Multipole Calculator
Real-time computation of quadrupole (Q) and octupole (O) moments from 3D geometry.
Computed Moments
| Object |
Q_xx |
Q_yy |
Q_zz |
O_zzz |
| Pyramid |
-- |
-- |
-- |
-- |
| Pinecone |
-- |
-- |
-- |
-- |
Normalized (max |Q_ii| = 1)
| Object |
q_xx |
q_yy |
q_zz |
o_zzz |
| Pyramid |
-- |
-- |
-- |
-- |
| Pinecone |
-- |
-- |
-- |
-- |
Coupling Products
| Product |
Value |
Meaning |
| Q_pyr · Q_pin |
-- |
Shape correlation |
| O_pyr · O_pin |
-- |
Orientation coupling |
Q_ij = ∫(3x_i x_j - r²δ_ij)ρ dV
O_ijk: rank-3, flips sign under 180° rotation
Q·Q > 0 = similar shapes |
Q·Q < 0 = dual shapes
Drag to rotate | Scroll to zoom | Moments computed from mesh geometry in real-time