#640 - Check for empty intersection of compact set with Hyperplane #650
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mforets
reviewed
Sep 22, 2018
src/is_intersection_empty.jl
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| ### Output | ||
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| * If `witness` option is deactivated: `true` iff ``P ∩ Q = ∅`` |
mforets
reviewed
Sep 22, 2018
src/is_intersection_empty.jl
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| witness::Bool=false | ||
| )::Union{Bool, Tuple{Bool,Vector{N}}} where N<:Real | ||
| sv_left = σ(-hp.a, X) | ||
| if -dot(sv_left, -hp.a) <= hp.b |
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maybe use ρ(d, X) directly. for eventual optimizations #600.
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I need the support vector below anyway.
mforets
reviewed
Sep 22, 2018
| left and right, and then take the intersection of the line with the hyperplane. | ||
| We follow | ||
| [this algorithm](https://en.wikipedia.org/wiki/Line%E2%80%93plane_intersection#Algebraic_form) | ||
| for the line-hyperplane intersection. |
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Nice idea!
I was thinking how can we use it outside this function but then realized we don't have "hyperlines". See #652.
mforets
reviewed
Sep 22, 2018
src/is_intersection_empty.jl
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| point_hp = an_element(hp) | ||
| point_line = sv_left | ||
| dir_line = sv_right - sv_left | ||
| d = dot((point_hp - point_line), hp.a) / dot(dir_line, hp.a) |
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maybe use normal_hp or normal_hyperplane here and above
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i was suggesting to give a variable name to hp.a. for readability of the code. not a big deal.
mforets
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Closes #640.