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Bundle of Planes

Definition

A set of planes sharing a point in common. For planes specified in Hessian normal form, a bundle of planes can therefore be specified as ((n_1)^^ x + p_1) + λ_1((n_2)^^ x + p_2) + λ_3((n_3)^^ x + p_3) = 0, where λ_1, λ_2 are free real parameters. This can be made more symmetrical by introducing homogeneous parameters λ_1 = μ_2/μ_1 and λ_2 = μ_3/μ_1 to obtain μ_1((n_1)^^ x + p_1) + μ_2((n_2)^^ x + p_2) + μ_3((n_3)^^ x + p_3) = 0 .

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