draw[dashed, thick]

    (E) --(A)  -- (F);

    draw[ultra thick]

    (S) -- (B) -- (C) -- (D)--cycle (S)--(C) (E) -- (K) --(F);

    draw [thick, dashed] (A) -- (K)  (E) -- (F) ;

    tkzMarkRightAngle(S,A,D)

    tkzMarkRightAngle(S,A,B)

    tkzMarkRightAngle(A,B,C)

    tkzMarkRightAngle(B,A,D)

    tkzMarkRightAngle(A,F,D)

    tkzMarkRightAngle(A,E,B)

    tkzMarkRightAngle(A,K,C)

    end{scope}



    foreach point/position in {A/left,B/below,C/below,S/above,D/right,E/left,D/right,F/right,K/above right,O/below,I/below}

    {

        fill (point) circle (1.5pt);

        node[position=3pt] at (point) {$point$};

    }

    end{tikzpicture}



end{document}


Second way



documentclass[border=3mm,12pt]{standalone}

usepackage{fouriernc}

usepackage{tikz,tikz-3dplot} 

usepackage{tkz-euclide}

usetkzobj{all}



newcounter{smuggle}

DeclareRobustCommandsmuggleone[1]{%

    stepcounter{smuggle}%

    expandafterglobalexpandafterletcsname smuggle@arabic{smuggle}endcsname#1%

    aftergroupletaftergroup#1expandafteraftergroupcsname smuggle@arabic{smuggle}endcsname

}

DeclareRobustCommandsmuggle[2][1]{%

    smuggleone{#2}%

    ifnum#1>1

    aftergroupsmuggleaftergroup[expandafteraftergroupthenumexpr#1-1aftergroup]aftergroup#2%

    fi

}



usetikzlibrary{intersections,calc,backgrounds}

tikzset{projection of point/.style args={(#1,#2,#3) on line through (#4,#5,#6)

        and (#7,#8,#9)}{%

        /utils/exec=pgfmathsetmacro{myprefactor}{((#1-#4)*(#7-#4)+(#2-#5)*(#8-#5)+(#3-#6)*(#9-#6))/((#7-#4)*(#7-#4)+(#8-#5)*(#8-#5)+(#9-#6)*(#9-#6))},

        insert path={%

            ({#4+myprefactor*(#7-#4)},{#5+myprefactor*(#8-#5)},{#6+myprefactor*(#9-#6)})}

}}



 begin{document}



    tdplotsetmaincoords{60}{120}

 begin{tikzpicture}[tdplot_main_coords,scale=1.5]

 pgfmathsetmacroa{3}

 pgfmathsetmacrob{4}

 pgfmathsetmacroh{5}



 % definitions

 path 

 coordinate(A) at (0,0,0)

 coordinate (B) at (a,0,0)

 coordinate (C) at (a,b,0) 

 coordinate (D) at (0,b,0)                            

 coordinate (S) at (0,0,h);   



 path[projection of point={(0,0,0) on line through (a,0,0) and  (0,0,h)}]

 coordinate (E)

 [projection of point={(0,0,0) on line through (0,0,h) and (0,b,0) }]

 coordinate (F)

 [projection of point={(0,0,0) on line through (0,0,h) and (a,b,0) }]

 coordinate (K);           



 begin{scope}

 draw [dashed, thick, name path=B--D] (B) -- (D);

 draw [dashed, thick, name path=C--A] (C) -- (A);

 path [name intersections={of=B--D and C--A,by=O}];

 end{scope}



 begin{scope}

 draw [dashed, thick, name path=S--O] (S) -- (O);

 draw [dashed, thick, name path=E--F] (E) -- (F);

 path [name intersections={of=S--O and E--F,by=I}];

 end{scope}





 begin{scope}

 draw[dashed, thick]

 (A) -- (B)   (D)--(A) (S)--(A);

 draw[dashed, thick]

 (E) --(A)  -- (F);

 draw[ultra thick]

 (S) -- (B) -- (C) -- (D)--cycle (S)--(C) (E) -- (K) --(F);

  draw [thick, dashed] (A) -- (K)  (E) -- (F) ;



 tkzMarkRightAngle(S,A,D)

 tkzMarkRightAngle(S,A,B)

 tkzMarkRightAngle(A,B,C)

 tkzMarkRightAngle(B,A,D)

 tkzMarkRightAngle(A,F,D)

 tkzMarkRightAngle(A,E,B)

 tkzMarkRightAngle(A,K,C)

 end{scope}



  foreach point/position in {A/left,B/below,C/below,S/above,D/right,E/left,D/right,F/right,K/above right,O/below,I/below}

 {

    fill (point) circle (1.5pt);

    node[position=3pt] at (point) {$point$};

 }



 end{tikzpicture}

 end{document}


enter image description here



Third way
Base on the answer Is there a command to find coordinates of projection of a point on a plane?



I defined command defVecMinus(#1,#2,#3)-(#4,#5,#6){(#1-#4,#2-#5,#3-#6)} and tried



documentclass[border=3.14mm,12pt,tikz]{standalone}

usepackage{tikz,tikz-3dplot} 

%% smuggling from https://tex.stackexchange.com/a/470979/121799

newcounter{smuggle}

DeclareRobustCommandsmuggleone[1]{%

    stepcounter{smuggle}%

    expandafterglobalexpandafterletcsname smuggle@arabic{smuggle}endcsname#1%

    aftergroupletaftergroup#1expandafteraftergroupcsname smuggle@arabic{smuggle}endcsname

}

DeclareRobustCommandsmuggle[2][1]{%

    smuggleone{#2}%

    ifnum#1>1

    aftergroupsmuggleaftergroup[expandafteraftergroupthenumexpr#1-1aftergroup]aftergroup#2%

    fi

}



defparsecoord(#1,#2,#3)>(#4,#5,#6){%

    def#4{#1}%

    def#5{#2}%

    def#6{#3}%

    smuggle{#4}%

    smuggle{#5}%

    smuggle{#6}%

}

defSPTD(#1,#2,#3).(#4,#5,#6){#1*#4+#2*#5+#3*#6}

defVPTD(#1,#2,#3)x(#4,#5,#6){(#2*#6-#3*#5,#3*#4-#1*#6,#1*#5-#2*#4)}

defVecMinus(#1,#2,#3)-(#4,#5,#6){(#1-#4,#2-#5,#3-#6)}

defVecAdd(#1,#2,#3)+(#4,#5,#6){(#1+#4,#2+#5,#3+#6)}

tikzset{intersection of line trough/.style args={#1 and #2 with plane

        containing #3 and normal #4}{%

        /utils/exec={pgfmathsetmacro{ltest}{abs(SPTD#2.#4-SPTD#1.#4)}

            parsecoord#1>(myAx,myAy,myAz)

            parsecoord#2>(myBx,myBy,myBz)

            ifdimltest pt<0.01pt

            typeout{Planespace andspace linespace arespace parallel!ltest}

            pgfmathsetmacro{myd}{0}

            else

            pgfmathsetmacro{myd}{(SPTD#3.#4-SPTD#1.#4)/(SPTD#2.#4-SPTD#1.#4)}

            fi

            %typeout{({myAx+myd*(myBx-myAx)},{myAy+myd*(myBy-myAy)},{myAz+myd*(myBz-myAz)})}

            defmyP{({myAx+myd*(myBx-myAx)},{myAy+myd*(myBy-myAy)},{myAz+myd*(myBz-myAz)})}

            smugglemyP},

        insert path={%

            myP}

}}



begin{document}

    tdplotsetmaincoords{75}{110}

    begin{tikzpicture}[tdplot_main_coords,scale=1.5]

    pgfmathsetmacroa{3}

    pgfmathsetmacrob{4}

    pgfmathsetmacroh{5}



    % definitions

    path 

    coordinate(A) at (0,0,0)

    coordinate (B) at (a,0,0)

    coordinate (C) at (a,b,0) 

    coordinate (D) at (0,b,0)                            

    coordinate (S) at (0,0,h);                

    defmynormal{VecMinus(a,b,0)-(0,0,h)}

    typeout{mynormal:(a,b,-h)}

    path[intersection of line trough={(0,0,h) and (a,0,0) with plane containing (0,0,0) and normal (a,b,-h)}]  coordinate (E)

    [intersection of line trough={(0,0,h) and  (0,b,0) with plane containing (0,0,0) and normal (a,b,-h)}]  coordinate (F)

    [intersection of line trough={(0,0,h) and  (a,b,0) with plane containing (0,0,0) and normal (a,b,-h)}]  coordinate (K);





    draw[dashed, thick]

    (A) -- (B)   (D)--(A) (S)--(A);

    draw[dashed, thick]

    (E) --(A)  -- (F);

    draw[ultra thick]

    (S) -- (B) -- (C) -- (D)--cycle (S)--(C);



    draw [thick, dashed] (A) -- (K) (A) -- (C) (B) -- (D) (E) -- (F) ;

    draw [thick] (E) -- (K) -- (F) ;



    foreach point/position in {A/left,B/below,C/below,S/above,D/right,E/left,D/right,F/right,K/above right}

    {

        fill (point) circle (1.5pt);

        node[position=3pt] at (point) {$point$};

    }



    end{tikzpicture}

        end{document}


I got
enter image description here






tikz-pgf tikz-3dplot







share|improve this question














Let SABCD be a pyramid, SA perpendicular to the plane ABC, the base of pyramid is a rectangle,SA=h, AB=a, AD=b. A plane P passing A and perpendicular to the line SC cut the lines SB, SD, SC respectively at E, F, K.
I tried it in three ways.



First way 



documentclass[border=3.14mm,12pt,tikz]{standalone}

usepackage{tikz,tikz-3dplot} 

usepackage{tkz-euclide}

usetkzobj{all}

usetikzlibrary{intersections,calc,backgrounds}

begin{document}

    tdplotsetmaincoords{60}{120}

    begin{tikzpicture}[tdplot_main_coords,scale=1.5]

    pgfmathsetmacroa{3}

    pgfmathsetmacrob{4}

    pgfmathsetmacroh{5}



    % definitions

    path 

    coordinate(A) at (0,0,0)

    coordinate (B) at (a,0,0)

    coordinate (C) at (a,b,0) 

    coordinate (D) at (0,b,0)                            

    coordinate (S) at (0,0,h)

    coordinate (E) at ({a*h^2/(a^2+h^2)}, 0, {a^2*h/(a^2+h^2)})

    coordinate (F) at (0, {b*h^2/(b^2+h^2)}, {b^2*h/(b^2+h^2)})

    coordinate (K) at ({a*h^2/(a^2+b^2+h^2)}, {b*h^2/(a^2+b^2+h^2)}, {(a^2+b^2)*h/(a^2+b^2+h^2)});              



begin{scope}

draw [dashed, thick, name path=B--D] (B) -- (D);

draw [dashed, thick, name path=C--A] (C) -- (A);

path [name intersections={of=B--D and C--A,by=O}];

end{scope}



begin{scope}

draw [dashed, thick, name path=S--O] (S) -- (O);

draw [dashed, thick, name path=E--F] (E) -- (F);

path [name intersections={of=S--O and E--F,by=I}];

end{scope}



    begin{scope}

    draw[dashed, thick]

    (A) -- (B)   (D)--(A) (S)--(A);

    draw[dashed, thick]

    (E) --(A)  -- (F);

    draw[ultra thick]

    (S) -- (B) -- (C) -- (D)--cycle (S)--(C) (E) -- (K) --(F);

    draw [thick, dashed] (A) -- (K)  (E) -- (F) ;

    tkzMarkRightAngle(S,A,D)

    tkzMarkRightAngle(S,A,B)

    tkzMarkRightAngle(A,B,C)

    tkzMarkRightAngle(B,A,D)

    tkzMarkRightAngle(A,F,D)

    tkzMarkRightAngle(A,E,B)

    tkzMarkRightAngle(A,K,C)

    end{scope}



    foreach point/position in {A/left,B/below,C/below,S/above,D/right,E/left,D/right,F/right,K/above right,O/below,I/below}

    {

        fill (point) circle (1.5pt);

        node[position=3pt] at (point) {$point$};

    }

    end{tikzpicture}



end{document}


Second way



documentclass[border=3mm,12pt]{standalone}

usepackage{fouriernc}

usepackage{tikz,tikz-3dplot} 

usepackage{tkz-euclide}

usetkzobj{all}



newcounter{smuggle}

DeclareRobustCommandsmuggleone[1]{%

    stepcounter{smuggle}%

    expandafterglobalexpandafterletcsname smuggle@arabic{smuggle}endcsname#1%

    aftergroupletaftergroup#1expandafteraftergroupcsname smuggle@arabic{smuggle}endcsname

}

DeclareRobustCommandsmuggle[2][1]{%

    smuggleone{#2}%

    ifnum#1>1

    aftergroupsmuggleaftergroup[expandafteraftergroupthenumexpr#1-1aftergroup]aftergroup#2%

    fi

}



usetikzlibrary{intersections,calc,backgrounds}

tikzset{projection of point/.style args={(#1,#2,#3) on line through (#4,#5,#6)

        and (#7,#8,#9)}{%

        /utils/exec=pgfmathsetmacro{myprefactor}{((#1-#4)*(#7-#4)+(#2-#5)*(#8-#5)+(#3-#6)*(#9-#6))/((#7-#4)*(#7-#4)+(#8-#5)*(#8-#5)+(#9-#6)*(#9-#6))},

        insert path={%

            ({#4+myprefactor*(#7-#4)},{#5+myprefactor*(#8-#5)},{#6+myprefactor*(#9-#6)})}

}}



 begin{document}



    tdplotsetmaincoords{60}{120}

 begin{tikzpicture}[tdplot_main_coords,scale=1.5]

 pgfmathsetmacroa{3}

 pgfmathsetmacrob{4}

 pgfmathsetmacroh{5}



 % definitions

 path 

 coordinate(A) at (0,0,0)

 coordinate (B) at (a,0,0)

 coordinate (C) at (a,b,0) 

 coordinate (D) at (0,b,0)                            

 coordinate (S) at (0,0,h);   



 path[projection of point={(0,0,0) on line through (a,0,0) and  (0,0,h)}]

 coordinate (E)

 [projection of point={(0,0,0) on line through (0,0,h) and (0,b,0) }]

 coordinate (F)

 [projection of point={(0,0,0) on line through (0,0,h) and (a,b,0) }]

 coordinate (K);           



 begin{scope}

 draw [dashed, thick, name path=B--D] (B) -- (D);

 draw [dashed, thick, name path=C--A] (C) -- (A);

 path [name intersections={of=B--D and C--A,by=O}];

 end{scope}



 begin{scope}

 draw [dashed, thick, name path=S--O] (S) -- (O);

 draw [dashed, thick, name path=E--F] (E) -- (F);

 path [name intersections={of=S--O and E--F,by=I}];

 end{scope}





 begin{scope}

 draw[dashed, thick]

 (A) -- (B)   (D)--(A) (S)--(A);

 draw[dashed, thick]

 (E) --(A)  -- (F);

 draw[ultra thick]

 (S) -- (B) -- (C) -- (D)--cycle (S)--(C) (E) -- (K) --(F);

  draw [thick, dashed] (A) -- (K)  (E) -- (F) ;



 tkzMarkRightAngle(S,A,D)

 tkzMarkRightAngle(S,A,B)

 tkzMarkRightAngle(A,B,C)

 tkzMarkRightAngle(B,A,D)

 tkzMarkRightAngle(A,F,D)

 tkzMarkRightAngle(A,E,B)

 tkzMarkRightAngle(A,K,C)

 end{scope}



  foreach point/position in {A/left,B/below,C/below,S/above,D/right,E/left,D/right,F/right,K/above right,O/below,I/below}

 {

    fill (point) circle (1.5pt);

    node[position=3pt] at (point) {$point$};

 }



 end{tikzpicture}

 end{document}


enter image description here



Third way
Base on the answer Is there a command to find coordinates of projection of a point on a plane?



I defined command defVecMinus(#1,#2,#3)-(#4,#5,#6){(#1-#4,#2-#5,#3-#6)} and tried



documentclass[border=3.14mm,12pt,tikz]{standalone}

usepackage{tikz,tikz-3dplot} 

%% smuggling from https://tex.stackexchange.com/a/470979/121799

newcounter{smuggle}

DeclareRobustCommandsmuggleone[1]{%

    stepcounter{smuggle}%

    expandafterglobalexpandafterletcsname smuggle@arabic{smuggle}endcsname#1%

    aftergroupletaftergroup#1expandafteraftergroupcsname smuggle@arabic{smuggle}endcsname

}

DeclareRobustCommandsmuggle[2][1]{%

    smuggleone{#2}%

    ifnum#1>1

    aftergroupsmuggleaftergroup[expandafteraftergroupthenumexpr#1-1aftergroup]aftergroup#2%

    fi

}



defparsecoord(#1,#2,#3)>(#4,#5,#6){%

    def#4{#1}%

    def#5{#2}%

    def#6{#3}%

    smuggle{#4}%

    smuggle{#5}%

    smuggle{#6}%

}

defSPTD(#1,#2,#3).(#4,#5,#6){#1*#4+#2*#5+#3*#6}

defVPTD(#1,#2,#3)x(#4,#5,#6){(#2*#6-#3*#5,#3*#4-#1*#6,#1*#5-#2*#4)}

defVecMinus(#1,#2,#3)-(#4,#5,#6){(#1-#4,#2-#5,#3-#6)}

defVecAdd(#1,#2,#3)+(#4,#5,#6){(#1+#4,#2+#5,#3+#6)}

tikzset{intersection of line trough/.style args={#1 and #2 with plane

        containing #3 and normal #4}{%

        /utils/exec={pgfmathsetmacro{ltest}{abs(SPTD#2.#4-SPTD#1.#4)}

            parsecoord#1>(myAx,myAy,myAz)

            parsecoord#2>(myBx,myBy,myBz)

            ifdimltest pt<0.01pt

            typeout{Planespace andspace linespace arespace parallel!ltest}

            pgfmathsetmacro{myd}{0}

            else

            pgfmathsetmacro{myd}{(SPTD#3.#4-SPTD#1.#4)/(SPTD#2.#4-SPTD#1.#4)}

            fi

            %typeout{({myAx+myd*(myBx-myAx)},{myAy+myd*(myBy-myAy)},{myAz+myd*(myBz-myAz)})}

            defmyP{({myAx+myd*(myBx-myAx)},{myAy+myd*(myBy-myAy)},{myAz+myd*(myBz-myAz)})}

            smugglemyP},

        insert path={%

            myP}

}}



begin{document}

    tdplotsetmaincoords{75}{110}

    begin{tikzpicture}[tdplot_main_coords,scale=1.5]

    pgfmathsetmacroa{3}

    pgfmathsetmacrob{4}

    pgfmathsetmacroh{5}



    % definitions

    path 

    coordinate(A) at (0,0,0)

    coordinate (B) at (a,0,0)

    coordinate (C) at (a,b,0) 

    coordinate (D) at (0,b,0)                            

    coordinate (S) at (0,0,h);                

    defmynormal{VecMinus(a,b,0)-(0,0,h)}

    typeout{mynormal:(a,b,-h)}

    path[intersection of line trough={(0,0,h) and (a,0,0) with plane containing (0,0,0) and normal (a,b,-h)}]  coordinate (E)

    [intersection of line trough={(0,0,h) and  (0,b,0) with plane containing (0,0,0) and normal (a,b,-h)}]  coordinate (F)

    [intersection of line trough={(0,0,h) and  (a,b,0) with plane containing (0,0,0) and normal (a,b,-h)}]  coordinate (K);





    draw[dashed, thick]

    (A) -- (B)   (D)--(A) (S)--(A);

    draw[dashed, thick]

    (E) --(A)  -- (F);

    draw[ultra thick]

    (S) -- (B) -- (C) -- (D)--cycle (S)--(C);



    draw [thick, dashed] (A) -- (K) (A) -- (C) (B) -- (D) (E) -- (F) ;

    draw [thick] (E) -- (K) -- (F) ;



    foreach point/position in {A/left,B/below,C/below,S/above,D/right,E/left,D/right,F/right,K/above right}

    {

        fill (point) circle (1.5pt);

        node[position=3pt] at (point) {$point$};

    }



    end{tikzpicture}

        end{document}


I got
enter image description here






tikz-pgf tikz-3dplot




tikz-pgf tikz-3dplot






share|improve this question













share|improve this question











share|improve this question




share|improve this question










asked Jan 28 at 3:52









minhthien_2016minhthien_2016

1,226916




1,226916








  • 2





    This was a really stupid error that I made. Sorry for this!

    – marmot
    Jan 28 at 6:01














  • 2





    This was a really stupid error that I made. Sorry for this!

    – marmot
    Jan 28 at 6:01








2




2





This was a really stupid error that I made. Sorry for this!

– marmot
Jan 28 at 6:01





This was a really stupid error that I made. Sorry for this!

– marmot
Jan 28 at 6:01










1 Answer
1






active

oldest

votes


















2














I am sorry, my original code has a flaw. I simply forgot to put brackets around the scalar products like SPTD#3.#4 and so on. And when testing this in the update to the previous answer, this did not matter. Once one adds these brackets, one gets



documentclass[border=3.14mm,12pt,tikz]{standalone}

usepackage{tikz,tikz-3dplot} 

%% smuggling from https://tex.stackexchange.com/a/470979/121799

newcounter{smuggle}

DeclareRobustCommandsmuggleone[1]{%

    stepcounter{smuggle}%

    expandafterglobalexpandafterletcsname smuggle@arabic{smuggle}endcsname#1%

    aftergroupletaftergroup#1expandafteraftergroupcsname smuggle@arabic{smuggle}endcsname

}

DeclareRobustCommandsmuggle[2][1]{%

    smuggleone{#2}%

    ifnum#1>1

    aftergroupsmuggleaftergroup[expandafteraftergroupthenumexpr#1-1aftergroup]aftergroup#2%

    fi

}



defparsecoord(#1,#2,#3)>(#4,#5,#6){%

    def#4{#1}%

    def#5{#2}%

    def#6{#3}%

    smuggle{#4}%

    smuggle{#5}%

    smuggle{#6}%

}

defSPTD(#1,#2,#3).(#4,#5,#6){((#1)*(#4)+1*(#2)*(#5)+1*(#3)*(#6))}

defVPTD(#1,#2,#3)x(#4,#5,#6){((#2)*(#6)-1*(#3)*(#5),(#3)*(#4)-1*(#1)*(#6),(#1)*(#5)-1*(#2)*(#4))}

defVecMinus(#1,#2,#3)-(#4,#5,#6){(#1-1*(#4),#2-1*(#5),#3-1*(#6))}

defVecAdd(#1,#2,#3)+(#4,#5,#6){(#1+1*(#4),#2+1*(#5),#3+1*(#6))}

% the line is given by vec x = vec ell_0 + t vec ell

% the points in the plane fulfill (vec P_0 - vec x)cdotvec n =0

% inserting the line equation in the plane equation gives

% (vec Q - vec ell_0 - d vec ell)cdot vec n = 0

% solving for d yields 

% d = (vec Q cdot vec n - vec ell_0cdotvec n)/(vecellcdot vec n)  

%

% in the macro vec ell_0 = #1 , vec ell = #2 - #1

% #3 : vec Q and #4 : vec n

% so d=(#3.#4-#1.#4)/(#2.#4-#1.#4) 

% and vec P = vec ell_0 + d * vec ell = #1 + d * (#2-#1)

tikzset{intersection of line trough/.style args={#1 and #2 with plane

        containing #3 and normal #4}{%

        /utils/exec={pgfmathsetmacro{ltest}{abs(SPTD#2.#4-(SPTD#1.#4))}

            parsecoord#1>(myAx,myAy,myAz)

            parsecoord#2>(myBx,myBy,myBz)

            ifdimltest pt<0.01pt

            typeout{Planespace andspace linespace arespace parallel!ltest}

            pgfmathsetmacro{myd}{0}

            else

            pgfmathsetmacro{myd}{((SPTD#3.#4)-(SPTD#1.#4))/((SPTD#2.#4)-(SPTD#1.#4))}

            fi

            %typeout{({myAx+myd*(myBx-myAx)},{myAy+myd*(myBy-myAy)},{myAz+myd*(myBz-myAz)})}

            defmyP{({myAx+myd*(myBx-myAx)},{myAy+myd*(myBy-myAy)},{myAz+myd*(myBz-myAz)})}

            smugglemyP},

        insert path={%

            myP}

}}



begin{document}

    tdplotsetmaincoords{75}{110}

    begin{tikzpicture}[tdplot_main_coords,scale=1.5]

    pgfmathsetmacroa{3}

    pgfmathsetmacrob{4}

    pgfmathsetmacroh{5}



    % definitions

    path 

    coordinate(A) at (0,0,0)

    coordinate (B) at (a,0,0)

    coordinate (C) at (a,b,0) 

    coordinate (D) at (0,b,0)                            

    coordinate (S) at (0,0,h);                

    defmynormal{VecMinus(a,b,0)-(0,0,h)}

    typeout{mynormal:(a,b,-h)}

    path[intersection of line trough={(0,0,h) and (a,0,0) with plane containing (0,0,0) and normal (a,b,-h)}]  coordinate (E)

    [intersection of line trough={(0,0,h) and  (0,b,0) with plane containing (0,0,0) and normal (a,b,-h)}]  coordinate (F)

    [intersection of line trough={(0,0,h) and  (a,b,0) with plane containing (0,0,0) and normal (a,b,-h)}]  coordinate (K);





    draw[dashed, thick]

    (A) -- (B)   (D)--(A) (S)--(A);

    draw[dashed, thick]

    (E) --(A)  -- (F);

    draw[ultra thick]

    (S) -- (B) -- (C) -- (D)--cycle (S)--(C);



    draw [thick, dashed] (A) -- (K) (A) -- (C) (B) -- (D) (E) -- (F) ;

    draw [thick] (E) -- (K) -- (F) ;



    foreach point/position in {A/left,B/below,C/below,S/above,D/right,E/left,D/right,F/right,K/above right}

    {

        fill (point) circle (1.5pt);

        node[position=3pt] at (point) {$point$};

    }



 end{tikzpicture}

end{document}


enter image description here



This agrees with what you got with your other very nice methods. Sorry for the confusion!






share|improve this answer





















  • 1





    Can you select all answers and make a package?

    – minhthien_2016
    Jan 28 at 6:08






  • 1





    @minhthien_2016 I can try to clean up and write the styles more similar. This is what I plan to do (I also want to make parsing the vectors more elegant.) I don't have much experience in package writing. Anybody who wants to write a package is very welcome to use these styles. I guess that collecting these and other tricks in a TikZ library may make sense. (There is a conceptual point that I would like solve: can one store the 3D coordinates in symbolic coordinates? That would make these things much more elegant.)

    – marmot
    Jan 28 at 6:13






  • 2





    I use Maple, so finding coordinates of points is not too difficult. This approach is easy to know when using Maple. I want it to be written in TeX for everyone to use TeX easily.

    – minhthien_2016
    Jan 28 at 6:20











  • Can you see at here tex.stackexchange.com/questions/400808/… ?

    – minhthien_2016
    Jan 31 at 8:22











  • And my question at here tex.stackexchange.com/questions/401630/…

    – minhthien_2016
    Jan 31 at 8:28











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I am sorry, my original code has a flaw. I simply forgot to put brackets around the scalar products like SPTD#3.#4 and so on. And when testing this in the update to the previous answer, this did not matter. Once one adds these brackets, one gets



documentclass[border=3.14mm,12pt,tikz]{standalone}

usepackage{tikz,tikz-3dplot} 

%% smuggling from https://tex.stackexchange.com/a/470979/121799

newcounter{smuggle}

DeclareRobustCommandsmuggleone[1]{%

    stepcounter{smuggle}%

    expandafterglobalexpandafterletcsname smuggle@arabic{smuggle}endcsname#1%

    aftergroupletaftergroup#1expandafteraftergroupcsname smuggle@arabic{smuggle}endcsname

}

DeclareRobustCommandsmuggle[2][1]{%

    smuggleone{#2}%

    ifnum#1>1

    aftergroupsmuggleaftergroup[expandafteraftergroupthenumexpr#1-1aftergroup]aftergroup#2%

    fi

}



defparsecoord(#1,#2,#3)>(#4,#5,#6){%

    def#4{#1}%

    def#5{#2}%

    def#6{#3}%

    smuggle{#4}%

    smuggle{#5}%

    smuggle{#6}%

}

defSPTD(#1,#2,#3).(#4,#5,#6){((#1)*(#4)+1*(#2)*(#5)+1*(#3)*(#6))}

defVPTD(#1,#2,#3)x(#4,#5,#6){((#2)*(#6)-1*(#3)*(#5),(#3)*(#4)-1*(#1)*(#6),(#1)*(#5)-1*(#2)*(#4))}

defVecMinus(#1,#2,#3)-(#4,#5,#6){(#1-1*(#4),#2-1*(#5),#3-1*(#6))}

defVecAdd(#1,#2,#3)+(#4,#5,#6){(#1+1*(#4),#2+1*(#5),#3+1*(#6))}

% the line is given by vec x = vec ell_0 + t vec ell

% the points in the plane fulfill (vec P_0 - vec x)cdotvec n =0

% inserting the line equation in the plane equation gives

% (vec Q - vec ell_0 - d vec ell)cdot vec n = 0

% solving for d yields 

% d = (vec Q cdot vec n - vec ell_0cdotvec n)/(vecellcdot vec n)  

%

% in the macro vec ell_0 = #1 , vec ell = #2 - #1

% #3 : vec Q and #4 : vec n

% so d=(#3.#4-#1.#4)/(#2.#4-#1.#4) 

% and vec P = vec ell_0 + d * vec ell = #1 + d * (#2-#1)

tikzset{intersection of line trough/.style args={#1 and #2 with plane

        containing #3 and normal #4}{%

        /utils/exec={pgfmathsetmacro{ltest}{abs(SPTD#2.#4-(SPTD#1.#4))}

            parsecoord#1>(myAx,myAy,myAz)

            parsecoord#2>(myBx,myBy,myBz)

            ifdimltest pt<0.01pt

            typeout{Planespace andspace linespace arespace parallel!ltest}

            pgfmathsetmacro{myd}{0}

            else

            pgfmathsetmacro{myd}{((SPTD#3.#4)-(SPTD#1.#4))/((SPTD#2.#4)-(SPTD#1.#4))}

            fi

            %typeout{({myAx+myd*(myBx-myAx)},{myAy+myd*(myBy-myAy)},{myAz+myd*(myBz-myAz)})}

            defmyP{({myAx+myd*(myBx-myAx)},{myAy+myd*(myBy-myAy)},{myAz+myd*(myBz-myAz)})}

            smugglemyP},

        insert path={%

            myP}

}}



begin{document}

    tdplotsetmaincoords{75}{110}

    begin{tikzpicture}[tdplot_main_coords,scale=1.5]

    pgfmathsetmacroa{3}

    pgfmathsetmacrob{4}

    pgfmathsetmacroh{5}



    % definitions

    path 

    coordinate(A) at (0,0,0)

    coordinate (B) at (a,0,0)

    coordinate (C) at (a,b,0) 

    coordinate (D) at (0,b,0)                            

    coordinate (S) at (0,0,h);                

    defmynormal{VecMinus(a,b,0)-(0,0,h)}

    typeout{mynormal:(a,b,-h)}

    path[intersection of line trough={(0,0,h) and (a,0,0) with plane containing (0,0,0) and normal (a,b,-h)}]  coordinate (E)

    [intersection of line trough={(0,0,h) and  (0,b,0) with plane containing (0,0,0) and normal (a,b,-h)}]  coordinate (F)

    [intersection of line trough={(0,0,h) and  (a,b,0) with plane containing (0,0,0) and normal (a,b,-h)}]  coordinate (K);





    draw[dashed, thick]

    (A) -- (B)   (D)--(A) (S)--(A);

    draw[dashed, thick]

    (E) --(A)  -- (F);

    draw[ultra thick]

    (S) -- (B) -- (C) -- (D)--cycle (S)--(C);



    draw [thick, dashed] (A) -- (K) (A) -- (C) (B) -- (D) (E) -- (F) ;

    draw [thick] (E) -- (K) -- (F) ;



    foreach point/position in {A/left,B/below,C/below,S/above,D/right,E/left,D/right,F/right,K/above right}

    {

        fill (point) circle (1.5pt);

        node[position=3pt] at (point) {$point$};

    }



 end{tikzpicture}

end{document}


enter image description here



This agrees with what you got with your other very nice methods. Sorry for the confusion!






share|improve this answer





















  • 1





    Can you select all answers and make a package?

    – minhthien_2016
    Jan 28 at 6:08






  • 1





    @minhthien_2016 I can try to clean up and write the styles more similar. This is what I plan to do (I also want to make parsing the vectors more elegant.) I don't have much experience in package writing. Anybody who wants to write a package is very welcome to use these styles. I guess that collecting these and other tricks in a TikZ library may make sense. (There is a conceptual point that I would like solve: can one store the 3D coordinates in symbolic coordinates? That would make these things much more elegant.)

    – marmot
    Jan 28 at 6:13






  • 2





    I use Maple, so finding coordinates of points is not too difficult. This approach is easy to know when using Maple. I want it to be written in TeX for everyone to use TeX easily.

    – minhthien_2016
    Jan 28 at 6:20











  • Can you see at here tex.stackexchange.com/questions/400808/… ?

    – minhthien_2016
    Jan 31 at 8:22











  • And my question at here tex.stackexchange.com/questions/401630/…

    – minhthien_2016
    Jan 31 at 8:28
















2














I am sorry, my original code has a flaw. I simply forgot to put brackets around the scalar products like SPTD#3.#4 and so on. And when testing this in the update to the previous answer, this did not matter. Once one adds these brackets, one gets



documentclass[border=3.14mm,12pt,tikz]{standalone}

usepackage{tikz,tikz-3dplot} 

%% smuggling from https://tex.stackexchange.com/a/470979/121799

newcounter{smuggle}

DeclareRobustCommandsmuggleone[1]{%

    stepcounter{smuggle}%

    expandafterglobalexpandafterletcsname smuggle@arabic{smuggle}endcsname#1%

    aftergroupletaftergroup#1expandafteraftergroupcsname smuggle@arabic{smuggle}endcsname

}

DeclareRobustCommandsmuggle[2][1]{%

    smuggleone{#2}%

    ifnum#1>1

    aftergroupsmuggleaftergroup[expandafteraftergroupthenumexpr#1-1aftergroup]aftergroup#2%

    fi

}



defparsecoord(#1,#2,#3)>(#4,#5,#6){%

    def#4{#1}%

    def#5{#2}%

    def#6{#3}%

    smuggle{#4}%

    smuggle{#5}%

    smuggle{#6}%

}

defSPTD(#1,#2,#3).(#4,#5,#6){((#1)*(#4)+1*(#2)*(#5)+1*(#3)*(#6))}

defVPTD(#1,#2,#3)x(#4,#5,#6){((#2)*(#6)-1*(#3)*(#5),(#3)*(#4)-1*(#1)*(#6),(#1)*(#5)-1*(#2)*(#4))}

defVecMinus(#1,#2,#3)-(#4,#5,#6){(#1-1*(#4),#2-1*(#5),#3-1*(#6))}

defVecAdd(#1,#2,#3)+(#4,#5,#6){(#1+1*(#4),#2+1*(#5),#3+1*(#6))}

% the line is given by vec x = vec ell_0 + t vec ell

% the points in the plane fulfill (vec P_0 - vec x)cdotvec n =0

% inserting the line equation in the plane equation gives

% (vec Q - vec ell_0 - d vec ell)cdot vec n = 0

% solving for d yields 

% d = (vec Q cdot vec n - vec ell_0cdotvec n)/(vecellcdot vec n)  

%

% in the macro vec ell_0 = #1 , vec ell = #2 - #1

% #3 : vec Q and #4 : vec n

% so d=(#3.#4-#1.#4)/(#2.#4-#1.#4) 

% and vec P = vec ell_0 + d * vec ell = #1 + d * (#2-#1)

tikzset{intersection of line trough/.style args={#1 and #2 with plane

        containing #3 and normal #4}{%

        /utils/exec={pgfmathsetmacro{ltest}{abs(SPTD#2.#4-(SPTD#1.#4))}

            parsecoord#1>(myAx,myAy,myAz)

            parsecoord#2>(myBx,myBy,myBz)

            ifdimltest pt<0.01pt

            typeout{Planespace andspace linespace arespace parallel!ltest}

            pgfmathsetmacro{myd}{0}

            else

            pgfmathsetmacro{myd}{((SPTD#3.#4)-(SPTD#1.#4))/((SPTD#2.#4)-(SPTD#1.#4))}

            fi

            %typeout{({myAx+myd*(myBx-myAx)},{myAy+myd*(myBy-myAy)},{myAz+myd*(myBz-myAz)})}

            defmyP{({myAx+myd*(myBx-myAx)},{myAy+myd*(myBy-myAy)},{myAz+myd*(myBz-myAz)})}

            smugglemyP},

        insert path={%

            myP}

}}



begin{document}

    tdplotsetmaincoords{75}{110}

    begin{tikzpicture}[tdplot_main_coords,scale=1.5]

    pgfmathsetmacroa{3}

    pgfmathsetmacrob{4}

    pgfmathsetmacroh{5}



    % definitions

    path 

    coordinate(A) at (0,0,0)

    coordinate (B) at (a,0,0)

    coordinate (C) at (a,b,0) 

    coordinate (D) at (0,b,0)                            

    coordinate (S) at (0,0,h);                

    defmynormal{VecMinus(a,b,0)-(0,0,h)}

    typeout{mynormal:(a,b,-h)}

    path[intersection of line trough={(0,0,h) and (a,0,0) with plane containing (0,0,0) and normal (a,b,-h)}]  coordinate (E)

    [intersection of line trough={(0,0,h) and  (0,b,0) with plane containing (0,0,0) and normal (a,b,-h)}]  coordinate (F)

    [intersection of line trough={(0,0,h) and  (a,b,0) with plane containing (0,0,0) and normal (a,b,-h)}]  coordinate (K);





    draw[dashed, thick]

    (A) -- (B)   (D)--(A) (S)--(A);

    draw[dashed, thick]

    (E) --(A)  -- (F);

    draw[ultra thick]

    (S) -- (B) -- (C) -- (D)--cycle (S)--(C);



    draw [thick, dashed] (A) -- (K) (A) -- (C) (B) -- (D) (E) -- (F) ;

    draw [thick] (E) -- (K) -- (F) ;



    foreach point/position in {A/left,B/below,C/below,S/above,D/right,E/left,D/right,F/right,K/above right}

    {

        fill (point) circle (1.5pt);

        node[position=3pt] at (point) {$point$};

    }



 end{tikzpicture}

end{document}


enter image description here



This agrees with what you got with your other very nice methods. Sorry for the confusion!






share|improve this answer





















  • 1





    Can you select all answers and make a package?

    – minhthien_2016
    Jan 28 at 6:08






  • 1





    @minhthien_2016 I can try to clean up and write the styles more similar. This is what I plan to do (I also want to make parsing the vectors more elegant.) I don't have much experience in package writing. Anybody who wants to write a package is very welcome to use these styles. I guess that collecting these and other tricks in a TikZ library may make sense. (There is a conceptual point that I would like solve: can one store the 3D coordinates in symbolic coordinates? That would make these things much more elegant.)

    – marmot
    Jan 28 at 6:13






  • 2





    I use Maple, so finding coordinates of points is not too difficult. This approach is easy to know when using Maple. I want it to be written in TeX for everyone to use TeX easily.

    – minhthien_2016
    Jan 28 at 6:20











  • Can you see at here tex.stackexchange.com/questions/400808/… ?

    – minhthien_2016
    Jan 31 at 8:22











  • And my question at here tex.stackexchange.com/questions/401630/…

    – minhthien_2016
    Jan 31 at 8:28














2












2








2







I am sorry, my original code has a flaw. I simply forgot to put brackets around the scalar products like SPTD#3.#4 and so on. And when testing this in the update to the previous answer, this did not matter. Once one adds these brackets, one gets



documentclass[border=3.14mm,12pt,tikz]{standalone}

usepackage{tikz,tikz-3dplot} 

%% smuggling from https://tex.stackexchange.com/a/470979/121799

newcounter{smuggle}

DeclareRobustCommandsmuggleone[1]{%

    stepcounter{smuggle}%

    expandafterglobalexpandafterletcsname smuggle@arabic{smuggle}endcsname#1%

    aftergroupletaftergroup#1expandafteraftergroupcsname smuggle@arabic{smuggle}endcsname

}

DeclareRobustCommandsmuggle[2][1]{%

    smuggleone{#2}%

    ifnum#1>1

    aftergroupsmuggleaftergroup[expandafteraftergroupthenumexpr#1-1aftergroup]aftergroup#2%

    fi

}



defparsecoord(#1,#2,#3)>(#4,#5,#6){%

    def#4{#1}%

    def#5{#2}%

    def#6{#3}%

    smuggle{#4}%

    smuggle{#5}%

    smuggle{#6}%

}

defSPTD(#1,#2,#3).(#4,#5,#6){((#1)*(#4)+1*(#2)*(#5)+1*(#3)*(#6))}

defVPTD(#1,#2,#3)x(#4,#5,#6){((#2)*(#6)-1*(#3)*(#5),(#3)*(#4)-1*(#1)*(#6),(#1)*(#5)-1*(#2)*(#4))}

defVecMinus(#1,#2,#3)-(#4,#5,#6){(#1-1*(#4),#2-1*(#5),#3-1*(#6))}

defVecAdd(#1,#2,#3)+(#4,#5,#6){(#1+1*(#4),#2+1*(#5),#3+1*(#6))}

% the line is given by vec x = vec ell_0 + t vec ell

% the points in the plane fulfill (vec P_0 - vec x)cdotvec n =0

% inserting the line equation in the plane equation gives

% (vec Q - vec ell_0 - d vec ell)cdot vec n = 0

% solving for d yields 

% d = (vec Q cdot vec n - vec ell_0cdotvec n)/(vecellcdot vec n)  

%

% in the macro vec ell_0 = #1 , vec ell = #2 - #1

% #3 : vec Q and #4 : vec n

% so d=(#3.#4-#1.#4)/(#2.#4-#1.#4) 

% and vec P = vec ell_0 + d * vec ell = #1 + d * (#2-#1)

tikzset{intersection of line trough/.style args={#1 and #2 with plane

        containing #3 and normal #4}{%

        /utils/exec={pgfmathsetmacro{ltest}{abs(SPTD#2.#4-(SPTD#1.#4))}

            parsecoord#1>(myAx,myAy,myAz)

            parsecoord#2>(myBx,myBy,myBz)

            ifdimltest pt<0.01pt

            typeout{Planespace andspace linespace arespace parallel!ltest}

            pgfmathsetmacro{myd}{0}

            else

            pgfmathsetmacro{myd}{((SPTD#3.#4)-(SPTD#1.#4))/((SPTD#2.#4)-(SPTD#1.#4))}

            fi

            %typeout{({myAx+myd*(myBx-myAx)},{myAy+myd*(myBy-myAy)},{myAz+myd*(myBz-myAz)})}

            defmyP{({myAx+myd*(myBx-myAx)},{myAy+myd*(myBy-myAy)},{myAz+myd*(myBz-myAz)})}

            smugglemyP},

        insert path={%

            myP}

}}



begin{document}

    tdplotsetmaincoords{75}{110}

    begin{tikzpicture}[tdplot_main_coords,scale=1.5]

    pgfmathsetmacroa{3}

    pgfmathsetmacrob{4}

    pgfmathsetmacroh{5}



    % definitions

    path 

    coordinate(A) at (0,0,0)

    coordinate (B) at (a,0,0)

    coordinate (C) at (a,b,0) 

    coordinate (D) at (0,b,0)                            

    coordinate (S) at (0,0,h);                

    defmynormal{VecMinus(a,b,0)-(0,0,h)}

    typeout{mynormal:(a,b,-h)}

    path[intersection of line trough={(0,0,h) and (a,0,0) with plane containing (0,0,0) and normal (a,b,-h)}]  coordinate (E)

    [intersection of line trough={(0,0,h) and  (0,b,0) with plane containing (0,0,0) and normal (a,b,-h)}]  coordinate (F)

    [intersection of line trough={(0,0,h) and  (a,b,0) with plane containing (0,0,0) and normal (a,b,-h)}]  coordinate (K);





    draw[dashed, thick]

    (A) -- (B)   (D)--(A) (S)--(A);

    draw[dashed, thick]

    (E) --(A)  -- (F);

    draw[ultra thick]

    (S) -- (B) -- (C) -- (D)--cycle (S)--(C);



    draw [thick, dashed] (A) -- (K) (A) -- (C) (B) -- (D) (E) -- (F) ;

    draw [thick] (E) -- (K) -- (F) ;



    foreach point/position in {A/left,B/below,C/below,S/above,D/right,E/left,D/right,F/right,K/above right}

    {

        fill (point) circle (1.5pt);

        node[position=3pt] at (point) {$point$};

    }



 end{tikzpicture}

end{document}


enter image description here



This agrees with what you got with your other very nice methods. Sorry for the confusion!






share|improve this answer















I am sorry, my original code has a flaw. I simply forgot to put brackets around the scalar products like SPTD#3.#4 and so on. And when testing this in the update to the previous answer, this did not matter. Once one adds these brackets, one gets



documentclass[border=3.14mm,12pt,tikz]{standalone}

usepackage{tikz,tikz-3dplot} 

%% smuggling from https://tex.stackexchange.com/a/470979/121799

newcounter{smuggle}

DeclareRobustCommandsmuggleone[1]{%

    stepcounter{smuggle}%

    expandafterglobalexpandafterletcsname smuggle@arabic{smuggle}endcsname#1%

    aftergroupletaftergroup#1expandafteraftergroupcsname smuggle@arabic{smuggle}endcsname

}

DeclareRobustCommandsmuggle[2][1]{%

    smuggleone{#2}%

    ifnum#1>1

    aftergroupsmuggleaftergroup[expandafteraftergroupthenumexpr#1-1aftergroup]aftergroup#2%

    fi

}



defparsecoord(#1,#2,#3)>(#4,#5,#6){%

    def#4{#1}%

    def#5{#2}%

    def#6{#3}%

    smuggle{#4}%

    smuggle{#5}%

    smuggle{#6}%

}

defSPTD(#1,#2,#3).(#4,#5,#6){((#1)*(#4)+1*(#2)*(#5)+1*(#3)*(#6))}

defVPTD(#1,#2,#3)x(#4,#5,#6){((#2)*(#6)-1*(#3)*(#5),(#3)*(#4)-1*(#1)*(#6),(#1)*(#5)-1*(#2)*(#4))}

defVecMinus(#1,#2,#3)-(#4,#5,#6){(#1-1*(#4),#2-1*(#5),#3-1*(#6))}

defVecAdd(#1,#2,#3)+(#4,#5,#6){(#1+1*(#4),#2+1*(#5),#3+1*(#6))}

% the line is given by vec x = vec ell_0 + t vec ell

% the points in the plane fulfill (vec P_0 - vec x)cdotvec n =0

% inserting the line equation in the plane equation gives

% (vec Q - vec ell_0 - d vec ell)cdot vec n = 0

% solving for d yields 

% d = (vec Q cdot vec n - vec ell_0cdotvec n)/(vecellcdot vec n)  

%

% in the macro vec ell_0 = #1 , vec ell = #2 - #1

% #3 : vec Q and #4 : vec n

% so d=(#3.#4-#1.#4)/(#2.#4-#1.#4) 

% and vec P = vec ell_0 + d * vec ell = #1 + d * (#2-#1)

tikzset{intersection of line trough/.style args={#1 and #2 with plane

        containing #3 and normal #4}{%

        /utils/exec={pgfmathsetmacro{ltest}{abs(SPTD#2.#4-(SPTD#1.#4))}

            parsecoord#1>(myAx,myAy,myAz)

            parsecoord#2>(myBx,myBy,myBz)

            ifdimltest pt<0.01pt

            typeout{Planespace andspace linespace arespace parallel!ltest}

            pgfmathsetmacro{myd}{0}

            else

            pgfmathsetmacro{myd}{((SPTD#3.#4)-(SPTD#1.#4))/((SPTD#2.#4)-(SPTD#1.#4))}

            fi

            %typeout{({myAx+myd*(myBx-myAx)},{myAy+myd*(myBy-myAy)},{myAz+myd*(myBz-myAz)})}

            defmyP{({myAx+myd*(myBx-myAx)},{myAy+myd*(myBy-myAy)},{myAz+myd*(myBz-myAz)})}

            smugglemyP},

        insert path={%

            myP}

}}



begin{document}

    tdplotsetmaincoords{75}{110}

    begin{tikzpicture}[tdplot_main_coords,scale=1.5]

    pgfmathsetmacroa{3}

    pgfmathsetmacrob{4}

    pgfmathsetmacroh{5}



    % definitions

    path 

    coordinate(A) at (0,0,0)

    coordinate (B) at (a,0,0)

    coordinate (C) at (a,b,0) 

    coordinate (D) at (0,b,0)                            

    coordinate (S) at (0,0,h);                

    defmynormal{VecMinus(a,b,0)-(0,0,h)}

    typeout{mynormal:(a,b,-h)}

    path[intersection of line trough={(0,0,h) and (a,0,0) with plane containing (0,0,0) and normal (a,b,-h)}]  coordinate (E)

    [intersection of line trough={(0,0,h) and  (0,b,0) with plane containing (0,0,0) and normal (a,b,-h)}]  coordinate (F)

    [intersection of line trough={(0,0,h) and  (a,b,0) with plane containing (0,0,0) and normal (a,b,-h)}]  coordinate (K);





    draw[dashed, thick]

    (A) -- (B)   (D)--(A) (S)--(A);

    draw[dashed, thick]

    (E) --(A)  -- (F);

    draw[ultra thick]

    (S) -- (B) -- (C) -- (D)--cycle (S)--(C);



    draw [thick, dashed] (A) -- (K) (A) -- (C) (B) -- (D) (E) -- (F) ;

    draw [thick] (E) -- (K) -- (F) ;



    foreach point/position in {A/left,B/below,C/below,S/above,D/right,E/left,D/right,F/right,K/above right}

    {

        fill (point) circle (1.5pt);

        node[position=3pt] at (point) {$point$};

    }



 end{tikzpicture}

end{document}


enter image description here



This agrees with what you got with your other very nice methods. Sorry for the confusion!







share|improve this answer














share|improve this answer



share|improve this answer








edited yesterday

























answered Jan 28 at 5:53









marmotmarmot

97.2k4112214




97.2k4112214








  • 1





    Can you select all answers and make a package?

    – minhthien_2016
    Jan 28 at 6:08






  • 1





    @minhthien_2016 I can try to clean up and write the styles more similar. This is what I plan to do (I also want to make parsing the vectors more elegant.) I don't have much experience in package writing. Anybody who wants to write a package is very welcome to use these styles. I guess that collecting these and other tricks in a TikZ library may make sense. (There is a conceptual point that I would like solve: can one store the 3D coordinates in symbolic coordinates? That would make these things much more elegant.)

    – marmot
    Jan 28 at 6:13






  • 2





    I use Maple, so finding coordinates of points is not too difficult. This approach is easy to know when using Maple. I want it to be written in TeX for everyone to use TeX easily.

    – minhthien_2016
    Jan 28 at 6:20











  • Can you see at here tex.stackexchange.com/questions/400808/… ?

    – minhthien_2016
    Jan 31 at 8:22











  • And my question at here tex.stackexchange.com/questions/401630/…

    – minhthien_2016
    Jan 31 at 8:28














  • 1





    Can you select all answers and make a package?

    – minhthien_2016
    Jan 28 at 6:08






  • 1





    @minhthien_2016 I can try to clean up and write the styles more similar. This is what I plan to do (I also want to make parsing the vectors more elegant.) I don't have much experience in package writing. Anybody who wants to write a package is very welcome to use these styles. I guess that collecting these and other tricks in a TikZ library may make sense. (There is a conceptual point that I would like solve: can one store the 3D coordinates in symbolic coordinates? That would make these things much more elegant.)

    – marmot
    Jan 28 at 6:13






  • 2





    I use Maple, so finding coordinates of points is not too difficult. This approach is easy to know when using Maple. I want it to be written in TeX for everyone to use TeX easily.

    – minhthien_2016
    Jan 28 at 6:20











  • Can you see at here tex.stackexchange.com/questions/400808/… ?

    – minhthien_2016
    Jan 31 at 8:22











  • And my question at here tex.stackexchange.com/questions/401630/…

    – minhthien_2016
    Jan 31 at 8:28








1




1





Can you select all answers and make a package?

– minhthien_2016
Jan 28 at 6:08





Can you select all answers and make a package?

– minhthien_2016
Jan 28 at 6:08




1




1





@minhthien_2016 I can try to clean up and write the styles more similar. This is what I plan to do (I also want to make parsing the vectors more elegant.) I don't have much experience in package writing. Anybody who wants to write a package is very welcome to use these styles. I guess that collecting these and other tricks in a TikZ library may make sense. (There is a conceptual point that I would like solve: can one store the 3D coordinates in symbolic coordinates? That would make these things much more elegant.)

– marmot
Jan 28 at 6:13





@minhthien_2016 I can try to clean up and write the styles more similar. This is what I plan to do (I also want to make parsing the vectors more elegant.) I don't have much experience in package writing. Anybody who wants to write a package is very welcome to use these styles. I guess that collecting these and other tricks in a TikZ library may make sense. (There is a conceptual point that I would like solve: can one store the 3D coordinates in symbolic coordinates? That would make these things much more elegant.)

– marmot
Jan 28 at 6:13




2




2





I use Maple, so finding coordinates of points is not too difficult. This approach is easy to know when using Maple. I want it to be written in TeX for everyone to use TeX easily.

– minhthien_2016
Jan 28 at 6:20





I use Maple, so finding coordinates of points is not too difficult. This approach is easy to know when using Maple. I want it to be written in TeX for everyone to use TeX easily.

– minhthien_2016
Jan 28 at 6:20













Can you see at here tex.stackexchange.com/questions/400808/… ?

– minhthien_2016
Jan 31 at 8:22





Can you see at here tex.stackexchange.com/questions/400808/… ?

– minhthien_2016
Jan 31 at 8:22













And my question at here tex.stackexchange.com/questions/401630/…

– minhthien_2016
Jan 31 at 8:28





And my question at here tex.stackexchange.com/questions/401630/…

– minhthien_2016
Jan 31 at 8:28


















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