SphereCircumscribed::usage="Given the vertices of a tetrahedron, the circumcenter, barycenter, the point of Monge and the circumscribed sphere are obtained. References: Function repository of Wolfram Mathematica; Personal.";
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BarycenterCircumcenterMonge[tet={{ax_,ay_,az_},{bx_,by_,bz_},{cx_,cy_,cz_},{dx_,dy_,dz_}}]:=Module{},prueba=Det[{{1,ax,ay,az},{1,bx,by,bz},{1,cx,cy,cz},{1,dx,dy,dz}}];Ifprueba==0,Print[PasteButton["It's not a tetrahedron"]],ρ=ResourceFunction["Monge"][tet];G=;Cir=2G-ρ[[1]];r=Norm[Cir-{ax,ay,az}];s=Grid[{{Barycenter(Black),Monge(Green),Circumcenter(Red),Circumradius},{G,ρ[[1]],Cir,r}},FrameAll];Print[s];Show[{Graphics3D[{Tube[#]&/@Subsets[tet,{2}],Green,Sphere[ρ[[1]],0.1],Opacity[.2],Red,Polygon/@Subsets[tet,{3}],Yellow,Opacity[.2],ρ[[2]]}],Graphics3D[{Blue,Opacity[0.1],Sphere[Cir,r]}],Graphics3D[{Red,Ball[Cir,0.1]}],Graphics3D[{Black,Ball[G,0.1]}],Graphics3D[{Black,Dashed,Thick,Line[{Cir,ρ[[1]]}]}]},AxesLabel->(Style[#,15,Blue]&/@{"X","Y","Z"}),AxesOrigin{0,0,0},AxesTrue,BoxedFalse,BoxRatiosAutomatic,PlotRangeAll]
{ax,ay,az}+{bx,by,bz}+{cx,cy,cz}+{dx,dy,dz}
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Example 1:
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BarycenterCircumcenterMonge[tet={{-1,0,3},{1,-1,1},{2,0,-2},{-2,-2,1}}]
Barycenter | Monge | Circumcenter | Circumradius |
0,- 3 4 3 4 | 61 38 63 19 43 19 | - 61 38 69 38 29 38 | 25739 38 |
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Example 2:
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BarycenterCircumcenterMonge[tet={{1,1,1},{3,6,0},{0,3,2},{2,3,7}}]
Barycenter | Monge | Circumcenter | Circumradius |
3 2 13 4 5 2 | - 159 118 201 59 217 118 | 513 118 365 118 373 118 | 282059 118 |
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Example 3:
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BarycenterCircumcenterMonge[tet={{1,1,1},{1,-1,-1},{-1,1,-1},{-1,-1,1}}]
Barycenter | Monge | Circumcenter | Circumradius |
{0,0,0} | {0,0,0} | {0,0,0} | 3 |
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Example 4:
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BarycenterCircumcenterMonge[tet={{1,0,0},{1,-1,-1},{-1,1,-1},{-1,-1,1}}]
Barycenter | Monge | Circumcenter | Circumradius |
0,- 1 4 1 4 | 1 2 | - 1 2 1 2 1 2 | 11 2 |
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