Regressive Product
group reg
The regressive product is implemented in terms of the exterior product. Given multivectors \(\mathbf{a}\) and \(\mathbf{b}\), the regressive product \(\mathbf{a}\vee\mathbf{b}\) is equivalent to \(J(J(\mathbf{a})\wedge J(\mathbf{b}))\). Thus, both meets and joins reside in the same algebraic structure.
Joining two points
kln::point p1{x1, y1, z1};
kln::point p2{x2, y2, z2};
// l contains both p1 and p2.
kln::line l = p1 & p2;
Joining a line and a point
kln::point p1{x, y, z};
kln::line l2{mx, my, mz, dx, dy, dz};
// p2 contains both p1 and l2.
kln::plane p2 = p1 & l2;
Summary
| Members | Descriptions |
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public line KLN_VEC_CALL operator&(point a,point b) noexcept |
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public plane KLN_VEC_CALL operator&(point a,line b) noexcept |
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public plane KLN_VEC_CALL operator&(line b,point a) noexcept |
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public plane KLN_VEC_CALL operator&(point a,branch b) noexcept |
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public plane KLN_VEC_CALL operator&(branch b,point a) noexcept |
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public plane KLN_VEC_CALL operator&(point a,ideal_line b) noexcept |
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public plane KLN_VEC_CALL operator&(ideal_line b,point a) noexcept |
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public dual KLN_VEC_CALL operator&(plane a,point b) noexcept |
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public dual KLN_VEC_CALL operator&(point a,plane b) noexcept |