#5 - Implement hrep from vrep for VPolygon #376

schillic · 2018-07-08T20:34:15Z

Closes #5.

docs
tests
manual handling of 2-vertices case (the current solution is unbounded)

schillic · 2018-07-08T20:35:05Z

using LazySets
points_all = [[0.9,0.2], [0.4,0.6], [0.2,0.1], [0.1,0.3], [0.3,0.28]]
for i in [0, 1, 2, 5]
    points = i == 0 ? Vector{Vector{Float64}}() : points_all[1:i]
    V = VPolygon(points, apply_convex_hull=i > 0)
    H1 = tohrep(V)
    H2 = HPolygon{Float64}() # check that constraints are sorted correctly
    for c in H1.constraints
        addconstraint!(H2, c)
    end
    println(V)
    println(H1)
    println(H1.constraints == H2.constraints)
    println()
end

Output:

LazySets.VPolygon{Float64}(Array{Float64,1}[])
LazySets.HPolygon{Float64}(LazySets.HalfSpace{Float64}[])
true

LazySets.VPolygon{Float64}(Array{Float64,1}[[0.9, 0.2]])
LazySets.HPolygon{Float64}(LazySets.HalfSpace{Float64}[LazySets.HalfSpace{Float64}([1.0, 1.0], 1.1), LazySets.HalfSpace{Float64}([-1.0, 0.0], -0.9), LazySets.HalfSpace{Float64}([0.0, -1.0], -0.2)])
true

LazySets.VPolygon{Float64}(Array{Float64,1}[[0.9, 0.2], [0.4, 0.6]])
LazySets.HPolygon{Float64}(LazySets.HalfSpace{Float64}[LazySets.HalfSpace{Float64}([0.4, 0.5], 0.46), LazySets.HalfSpace{Float64}([-0.5, 0.4], 0.04), LazySets.HalfSpace{Float64}([-0.4, -0.5], -0.46), LazySets.HalfSpace{Float64}([0.5, -0.4], 0.37)])
true

LazySets.VPolygon{Float64}(Array{Float64,1}[[0.1, 0.3], [0.2, 0.1], [0.9, 0.2], [0.4, 0.6]])
LazySets.HPolygon{Float64}(LazySets.HalfSpace{Float64}[LazySets.HalfSpace{Float64}([0.4, 0.5], 0.46), LazySets.HalfSpace{Float64}([-0.3, 0.3], 0.06), LazySets.HalfSpace{Float64}([-0.2, -0.1], -0.05), LazySets.HalfSpace{Float64}([0.1, -0.7], -0.05)])
true

mforets · 2018-07-10T11:01:02Z

Before I add the tests, what do you think?

i didn't check the details yet, but i would suppose that we want to exploit that fact that a VPolygon has its vertices ordered. Hence we can go through the vertices in, say, counter clockwise-order and for each pair of vertices add the corresponding constraint.

schillic · 2018-07-10T11:03:08Z

i would suppose that we want to exploit that fact that a VPolygon has its vertices ordered

Yes, I do that. Even better, I start with the vertex pair that corresponds to the first constraint in the resulting HPolygon. This avoids additional sorting.

schillic · 2018-07-20T17:36:49Z

Thanks for the documentation.

we can equally choose q instead of p

No, that is why it is called halfspace_left 😉

mforets · 2018-07-20T19:10:27Z

src/HalfSpace.jl

+"""
+function halfspace_left(p::AbstractVector{N},
+                        q::AbstractVector{N})::HalfSpace{N} where {N<:Real}
+    @assert p != q "the points must not be equal"


this notion of "left", i think, only makes sense in 2D, but HalfSpace is general so i think we should make this check here and throw an error otherwise. i can add it and see if you agree.

EDIT: Forget it, this was silly.

Do you think we should also add a version from a LineSegment (which is just the one-liner which unwraps the two vertices and calls this function here)?

Should we move the function to AbstractHPolygon instead?

Do you think we should also add a version from a LineSegment (which is just the one-liner which unwraps the two vertices and calls this function here)?

sounds good, i'll do in the next push.

also and while we are at this, add halfspace_right.

Should we move the function to AbstractHPolygon instead?

i think that in HalfSpace.jl is fine.

mforets · 2018-07-20T19:32:53Z

No, that is why it is called halfspace_left

My formulation was not the best, my point being that for choosing b (not a) one can pick either p or q, since dot(p, a) = dot(q, a) for the given a.

mforets · 2018-07-20T20:06:05Z

That said, i think that it looks better without that part.

mforets · 2018-07-20T20:23:29Z

src/convert.jl

+    line_dir = -line_dir
+    addconstraint!(H, LinearConstraint(line_dir, dot(L.p, line_dir)))
+    return H
+end


mforets · 2018-07-20T20:58:53Z

I wonder how does this tohrep function compare to the (for me simpler):

(EDIT)

constraints_list = vcat([halfspace_left(P.vertices_list[i], P.vertices_list[i+1]) for i in 1:length(P.vertices_list)-1],
                        [halfspace_left(P.vertices_list[end], P.vertices_list[1])])
return HPolygon(constraints_list)

schillic · 2018-07-21T04:48:57Z

src/HalfSpace.jl

+### Examples
+
+The left half-space of the "east" and "west" directions in two-dimensions are the
+upper and lower half-spaces:


schillic · 2018-07-21T05:00:16Z

I wonder how does this tohrep function compare to the (for me simpler):

constraints_list = vcat([halfspace_left(P.vertices_list[i], P.vertices_list[i+1]) for i in 1:length(P.vertices_list)-1],
                       [halfspace_left(P.vertices_list[end], P.vertices_list[1])])
return HPolygon(constraints_list)

Good thinking, but you need to start at the index that was found before (i in my code). Basically it should do what you did but with three lists and different start index. Maybe like this (not tested):

vl = P.vertices_list
constraints_list = vcat(
    [halfspace_left(vl[j], vl[j+1]) for j in i:length(vl)-1],
    [halfspace_left(vl[end], vl[1])],
    [halfspace_left(vl[j], vl[j+1]) for j in 1:i-1])
return HPolygon(constraints_list)

My usual way of thinking is to write the code myself, but I prefer your version. Do you want to add it?

mforets · 2018-07-21T20:17:05Z

My usual way of thinking is to write the code myself, but I prefer your version. Do you want to add it?

ok. it took me a while to understand what was wrong with my version 😄

schillic · 2018-07-22T20:24:04Z

I just realized that this PR conflicts with #386. We should merge only one of them (the order does not matter) and then rebase and replace the missing vertices_list.

schillic

thanks

schillic · 2018-07-22T20:35:40Z

src/HalfSpace.jl

+function halfspace_right(p::AbstractVector{N},
+                         q::AbstractVector{N})::HalfSpace{N} where {N<:Real}
+    return halfspace_right(q, p)
+end


schillic · 2018-07-22T20:35:48Z

src/LineSegment.jl

+
+halfspace_left(L::LineSegment) = halfspace_left(L.p, L.q)
+
+halfspace_right(L::LineSegment) = halfspace_right(L.p, L.q)


schillic · 2018-07-22T20:41:01Z

The build fail with Julia v0.6 is the same as in #386. It could also be a recent bug in IntervalArithmetic.jl that only occurs with v6.0?
EDIT: Could be this... but then why does it work with v0.6.1? Below they also announce that v0.6 support will vanish with the next release, so maybe they already broke it... 😟

mforets · 2018-07-22T20:49:28Z

The build fail with Julia v0.6 is the same as in #386. It could also be a recent bug in IntervalArithmetic.jl that only occurs with v6.0?

Hmm in my machine the tests pass (v0.6.1) and

julia> Pkg.installed("IntervalArithmetic")
v"0.13.0+"

mforets · 2018-07-22T21:02:09Z

Hmm we can always pick the version that we use in REQUIRE, such as v0.13.

Sooner or later we should also switch to 0.7 .. 1.0

schillic · 2018-07-22T21:02:27Z

Here (v0.6.2) they pass as well (I also updated the package). Note that the Travis builds for v0.6.1 and v0.6.1 pass; only v0.6 fails. The thing is that as soon as we merge, the green badge on the front page will become red 😞

schillic · 2018-07-25T18:58:51Z

Note to myself: I want to do this before merging.
EDIT: done

schillic requested a review from mforets July 8, 2018 20:34

schillic force-pushed the schillic/5 branch from fa09c62 to 82b08a8 Compare July 9, 2018 20:06

schillic changed the title ~~[WIP #5] Implement hrep from vrep for VPolygon~~ #5 - Implement hrep from vrep for VPolygon Jul 11, 2018

mforets reviewed Jul 20, 2018

View reviewed changes

src/convert.jl

line_dir = -line_dir

addconstraint!(H, LinearConstraint(line_dir, dot(L.p, line_dir)))

return H

end

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mforets Jul 20, 2018

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well done!

schillic commented Jul 21, 2018

View reviewed changes

schillic commented Jul 22, 2018

View reviewed changes

schillic force-pushed the schillic/5 branch from e1355b4 to d90f229 Compare July 25, 2018 18:49

schillic added 7 commits July 25, 2018 21:36

change load order

6dd457d

conversion from line segment to half-space

7ed293d

conversion from singleton to HPolygon

4f01383

conversion from line segment to HPolygon

51b69c1

tohrep from VPolygon

3176719

add docs

158455d

generalize unit tests

d87b8f9

schillic and others added 8 commits July 25, 2018 21:40

add unit tests for tohrep

eb40247

minor add-on for halfspace_left Algorithm docstring

9a9c6f9

fix docstring call

884a35e

add 2D assertion and update docstring

30824a2

add algorithm text

d6af0f0

use XX_hull in VPolygon tohrep

5247e5c

add halfspace_right and function for LineSegment

85b6b32

add spaces and docs

c42b8a4

schillic force-pushed the schillic/5 branch from d90f229 to c42b8a4 Compare July 25, 2018 19:41

schillic merged commit 46b8d58 into master Jul 26, 2018

schillic deleted the schillic/5 branch July 26, 2018 04:37

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#5 - Implement hrep from vrep for VPolygon #376

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		halfspace_left(L::LineSegment) = halfspace_left(L.p, L.q)

		halfspace_right(L::LineSegment) = halfspace_right(L.p, L.q)

#5 - Implement hrep from vrep for VPolygon #376

#5 - Implement hrep from vrep for VPolygon #376

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