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Generalize check if point is in hyperplane #3304

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Apr 17, 2023
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Generalize check if point is in hyperplane #3304

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1d48bc8
generalize check if point is in hyperplane
Apr 17, 2023
c9e775b
Update test/Sets/Tetrahedron.jl
mforets Apr 17, 2023
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12 changes: 7 additions & 5 deletions src/Sets/Tetrahedron.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -12,7 +12,7 @@ Type that represents a tetrahedron in vertex representation.
### Examples

A tetrahedron can be constructed by passing the list of vertices.
The following builds the tetrahedron with edge length 2 from the [wikipedia page Tetrahedron](https://en.wikipedia.org/wiki/Tetrahedron):
The following builds the tetrahedron with edge length 2 from the [wikipedia page Tetrahedron](https://en.wikipedia.org/wiki/Tetrahedron):

```jldoctest
julia> vertices = [[1, 0, -1/sqrt(2)], [-1, 0, -1/sqrt(2)], [0, 1, 1/sqrt(2)], [0, -1, 1/sqrt(2)]];
Expand Down Expand Up @@ -110,20 +110,22 @@ function ∈(x::AbstractVector, T::Tetrahedron)
same_side(v[2], v[3], v[4], v[1], x)
end

# Return `true` iff point `x` lies in the same half-space as `v4` with respect to the hyperplane determined by `v1`, `v2` and `v3`.
# Return `true` iff point `x` lies in the same half-space as `v4` with respect to the hyperplane `H` determined by `v1`, `v2` and `v3`.
function same_side(v1, v2, v3, v4, x)
normal = cross(v2 - v1, v3 - v1)
dotv4 = dot(normal, v4 - v1)
dotx = dot(normal, x - v1)
return signbit(dotv4) == signbit(dotx)
# If the point `x` lies in `H` then `dotx` is zero.
return signbit(dotv4) == signbit(dotx) || isapproxzero(dotx)
end

function rand(::Type{Tetrahedron}; N::Type{<:Real}=Float64, rng::AbstractRNG=GLOBAL_RNG, seed::Union{Int,Nothing}=nothing)
function rand(::Type{Tetrahedron}; N::Type{<:Real}=Float64, rng::AbstractRNG=GLOBAL_RNG,
seed::Union{Int,Nothing}=nothing)
P = rand(VPolytope; N=N, dim=3, rng=rng, seed=seed, num_vertices=4)
vertices = P.vertices
return Tetrahedron(vertices)
end

function constraints_list(T::Tetrahedron)
constraints_list(convert(VPolytope, T))
return constraints_list(convert(VPolytope, T))
end
9 changes: 7 additions & 2 deletions test/Sets/Tetrahedron.jl
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@@ -1,6 +1,7 @@
for N in [Float64, Float32, Rational{Int}]
# constructor
vertices = [N[1, 0, -1/sqrt(2)], N[-1, 0, -1/sqrt(2)], N[0, 1, 1/sqrt(2)], N[0, -1, 1/sqrt(2)]]
vertices = [N[1, 0, -1 / sqrt(2)], N[-1, 0, -1 / sqrt(2)], N[0, 1, 1 / sqrt(2)],
N[0, -1, 1 / sqrt(2)]]
T = Tetrahedron(vertices)
@test eltype(T) == N
@test dim(T) == 3
Expand All @@ -10,11 +11,15 @@ for N in [Float64, Float32, Rational{Int}]
@test Tmat == T

# suport vector
@test σ(ones(3), T) == N[0, 1, 1/sqrt(2)]
@test σ(ones(3), T) == N[0, 1, 1 / sqrt(2)]

# membership
@test zeros(N, 3) ∈ T

# is_polyhedral
@test is_polyhedral(T)

# LazySets#3303
T = Tetrahedron([N[0, 0, 0], N[0, 1, 0], N[1, 0, 0], N[1, 0, 1]])
@test zeros(N, 3) ∈ T
end