Poincare Dual
group dual
The Poincaré Dual of an element is the "subspace complement" of the argument with respect to the pseudoscalar in the exterior algebra. In practice, it is a relabeling of the coordinates to their dual-coordinates and is used most often to implement a "join" operation in terms of the exterior product of the duals of each operand.
Ex: The dual of the point \(\mathbf{e}_{123} + 3\mathbf{e}_{013} - 2\mathbf{e}_{021}\) (the point at \((0, 3, -2)\)) is the plane \(\mathbf{e}_0 + 3\mathbf{e}_2 - 2\mathbf{e}_3\).
Summary
| Members | Descriptions |
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public KLN_INLINE point KLN_VEC_CALL operator!(plane in) noexcept |
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public KLN_INLINE plane KLN_VEC_CALL operator!(point in) noexcept |
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public KLN_INLINE line KLN_VEC_CALL operator!(line in) noexcept |
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public KLN_INLINE branch KLN_VEC_CALL operator!(ideal_line in) noexcept |
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public KLN_INLINE ideal_line KLN_VEC_CALL operator!(branch in) noexcept |
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public KLN_INLINE dual KLN_VEC_CALL operator!(dual in) noexcept |