SimplexCellLists WIP

This Julia package accelerates computations on all pairs of 3D points, line segments, and triangles within a cutoff distance.

This package is largely inspired by CellListMap.jl.

However, there is no support for periodic boundary conditions, 2D systems, or types other than Float32.

See CellListMap.jl if you want these features, or higher performance on systems without triangles and line segments.

Setup

• Simplex{N} is SVector{N, SVector{3, Float32}}
• Point is Simplex{1}
• Line is Simplex{2}
• Triangle is Simplex{3}

There are multiple algorithms that implement the SimplexCellList abstract type interface. Currently:

• Naive: A simple SimplexCellList with no extra options that uses double for loops.
• Painter: A grid is painted with element ids based on a max range. Based on the ideas in cytosim.

Let T be a concrete subtype of SimplexCellList

Constructor

Construct T:

T(numpointgroups::Integer, numlinegroups::Integer, numtrianglegroups::Integer; kwargs...)::T

Where numpointgroups is the number of groups of points, numlinegroups is the number of groups of lines, and numtrianglegroups is the number of groups of triangles.

kwargs are options specific for T

setElements!

Reset the elements stored in s in batch:

setElements!(s::T, points, lines, triangles)::Nothing

Where points, lines and triangles are collections of collections of objects convertible to Point, Line, and Triangle respectively.

For example, each collection in points is a group of points that can be mapped over independently from, or together with, other groups.

Added elements will have a group index and element index based on the order of the inputs. The first group in each type has group index 1, and the first element in each group has element index 1.

addElement!

Add a new element to s, and return its element index:

addElement!(s::T, group_idx::Integer, element::Simplex{N})::Int32

The new element will be pushed to the end of the specified group.

deactivate!

Deactivate an existing element in s

deactivate!(s::T, group_idx::Integer, element_idx::Integer, element_type::Type{Simplex{N}})::Nothing

Inactive elements are not mapped over. Elements are active by default.

activate!

Re-activate an existing element in s

activate!(s::T, group_idx::Integer, element_idx::Integer, element_type::Type{Simplex{N}})::Nothing

Inactive elements are not mapped over. Elements are active by default.

isActive

Return if an existing element in s is active.

isActive(s::T, group_idx::Integer, element_idx::Integer, element_type::Type{Simplex{N}})::Bool

Inactive elements are not mapped over. Elements are active by default.

Mapping

The following functions allow mapping a custom function over pairs of simplexes within some cutoff.

Mapped function f

The function f should have the same form as used in CellListMap.jl.

i is the element index of simplex x, j is the element index of simplex y.

d2 is an approximate Float32 squared distance between x and y.

Except here x and y are Simplex{N}, Simplex{M}

    function f(x,y,i,j,d2,output)
        # update output
        return output
    end

The order in which pairs of elements in range are mapped is implementation dependent.

The elements passed to f may be slightly different from the elements added to T due to implementation dependent floating point rounding errors.

If a pair distance is very near the cutoff, it is implementation dependent whether the pair gets mapped or not due to floating point rounding errors.

Therefore, if more precision is needed, add some extra distance to the cutoff, store the elements externally in 64 bit precision, and in f use i and j to get the precise elements and again check distances.

mapSimplexElements

Map f to all simplexes in a group close to a single simplex.

mapSimplexElements(f, output, s::T, x::Simplex{N}, group_idx::Integer, elements_type::Type{Simplex{M}}, cutoff::Float32) where {N, M}

Apply function f to all elements in group group_idx within the cutoff range of the simplex x, and return the output of the final f call.

x is always x and i is always 0, in calls to f.

mapPairElements

Map f to all pairs of nearby simplexes in a single group.

mapPairElements(f, output, s::T, group_idx::Integer, elements_type::Type{Simplex{N}}, cutoff::Float32) where {N}

Apply function f to all unordered pairs of elements in group group_idx within cutoff range, and return the output of the final f call.

f is never called more than once per unordered pair. Which element is x and y in calls to f is implementation dependent.

mapElementsElements

Map f to all pairs of nearby simplexes between two different groups.

mapElementsElements(
        f, 
        output, 
        s::T, 
        x_group_idx::Integer, 
        x_type::Type{Simplex{N}}, 
        y_group_idx::Integer, 
        y_type::Type{Simplex{M}}, 
        cutoff::Float32,
    ) where {N, M}

Apply function f to each pair of elements from two different groups that are within cutoff range of each other, and return the output of the final f call.

The first element has is an x_type in group x_group_idx and the second element is a y_type in group y_group_idx.

f is never called more than once per pair.