Rotating an ellipsoid's demagnetizing tensor exactly reproduces the single-axis force and torque formulas, and an SVD-based area-projection approximation works reasonably well (R^2 = 0.86 to 0.97).
Demagnetizing Factors for Rectangular Prisms,
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On the Role of Demagnetizing Tensors in Arbitrary Orientations of General Ellipsoid: Implications for MRI Safety Assessment
Rotating an ellipsoid's demagnetizing tensor exactly reproduces the single-axis force and torque formulas, and an SVD-based area-projection approximation works reasonably well (R^2 = 0.86 to 0.97).