Example: ConvexPGL ⮵
Volume A: {{volumeA.toFixed(3)}}
Transform :
In isotropic position:

Show centered at
Conjecture : The normalized Binet is not inside the normalized Legendre of the dual (at critical ? isotropic ? position).
VA*VD={{volumeAD.toFixed(4)}}
-12 x ({{volumeD.toFixed(4)}})
{{z2A[0].toFixed(4)}} {{z2A[2].toFixed(4)}}
{{z2A[1].toFixed(4)}} {{z2A[3].toFixed(4)}}
(Id - 16/{{volumeAD.toFixed(4)}}
{{z2D[0].toFixed(4)}} {{z2D[2].toFixed(4)}}
{{z2D[1].toFixed(4)}} {{z2D[3].toFixed(4)}}
{{z2A[0].toFixed(4)}} {{z2A[2].toFixed(4)}}
{{z2A[1].toFixed(4)}} {{z2A[3].toFixed(4)}}
)
({{(-12*volumeD).toFixed(4)}})
{{z2A[0].toFixed(4)}} {{z2A[2].toFixed(4)}}
{{z2A[1].toFixed(4)}} {{z2A[3].toFixed(4)}}
{{factorDA[0].toFixed(4)}} {{factorDA[2].toFixed(4)}}
{{factorDA[1].toFixed(4)}} {{factorDA[3].toFixed(4)}}
=
{{hessianDA[0].toFixed(4)}} {{hessianDA[2].toFixed(4)}}
{{hessianDA[1].toFixed(4)}} {{hessianDA[3].toFixed(4)}}

tr(
{{factorDA[0].toFixed(4)}} {{factorDA[2].toFixed(4)}}
{{factorDA[1].toFixed(4)}} {{factorDA[3].toFixed(4)}}
)= {{(factorDA[0]+factorDA[3]).toFixed(4)}},
tr(
{{hessianDA[0].toFixed(4)}} {{hessianDA[2].toFixed(4)}}
{{hessianDA[1].toFixed(4)}} {{hessianDA[3].toFixed(4)}}
) = {{(hessianDA[0]+hessianDA[3]).toFixed(4)}},  det(
{{hessianDA[0].toFixed(4)}} {{hessianDA[2].toFixed(4)}}
{{hessianDA[1].toFixed(4)}} {{hessianDA[3].toFixed(4)}}
) = {{(hessianDA[0]*hessianDA[3] - hessianDA[1]*hessianDA[2]).toFixed(4)}}
Volume D: {{volumeD.toFixed(3)}}
Transform :

Show centered at

Settings

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  • {{ useCtrl ? "Ctrl": "Cmd"}}+A => select/deselect it;