From 77487faa6e2562fa1f9565b7f6d0fdc41c60384d Mon Sep 17 00:00:00 2001 From: "Documenter.jl" Date: Mon, 30 Oct 2023 10:51:32 +0000 Subject: [PATCH] build based on 50c0e6c --- dev/index.html | 2 +- dev/search/index.html | 2 +- 2 files changed, 2 insertions(+), 2 deletions(-) diff --git a/dev/index.html b/dev/index.html index 10127cf..f46d5a6 100644 --- a/dev/index.html +++ b/dev/index.html @@ -1,2 +1,2 @@ -Home · VoronoiGraph.jl
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VoronoiGraph

Documentation for VoronoiGraph.

VoronoiGraph.adjacency — Method

given vertices in generator-coordinates, collect the verts belonging to generator pairs, i.e. boundary vertices

source
VoronoiGraph.boundary_area — Method

given two generators g1, g2, vertices of their common boundary (in generator representation) and the list of all generators, compute the boundary volume. It works by constructing a polytope from halfspaces between the generators of the boundary vertices. We use an affine transformation to get rid of the dimension in direction g1->g2

source
VoronoiGraph.expected_vertices — Method

vertexheuristic(d, n)

expected number of vertices for n points in d dimensions c.f. [Dwyer, The expected number of k-faces of a Voronoi Diagram (1993)]

source
VoronoiGraph.mc_integrate — Function
mc_integrate(f::Function, i::Int, xs::Points, nmc=1000, nmc2=1000, searcher=Raycast(xs))

Integrate function f over cell i and its boundary using nmc rays per cell and nmc2 points per ray for the volume integral.

Returns:

  • Vf::Real: the volume integral of f
  • Af::SparseVector: Af[j] is the surface integral of f over the intersection between cells i and j.
  • V::Real: the volume of cell i
  • A::SparseVector: A[j] is the surface area of the intersection between cells i and j.
source
VoronoiGraph.mc_volume — Function
mc_volume(i, xs, nmc, searcher)

Estimate the area and volume of the i-th Voronoi cell from the Voronoi Diagram generated by xs by a Monte Carlo estimate from random rays

source
VoronoiGraph.mc_volumes — Function
mc_volumes(xs::Points, nmc=1000)

Estimate the areas and volumes of the Voronoi Cells generated by xs using nmc Monte Carlo samples.

Returns

  • SparseMatrix: the areas of the common boundaries of two cells
  • Vector: the volumes of each cell
source
VoronoiGraph.mc_volumes — Function
mc_volumes(sig::Vertices, xs::Points, nmc=1000)

In the case when the simplicial complex is already known this information can be used to speed up the Monte-Carlo sampling by restricting the search space

source
VoronoiGraph.raycast — Method

shooting a ray in the given direction, find the next connecting point. This variant (by Poliaski, Pokorny) uses a binary search

source
VoronoiGraph.raycast — Method

Shooting a ray in the given direction, find the next connecting point. This variant uses an iterative NN search

source
VoronoiGraph.raycast — Method

shooting a ray in the given direction, find the next connecting point. This is the bruteforce variant, using a linear search to find the closest point

source
VoronoiGraph.transformation — Method

affine transformation rotatinig and translating such that the boundary is aligned with the first dimension. A->B will be mapped to const*[1,0,0,...] and (A+B)/2 to [0,0,...]

source
+Home · VoronoiGraph.jl
Edit on GitHub

VoronoiGraph

Documentation for VoronoiGraph.

VoronoiGraph.adjacency — Method

given vertices in generator-coordinates, collect the verts belonging to generator pairs, i.e. boundary vertices

source
VoronoiGraph.boundary_area — Method

given two generators g1, g2, vertices of their common boundary (in generator representation) and the list of all generators, compute the boundary volume. It works by constructing a polytope from halfspaces between the generators of the boundary vertices. We use an affine transformation to get rid of the dimension in direction g1->g2

source
VoronoiGraph.expected_vertices — Method

vertexheuristic(d, n)

expected number of vertices for n points in d dimensions c.f. [Dwyer, The expected number of k-faces of a Voronoi Diagram (1993)]

source
VoronoiGraph.mc_integrate — Function
mc_integrate(f::Function, i::Int, xs::Points, nmc=1000, nmc2=1000, searcher=Raycast(xs))

Integrate function f over cell i and its boundary using nmc rays per cell and nmc2 points per ray for the volume integral.

Returns:

  • Vf::Real: the volume integral of f
  • Af::SparseVector: Af[j] is the surface integral of f over the intersection between cells i and j.
  • V::Real: the volume of cell i
  • A::SparseVector: A[j] is the surface area of the intersection between cells i and j.
source
VoronoiGraph.mc_volume — Function
mc_volume(i, xs, nmc, searcher)

Estimate the area and volume of the i-th Voronoi cell from the Voronoi Diagram generated by xs by a Monte Carlo estimate from random rays

source
VoronoiGraph.mc_volumes — Function
mc_volumes(xs::Points, nmc=1000)

Estimate the areas and volumes of the Voronoi Cells generated by xs using nmc Monte Carlo samples.

Returns

  • SparseMatrix: the areas of the common boundaries of two cells
  • Vector: the volumes of each cell
source
VoronoiGraph.mc_volumes — Function
mc_volumes(sig::Vertices, xs::Points, nmc=1000)

In the case when the simplicial complex is already known this information can be used to speed up the Monte-Carlo sampling by restricting the search space

source
VoronoiGraph.raycast — Method

shooting a ray in the given direction, find the next connecting point. This variant (by Poliaski, Pokorny) uses a binary search

source
VoronoiGraph.raycast — Method

Shooting a ray in the given direction, find the next connecting point. This variant uses an iterative NN search

source
VoronoiGraph.raycast — Method

shooting a ray in the given direction, find the next connecting point. This is the bruteforce variant, using a linear search to find the closest point

source
VoronoiGraph.transformation — Method

affine transformation rotatinig and translating such that the boundary is aligned with the first dimension. A->B will be mapped to const*[1,0,0,...] and (A+B)/2 to [0,0,...]

source
diff --git a/dev/search/index.html b/dev/search/index.html index db82108..a6ff338 100644 --- a/dev/search/index.html +++ b/dev/search/index.html @@ -1,2 +1,2 @@ -Search · VoronoiGraph.jl

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