MATLAB: Deleting Triangulation Entries from a Delaunay Triangulation Based on Indices Given by a Logical Array

delaunaylogical arraytriangulation

Hello,

I am using Delaunay Triangulations to map a 3D space. Given certain criteria, I select a certain number of points to be removed both from my coordinates vector and the triangulation matrix. I am using a logical array to define the coordinates vector indices to remove, now I want to use that directly to detect which rows of the triangulation contain those indices and delete them. A little example:

A = [1 2 3;4 5 6;7 8 9;10 11 12]; % Coordinate Matrix
bound = [5 3 3]; % Spatial Bounds
ids = bound(1,1) <= A(:,1) & bound(1,2) <= A(:,2) & bound(1,3) <= A(:,3); % logical operator

This code gives

ids = [0 0 1 1]

This means I can delete the coordinates not satistying my boundaries with

A(ids,:) = [];

But how can I search for the indices 3 and 4 (the one resulting from the logical operation) inside a big Triangulation matrix (of size n*4) and delete every row containing one of those indices? I obviously only care about rows.

Thanks

Best Answer

If my comment above is a correct interpretation of what you want, then this code will do it:

T(any(ismember(T,find(ids)),2),:) = [];

Related Solutions

MATLAB: Find which tetrahedron in a Triangulation contains a Given Facet

Um, can you say easy, peasy?

1. Sort the facet indices in your target facet.

2. Sort the facet indices in your triangulation.

3. Form a list of all facets. Each tetrahedron has 4 facets, so there will be 4 facets for each simplex in the complex.

FACET = sort(FACET);
TRI = sort(TRI,2);
facetlist = [TRI(:,[1 2 3]);TRI(:,[1 2 4]);TRI(:,[1 3 4]);TRI(:,[2 3 4])];

Now a simple application of ismember will find the facet of interest. Note that the facet may appear once or twice. This depends upon whether the simplex shares that facet with another simplex in the tessellation.

How do you identify which simplex the facets you have just identified came from? One simple solution would be ind2sub, but mod will also suffice.

For example:

tri = delaunayn(rand(7,3))
tri =
     3     1     6     5
     2     6     1     5
     7     3     4     5
     7     4     2     5
     7     1     3     5
     7     2     1     5
tri = sort(tri,2)
tri =
     1     3     5     6
     1     2     5     6
     3     4     5     7
     2     4     5     7
     1     3     5     7
     1     2     5     7
facet = [1 5 7];
facetlist = [tri(:,[1 2 3]);tri(:,[1 2 4]);tri(:,[1 3 4]);tri(:,[2 3 4])];
[~,ind] = ismember(facetlist,facet,'rows');
ind = find(ind)
ind =
    17
    18

Now, which simplex did each of those facets arise from?

ntri = size(tri,1);
mod(ind-1,ntri) + 1
ans =
     5
     6

That particular facet was shared between simplex 5 and simplex 6 in the list. If you look back at the original triangulation, it did appear in each of those places. As I said, if a facet is on the boundary of the tessellation, then it will appear only once.

Now you should see why the sorts were necessary, as otherwise the ismember search may well fail.

As I said, easy. A few simple lines of code.

MATLAB: Delaunay Triangulation

Here is a simple example, adapted from the documentation from DelaunayTri:

x = rand(4,1);
y = rand(4,1);
dt = DelaunayTri(x,y)
triplot(dt)

dt.X is a 4x2 array, listing the (x,y) coordinates of the four input points. Consider these to be points 1,2,3,4 in the order listed by dt.X, NOT the order of the input.

The triangulation will create three triangles. Each row of the output variable dt.triangulation tells you information about ONE of those triangles. So, for example, if one row of dt.triangulation is

2 4 3

then that is saying that the 2nd, 4th, and 3rd points from dt.X form one of the Delaunay triangles.

Note that

doc DelauneyTri

lists many more methods for the DelaunayTri class.

I hope that helps.

Best Answer

Related Solutions

MATLAB: Find which tetrahedron in a Triangulation contains a Given Facet

MATLAB: Delaunay Triangulation

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