How to draw a cone that height does not perpendicular to xy plane? - TeX

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user 3.14159

I can currently only answer the first part of the question. It is as simple as finding an appropriate coordinate system, in which the z-axis points into the direction of axis of the cone.
```
\documentclass[tikz,border=3mm]{standalone}
\usetikzlibrary{calc,3dtools}% https://github.com/marmotghost/tikz-3dtools
\begin{document}
\foreach \Angle in {5,15,...,355}
{\begin{tikzpicture}[3d/install view={phi=\Angle,theta=65,psi=20},
		line cap=round,line join=round,same bounding box=A,
		declare function={a=4;}]
  \path (0,0,a) coordinate (A')
	(a,0,0) coordinate (B)
	(0,a,0) coordinate (D)
	(a,a,a) coordinate (C');
  \path[3d/circumcircle center={A={(D)},B={(B)},C={(C')}}] coordinate (G);
  \pgfmathsetmacro{\R}{sqrt(TD("(G)-(B)o(G)-(B)"))}
  \pgfmathsetmacro{\h}{sqrt(TD("(G)-(A')o(G)-(A')"))}
  \tikzset{3d/define orthonormal dreibein={A={(D)},B={(B)},C={(C')}}}
  \path[x={(ex)},y={(ey)},z={(ez)}]
    (G) pic{3d/cone={r=\R,h=\h}};
  \foreach \p/\g in {G/-90,A'/-90,B/-90,C'/-90,D/90}
  {\draw[fill=black] (\p) circle[radius=1.2pt]+(\g:3mm) node{$\p$};}
\end{tikzpicture}}
\end{document} 
```
![ani.gif](/image?hash=7860aa64f0b42b8f1f1d3929496b0227264b2f7600bf9d9a5601cab843927b28)

The second part is much harder. One would have to compute a number of intersections. It would be even harder to make this fully rotatable.

The problem is that you compute the normal is the scope with a new coordinate system. In this frame, the normal looks differently. However, we still use the coordinates from outside of the scope. One way to go would be to use "physical" coordinates, but in this case you can just make the test outside of the scope. ``` \documentclass[border=1mm,12pt,tikz]{standalone} \usetikzlibrary{3dtools,calc}% https://github.com/marmotghost/tikz-3dtools \begin{document} \foreach \Angle in {5,15,...,355} {\begin{tikzpicture}[3d/install view={phi=\Angle,psi=0,theta=70}, line join = round, line cap = round,same bounding box=A,c/.style={circle,fill,inner sep=1pt}, declare function={a=6;h=a*sqrt(2)/2;}] \path (-a/2,a/2,0) coordinate (A) (-a/2,-a/2,0) coordinate (B) (a/2,-a/2,0) coordinate (C) (a/2,a/2,0) coordinate (D) (0,0,h) coordinate (S) (0,0,0) coordinate (O); \path[3d/plane through={(A) and (B) and (S) named pABS}]; \path[3d/circumcircle center={A={(A)},B={(B)},C={(S)}}] coordinate (O'); \path[3d coordinate={(M) = 0.5*(A) + 0.5*(B)}]; \pgfmathsetmacro{\mybarycenter}{barycenter("(A),(B),(C),(D),(S)")} \path (\mybarycenter) coordinate (O''); \tikzset{3d/polyhedron/.cd,O={(O'')}, fore/.append style={fill=none,/tikz/3d/visible}, back/.append style={fill=none,/tikz/3d/hidden}, draw face with corners={{(A)},{(B)},{(C)},{(D)}}, draw face with corners={{(S)},{(A)},{(B)}}, draw face with corners={{(S)},{(B)},{(C)}}, draw face with corners={{(S)},{(C)},{(D)}}, draw face with corners={{(S)},{(A)},{(D)}} } \draw[3d/hidden] (O) -- (O') (S) -- (O); \pgfmathsetmacro{\myh}{tddistance("(O)","(O')")} \pgfmathsetmacro{\myr}{tddistance("(M)","(O')")} \tikzset{3d/define orthonormal dreibein={A={(A)},B={(B)},C={(S)}}} \path[x={(ex)},y={(ey)},z={(ez)}] (O')[3d/visible/.style={draw,very thin,cheating dash}, 3d/hidden/.style={draw=none}] pic{3d/cone={r=\myr,h=-\myh}}; \pgfmathsetmacro{\myn}{TD("(B)-(S)x(B)-(A)")} \pgfmathtruncatemacro{\itest}{screendepth(\myn)>0?1:0} \begin{scope}[x={(ex)},y={(ey)},z={(ez)}] \ifnum\itest=0 \draw[3d/hidden] (O') circle[radius=\myr]; \else \draw[3d/visible] (O') circle[radius=\myr]; \fi \end{scope} \path foreach \p/\g in {A/-90,B/90,C/-90,D/-90,S/90,O/-90,O'/90} {(\p)node[c]{}+(\g:2.5mm) node{$\p$}}; \end{tikzpicture}} \end{document} ```

@marmot, re: [your answer](#a1948), I tried with another way, still incorect ``` \documentclass[border=1mm,12pt,tikz]{standalone} \usetikzlibrary{3dtools,calc}% https://github.com/marmotghost/tikz-3dtools \begin{document} \foreach \Angle in {5,10,...,355} {\begin{tikzpicture}[3d/install view={phi=\Angle,psi=0,theta=70}, line join = round, line cap = round,same bounding box=A,c/.style={circle,fill,inner sep=1pt}, declare function={a=6;h=a*sqrt(2)/2;}] \path (-a/2,a/2,0) coordinate (A) (-a/2,-a/2,0) coordinate (B) (a/2,-a/2,0) coordinate (C) (a/2,a/2,0) coordinate (D) (0,0,h) coordinate (S) (0,0,0) coordinate (O); \path[3d/plane through={(A) and (B) and (S) named pABS}]; \path[3d/circumcircle center={A={(A)},B={(B)},C={(S)}}] coordinate (O'); \path[3d coordinate={(M) = 0.5*(A) + 0.5*(B)}]; \pgfmathsetmacro{\mybarycenter}{barycenter("(A),(B),(C),(D),(S)")} \path (\mybarycenter) coordinate (O''); \tikzset{3d/polyhedron/.cd,O={(O'')}, fore/.append style={fill=none,/tikz/3d/visible}, back/.append style={fill=none,/tikz/3d/hidden}, draw face with corners={{(A)},{(B)},{(C)},{(D)}}, draw face with corners={{(S)},{(A)},{(B)}}, draw face with corners={{(S)},{(B)},{(C)}}, draw face with corners={{(S)},{(C)},{(D)}}, draw face with corners={{(S)},{(A)},{(D)}} } \draw[3d/hidden] (O) -- (O') (S) -- (O); \pgfmathsetmacro{\myh}{tddistance("(O)","(O')")} \pgfmathsetmacro{\myr}{tddistance("(M)","(O')")} %\pgfmathsetmacro{\myr}{tddistance("(A)","(O')")} \tikzset{3d/define orthonormal dreibein={A={(A)},B={(B)},C={(S)}}} \path[x={(ex)},y={(ey)},z={(ez)}] (O')[3d/visible/.style={draw,very thin,cheating dash}, 3d/hidden/.style={draw=none}] pic{3d/cone={r=\myr,h=-\myh}}; \begin{scope}[x={(ex)},y={(ey)},z={(ez)}] \pgfmathsetmacro{\myn}{TD("(B)-(S)x(B)-(A)")} \pgfmathtruncatemacro{\itest}{screendepth(\myn)>0?1:0} \ifnum\itest=0 \draw[3d/hidden] (O') circle[radius=\myr]; \else \draw[3d/visible] (O') circle[radius=\myr]; \fi \end{scope} \path foreach \p/\g in {A/-90,B/90,C/-90,D/-90,S/90,O/-90,O'/90} {(\p)node[c]{}+(\g:2.5mm) node{$\p$}}; \end{tikzpicture}} \end{document} ```

Please see some places like this ![ScreenHunter 175.png](/image?hash=4e036f0910d149148df5d3f2a002f2d5721acc72386e463f72c1e8cfd96e3e1a) ![ScreenHunter 176.png](/image?hash=e021df455de5c1e1439fd6b55ba09a2b701051faa54c40db4c713f3f5f688acc) I think, dashed line at `AG, AE`.

One step at a time, please. ``` \documentclass[border=1mm,12pt,tikz]{standalone} \usetikzlibrary{3dtools,calc}% https://github.com/marmotghost/tikz-3dtools \begin{document} \foreach \Angle in {5,15,...,355} {\begin{tikzpicture}[3d/install view={phi=\Angle,psi=0,theta=70}, line join = round, line cap = round,same bounding box=A, c/.style={circle,fill,inner sep=1pt}, declare function={a=4;b=4;h=5;H=3;}] \path (0,0,0) coordinate (A) (a,0,0) coordinate (B) (a,b,0) coordinate (C) (0,b,0) coordinate (D) (0,0,h) coordinate (S) (0,0,H) coordinate (M); \path[3d/plane with normal={(0,0,1) through (M) named p},3d/plane with normal={(0,0,1) through (0,0,0) named p1},3d/line through={(S) and (B) named lSB},3d/line through={(S) and (C) named lSC},3d/line through={(S) and (D) named lSD}]; \path[3d/intersection of={lSB with p}] coordinate (N); \path[3d/intersection of={lSC with p}] coordinate (P); \path[3d/intersection of={lSD with p}] coordinate (Q); \path[3d coordinate ={(O') =0.5*(M) + 0.5*(P)}]; \path[3d/project={(N) on p1}] coordinate (E); \path[3d/project={(P) on p1}] coordinate (F); \path[3d/project={(Q) on p1}] coordinate (G); \path[3d/project={(O') on p1}] coordinate (O); \pgfmathsetmacro{\myr}{tddistance("(O)","(A)")} \pgfmathsetmacro{\mybarycenter}{barycenter("(A),(B),(C),(D),(S)")} \path (\mybarycenter) coordinate (O''); \tikzset{3d/polyhedron/.cd,O={(O'')},edges have complete dashes, fore/.append style={fill=none,/tikz/3d/visible}, back/.append style={fill=none,/tikz/3d/hidden}, draw face with corners={{(A)},{(B)},{(C)},{(D)}}, draw face with corners={{(S)},{(A)},{(B)}}, draw face with corners={{(S)},{(B)},{(C)}}, draw face with corners={{(S)},{(C)},{(D)}}, draw face with corners={{(S)},{(A)},{(D)}} } %\path (O) pic{3d/frustum={R=\myr,r=\myr,h=H}}; \pgfmathsetmacro{\myx}{TDunit("(0,0,1)x(nscreenx,nscreeny,nscreenz)")} \pgfmathsetmacro{\myX}{TD("\myr*(\myx)")} \path[3d coordinate/.list={{(L_1)=(O)-(\myX)}, {(L_2)=(O')-(\myX)},{(R_1)=(O)+(\myX)}, {(R_2)=(O')+(\myX)}}]; \path[save named path=bot] (O) circle[radius=\myr] (L_1) -- (L_2) (R_1) -- (R_2); \path[save named path=block,convex hull of={M,N,P,Q,S}]; \path[save named path=Block,convex hull of={A,B,C,D,S}]; \path[save named path=circ] (O') circle[radius=\myr]; \tikzset{3d/ordered paths/.cd,block/.style={draw=none}, Block/.style={draw=none}} \tikzset{3d/draw ordered paths={circ,block}} \tikzset{3d/draw ordered paths={bot,Block}} \path foreach \p/\g in {A/90,B/90,C/200,D/-90,S/0,M/0,N/0,P/0,Q/0,O'/0,E/0,F/0,G/0,O/0} {(\p)node[c]{}+(\g:2.5mm) node{$\p$}}; \end{tikzpicture}} \end{document} ```

@marmot, re: [your answer](#a1948), I have not yet get the correct rerult of the cone in this code ``` \documentclass[border=1mm,12pt,tikz]{standalone} \usetikzlibrary{3dtools,calc}% https://github.com/marmotghost/tikz-3dtools \begin{document} \foreach \Angle in {10,20,...,360} {\begin{tikzpicture}[3d/install view={phi=\Angle,psi=0,theta=70}, line join = round, line cap = round,same bounding box=A,c/.style={circle,fill,inner sep=1pt}, declare function={a=8;h=a*sqrt(2)/2;}] \path (-a/2,a/2,0) coordinate (A) (-a/2,-a/2,0) coordinate (B) (a/2,-a/2,0) coordinate (C) (a/2,a/2,0) coordinate (D) (0,0,h) coordinate (S) (0,0,0) coordinate (O); \path[3d/plane through={(A) and (B) and (S) named pABS}]; \path[3d/circumcircle center={A={(A)},B={(B)},C={(S)}}] coordinate (O'); \path[3d coordinate={(M) = 0.5*(A) + 0.5*(B)}]; \pgfmathsetmacro{\mybarycenter}{barycenter("(A),(B),(C),(D),(S)")} \path (\mybarycenter) coordinate (O''); \tikzset{3d/polyhedron/.cd,O={(O'')}, fore/.append style={fill=none,/tikz/3d/visible}, back/.append style={fill=none,/tikz/3d/hidden}, draw face with corners={{(A)},{(B)},{(C)},{(D)}}, draw face with corners={{(S)},{(A)},{(B)}}, draw face with corners={{(S)},{(B)},{(C)}}, draw face with corners={{(S)},{(C)},{(D)}}, draw face with corners={{(S)},{(A)},{(D)}} } \draw[3d/hidden] (O) -- (O') (S) -- (O); \pgfmathsetmacro{\myh}{tddistance("(O)","(O')")} \pgfmathsetmacro{\myr}{tddistance("(M)","(O')")} %\pgfmathsetmacro{\myr}{tddistance("(A)","(O')")} \tikzset{3d/define orthonormal dreibein={A={(A)},B={(B)},C={(S)}}} \path[x={(ex)},y={(ey)},z={(ez)}] (O')[3d/visible/.style={draw,very thin,cheating dash}, 3d/hidden/.style={draw=none}] pic{3d/cone={r=\myr,h=-\myh}}; \path foreach \p/\g in {A/90,B/90,C/200,D/-90,S/0,O/0,O'/90} {(\p)node[c]{}+(\g:2.5mm) node{$\p$}}; \end{tikzpicture}} \end{document} ```

@marmot, re: [your answer](#a1948), Let `M` moves on the segment `SA`, I get ![ScreenHunter 169.png](/image?hash=e0a81d3099e286caef812ab440a96a5c2ebd9fd9b74be7024a7f55f0dbf8acc0) ![ScreenHunter 170.png](/image?hash=788b5138fa17f39a5b72110d26ab1f9a55dd2b24e34ff2115531d9d5dbc823a8) ![ScreenHunter 172.png](/image?hash=e825518af1dd700662f07685b53d615ba4d6924e8bf62bdbedf95cefd089d851)

This is my code. How to correct line of cylinder? ``` \documentclass[border=1mm,12pt,tikz]{standalone} \usetikzlibrary{3dtools,calc}% https://github.com/marmotghost/tikz-3dtools \begin{document} \foreach \Angle in {150} {\begin{tikzpicture}[3d/install view={phi=\Angle,psi=0,theta=70}, line join = round, line cap = round,same bounding box=A,c/.style={circle,fill,inner sep=1pt}, declare function={a=4;b=4;h=5;H=3;}] \path (0,0,0) coordinate (A) (a,0,0) coordinate (B) (a,b,0) coordinate (C) (0,b,0) coordinate (D) (0,0,h) coordinate (S) (0,0,H) coordinate (M) ; \path[3d/plane with normal={(0,0,1) through (M) named p},3d/plane with normal={(0,0,1) through (0,0,0) named p1},3d/line through={(S) and (B) named lSB},3d/line through={(S) and (C) named lSC},3d/line through={(S) and (D) named lSD}]; \path[3d/intersection of={lSB with p}] coordinate (N); \path[3d/intersection of={lSC with p}] coordinate (P); \path[3d/intersection of={lSD with p}] coordinate (Q); \path[3d coordinate ={(O') =0.5*(M) + 0.5*(P)}]; \path[3d/project={(N) on p1}] coordinate (E); \path[3d/project={(P) on p1}] coordinate (F); \path[3d/project={(Q) on p1}] coordinate (G); \path[3d/project={(O') on p1}] coordinate (O); \pgfmathsetmacro{\myr}{tddistance("(O)","(A)")} \pgfmathsetmacro{\mybarycenter}{barycenter("(A),(B),(C),(D),(S)")} \path (\mybarycenter) coordinate (O''); \tikzset{3d/polyhedron/.cd,O={(O'')}, fore/.append style={fill=none,/tikz/3d/visible}, back/.append style={fill=none,/tikz/3d/hidden}, draw face with corners={{(A)},{(B)},{(C)},{(D)}}, draw face with corners={{(S)},{(A)},{(B)}}, draw face with corners={{(S)},{(B)},{(C)}}, draw face with corners={{(S)},{(C)},{(D)}}, draw face with corners={{(S)},{(A)},{(D)}} } \path (O) pic{3d/frustum={R=\myr,r=\myr,h=H}}; \path foreach \p/\g in {A/90,B/90,C/200,D/-90,S/0,M/0,N/0,P/0,Q/0,O'/0,E/0,F/0,G/0,O/0} {(\p)node[c]{}+(\g:2.5mm) node{$\p$}}; \end{tikzpicture}} \end{document} ```

``` \documentclass[tikz,border=3mm]{standalone} \usetikzlibrary{3dtools}% https://github.com/marmotghost/tikz-3dtools \tikzset{3d/do/.code 2 args={% \path[save named path=A_#1-A_#2] (A_#1) -- (A_#2); \pgfmathsetmacro{\tmp}{TD("0.5*(A_#1)+0.5*(A_#2)")} \pgfmathtruncatemacro{\itest}{screendepth(\tmp)<0?0:1} \ifnum\itest=0 \edef\lsto{A_#1-A_#2,\lsto} \else \edef\lsto{\lsto,A_#1-A_#2} \fi }} \begin{document} \foreach \Angle in {5,15,...,355} {\begin{tikzpicture}[3d/install view={phi=\Angle,theta=70}, same bounding box=A, line cap=butt,line join=round,c/.style={circle,fill,inner sep=1pt}, declare function={R=3;alpha=45;a=4.8; h=2*R*pow(sin(alpha),2)/cos(alpha); H=h+2*R*cos(alpha);}] \path (0,0,-H/2) coordinate (C_1) (0,0,H/2) coordinate (C_2) ({-a*cos(alpha)},{-a},{-a*sin(alpha)}) coordinate (A_1) ({-a*cos(alpha)},{a},{-a*sin(alpha)}) coordinate (A_2) ({a*cos(alpha)},{a},{a*sin(alpha)}) coordinate (A_3) ({a*cos(alpha)},{-a},{a*sin(alpha)}) coordinate (A_4); \foreach \X in {1,2} {\draw[3d/hidden,3d/screen coords,save named path=sphere\X] (C_\X) circle[radius=R];} \path (C_1) pic[3d/visible/.style={save named path=forearc1,draw=none}] {3d/circle on sphere={R=R,P={(0,0,0)}}}; \path (C_2) pic[3d/visible/.style={save named path=forearc2,draw=none}] {3d/circle on sphere={R=R,P={(0,0,0)}}}; \pgfmathsetmacro{\myx}{TDunit("(0,0,1)x(nscreenx,nscreeny,nscreenz)")} \pgfmathsetmacro{\myc}{atan2(TD("(0,1,0)o(\myx)"),TD("(1,0,0)o(\myx)"))} \tikzset{3d/define orthonormal dreibein={A={(A_3)},B={(A_2)},C={(A_1)}}} \begin{scope}[x={(ex)},y={(ey)},z={(ez)}] \pgfmathsetmacro{\myR}{R/cos(alpha)} \draw[3d/hidden] (\myc:{\myR} and R) arc[start angle=\myc,end angle=\myc-180, x radius=\myR,y radius=R]; \draw[3d/visible] (\myc:{\myR} and R) arc[start angle=\myc,end angle=\myc+180, x radius=\myR,y radius=R]; \end{scope} \pgfmathsetmacro{\myX}{TD("R*(\myx)")} \path[3d coordinate/.list={{(L_1)=(0,0,-H/2-1.2*R)-(\myX)}, {(L_2)=(0,0,H/2+1.2*R)-(\myX)},{(R_1)=(0,0,-H/2-1.2*R)+(\myX)}, {(R_2)=(0,0,H/2+1.2*R)+(\myX)}}]; \tikzset{3d/.cd,line through={(L_1) and (L_2) named l1}, line through={(R_1) and (R_2) named l2}, plane through={(A_1) and (A_2) and (A_3) named pA}} \path[3d/intersection of={l1 with pA}] coordinate (I_1) [3d/intersection of={l2 with pA}] coordinate (I_2); \path[save named path=cyl] (L_1) -- (L_2) -- (R_2) -- (R_1) -- cycle; \path[save named path=plane] (A_1) -- (A_2) -- (A_3) -- (A_4) -- cycle; \path[save named path=u1] (I_1) -- (L_2); \path[save named path=u2] (I_2) -- (R_2); \path[save named path=d1] (I_1) -- (L_1); \path[save named path=d2] (I_2) -- (R_1); \tikzset{3d/ordered paths/sphere1/.style={draw=none}, 3d/ordered paths/sphere2/.style={draw=none}, 3d/ordered paths/plane/.style={draw=none}, 3d/ordered paths/cyl/.style={draw=none}} \pgfmathtruncatemacro{\itest}{screendepth(1,0,0)<0?0:1} \ifnum\itest=0 \tikzset{3d/draw ordered paths={d1,d2,sphere1,forearc1,plane,sphere2,forearc2,u1,u2}} \else \tikzset{3d/draw ordered paths={u1,u2,sphere2,forearc2,plane,sphere1,forearc1,d1,d2}} \fi \edef\lsto{cyl} \tikzset{3d/do/.list={12,23,34,41}} \tikzset{3d/draw ordered paths/.expanded=\lsto} \path foreach \p/\g in {C_1/-90,C_2/90,L_1/-90,L_2/90,R_1/-90,R_2/90,I_1/180,I_2/0}{ (\p)node[c]{}+(\g:2.5mm) node{$\p$}}; \end{tikzpicture}} \end{document} ``` ![ani.gif](/image?hash=075640b78938d577b7e0de7756bfb7c6a0cd4cf763178d5774da9cc431ad7dcd)

I'll try to do that when I come across interesting examples. (In hindsight it might have been better if everything like intersections would have computed in physical coordinates so that the user does not have to care about using different frames. Overall, things are rather limited because of Ti*k*Z behavior of throwing the third component away.)

Yes, of course. LaTeX isn't really made for such things. This is not a CAD program. (But with the new additions it can transform into different frames and invert the transformation so that the user can define paths and other constructions in a frame that is convenient, and then transfer them to other frames.)

I made several updates to `3dtools`. Obviously it cannot compete with GeoSpace. But now one can determine the local coordinates of recorded physical coordinates. ``` \documentclass[tikz,border=3mm]{standalone} \usetikzlibrary{calc,3dtools}% https://github.com/marmotghost/tikz-3dtools \begin{document} \begin{tikzpicture}[3d/install view={phi=120,theta=60},line cap=butt,line join=round,c/.style={circle,fill,inner sep=1pt}, declare function={a=3;}] \path[3d/record physical components] (a,-a,-a) coordinate (A) (a,a,-a) coordinate (B) (-a,a,-a) coordinate (C) (-a,-a,-a) coordinate (D) (a,-a,a) coordinate (E) (a,a,a) coordinate (F) (-a,a,a) coordinate (G) (-a,-a,a) coordinate (H) (0,0,0) coordinate (O); \tikzset{3d/polyhedron/.cd,O={(O)}, back/.style={3d/polyhedron/complete dashes,fill=none}, fore/.style={3d/visible,fill=none}, %draw face with corners={{(B)},{(C)},{(G)},{(F)}}, draw face with corners={{(D)},{(C)},{(G)},{(H)}}, draw face with corners={{(E)},{(F)},{(G)},{(H)}}, draw face with corners={{(A)},{(B)},{(C)},{(D)}}, %draw face with corners={{(A)},{(B)},{(F)},{(E)}}, draw face with corners={{(A)},{(E)},{(H)},{(D)}} } \path[3d/record physical components,3d/circumcircle center={A={(A)},B={(C)},C={(F)}}] coordinate (I); \pgfmathsetmacro{\R}{sqrt(TD("(I)-(A)o(I)-(A)"))} \pgfmathsetmacro{\h}{sqrt(TD("(I)-(H)o(I)-(H)"))} \tikzset{3d/define orthonormal dreibein={A={(A)},B={(C)},C={(F)}}} \begin{scope}[x={(ex)},y={(ey)},z={(ez)},3d/record physical components] \path[3d/cone/inner/.style={save named path=base,draw=none}, 3d/cone/outer/.style={draw=none}] (I) pic{3d/cone={r=\R,h=-\h}}; \pgfmathsetmacro{\myey}{TDunit("(0,0,1)x(nscreenx,nscreeny,nscreenz)")}% \pgfmathsetmacro{\sdtip}{screendepth(0,0,\h)} \pgfmathsetmacro{\aspectangle}{atan2(\sdtip,sqrt(\h*\h-\sdtip*\sdtip))} \pgfmathsetmacro{\alphacrit}{acos(tan(\aspectangle)*\R/\h)} \path (0,0,{tan(\aspectangle)}) coordinate (-tmpex) (\myey) coordinate (-tmpey); \pgfmathsetmacro{\mya}{-1*cos(\alphacrit)*\R} \pgfmathsetmacro{\myb}{sin(\alphacrit)*\R} \pgfmathsetmacro{\Ix}{TD("(I)o(ex)")} \pgfmathsetmacro{\Iy}{TD("(I)o(ey)")} \pgfmathsetmacro{\Iz}{TD("(I)o(ez)")} \pgfmathsetmacro{\myP}{TD("{(\Ix,\Iy,\Iz)+\mya*(-tmpex)+\myb*(-tmpey)}")} \path (\myP) coordinate (P_1); \pgfmathsetmacro{\myP}{TD("{(\Ix,\Iy,\Iz)+\mya*(-tmpex)-\myb*(-tmpey)}")} \path (\myP) coordinate (P_2); \end{scope} \pgfmathsetmacro{\Plocal}{TDlocal("P_1")} \path (\Plocal) coordinate (P_1'); \pgfmathsetmacro{\Plocal}{TDlocal("P_2")} \path (\Plocal) coordinate (P_2'); \path[save named path=pABCD] (A) -- (B) -- (C) -- (D); \foreach \X/\Y in {A/E,C/G,A/B,B/F,F/E,F/G,B/C} {\path[save named path=l\X\Y] (\X) -- (\Y);} \tikzset{3d/ordered paths/pABCD/.style={draw=none}, 3d/draw ordered paths={lAE,lCG,base,pABCD,lAB,lBF,lFE,lFG,lBC}} \tikzset{3d/.cd,line through={(P_1') and (H) named lHP1}, line through={(P_2') and (H) named lHP2}, plane through={(A) and (B) and (E) named pABF}, plane through={(B) and (C) and (F) named pBCF}} \path[3d/intersection of={lHP1 with pABF}] coordinate (P_1''); \path[3d/intersection of={lHP2 with pBCF}] coordinate (P_2''); \path[3d/hidden] (P_1'') edge (H) (P_2'') edge (H); \path[3d/visible] (P_1'') edge (P_1') (P_2'') edge (P_2'); \draw [3d/hidden] (H) -- (I); \path foreach \p/\g in {A/-90,B/90,C/0,D/0,E/0,F/0,G/0,H/0,I/0,% P_1'/-90,P_2'/-90,P_1''/-90,P_2''/-90}{ (\p)node[c]{}+(\g:2.5mm) node{$\p$}}; \end{tikzpicture} \end{document} ```

I cannot make any judgment, also because I do not know GeoSpace, but Ti*k*Z can only do what it is programmed to do. The more complex the ingredients become, the less straightforward it is to program Ti*k*Z correctly. This is not to say that one cannot compute the relevant points. One can, but one has to sit down and do it.

Yes, as expected it does not magically draw some of the lines dashed. To achieve this, you'd need to compute the intersections between the straight boundaries of the cone and the cube. This is easy once you know the 3d coordinates at which these lines attach to the base. The computation of the latter is not that easy.

@marmot, re: [your answer](#a1948), I tried for second picture ``` \documentclass[tikz,border=3mm]{standalone} \usetikzlibrary{calc,3dtools}% https://github.com/marmotghost/tikz-3dtools \begin{document} \begin{tikzpicture}[3d/install view={phi=120,theta=70},line cap=butt,line join=round,c/.style={circle,fill,inner sep=1pt}, declare function={a=3;}] \path (a,-a,-a) coordinate (A) (a,a,-a) coordinate (B) (-a,a,-a) coordinate (C) (-a,-a,-a) coordinate (D) (a,-a,a) coordinate (E) (a,a,a) coordinate (F) (-a,a,a) coordinate (G) (-a,-a,a) coordinate (H) (0,0,0) coordinate (O) ; \tikzset{3d/polyhedron/.cd,O={(O)}, back/.style={3d/polyhedron/complete dashes,fill=none}, fore/.style={3d/visible,fill=none},draw face with corners={{(B)},{(C)},{(G)},{(F)}}, draw face with corners={{(D)},{(C)},{(G)},{(H)}}, draw face with corners={{(E)},{(F)},{(G)},{(H)}}, draw face with corners={{(A)},{(B)},{(C)},{(D)}}, draw face with corners={{(A)},{(B)},{(F)},{(E)}}, draw face with corners={{(A)},{(E)},{(H)},{(D)}} } \path[3d/circumcircle center={A={(A)},B={(C)},C={(F)}}] coordinate (I); \pgfmathsetmacro{\R}{sqrt(TD("(I)-(A)o(I)-(A)"))} \pgfmathsetmacro{\h}{sqrt(TD("(I)-(H)o(I)-(H)"))} \tikzset{3d/define orthonormal dreibein={A={(A)},B={(C)},C={(F)}}} \path[x={(ex)},y={(ey)},z={(ez)}] (I) pic{3d/cone={r=\R,h=-\h}}; \draw [3d/hidden] (H) -- (I); \path foreach \p/\g in {A/-90,B/90,C/0,D/0,E/0,F/0,G/0,H/0,I/0}{(\p)node[c]{}+(\g:2.5mm) node{$\p$}}; \end{tikzpicture} \end{document} ```

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