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CGAL's documentation for Delaunay Triangulations


CGAL's documentation for Delaunay Triangulations

By : ark
Date : November 20 2020, 09:01 AM
This might help you From here: Locate is implemented by a line walk. The walk begins at a vertex of the face which is given as an optional argument or at an arbitrary vertex of the triangulation if no optional argument is given.
This is particularly useful if you have a bunch of points you want to locate in the triangulation. You can sort the point along a Hilbert curve and locate each point using a face containing the closest vertex to the previous point to initialize the walk.
code :


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How to find all neighbors of a given point in a delaunay triangulation using scipy.spatial.Delaunay?

How to find all neighbors of a given point in a delaunay triangulation using scipy.spatial.Delaunay?


By : Ilva Veidemane
Date : March 29 2020, 07:55 AM
wish helps you I figured it out on my own, so here's an explanation for anyone future person who is confused by this.
As an example, let's use the simple lattice of points that I was working with in my code, which I generate as follows
code :
import numpy as np
import itertools as it
from matplotlib import pyplot as plt
import scipy as sp

inputs = list(it.product([0,1,2],[0,1,2]))
i = 0
lattice = range(0,len(inputs))
for pair in inputs:
    lattice[i] = mksite(pair[0], pair[1])
    i = i +1
plt.plot(*np.transpose(lattice), marker = 'o', ls = '')
axes().set_aspect('equal')
dela = sp.spatial.Delaunay
triang = dela(lattice)
triang.points
array([[ 0.        ,  0.        ],
       [ 0.5       ,  0.8660254 ],
       [ 1.        ,  1.73205081],
       [ 1.        ,  0.        ],
       [ 1.5       ,  0.8660254 ],
       [ 2.        ,  1.73205081],
       [ 2.        ,  0.        ],
       [ 2.5       ,  0.8660254 ],
       [ 3.        ,  1.73205081]])
triang.vertices
array([[4, 3, 6],
       [5, 4, 2],
       [1, 3, 0],
       [1, 4, 2],
       [1, 4, 3],
       [7, 4, 6],
       [7, 5, 8],
       [7, 5, 4]], dtype=int32)
[ 1.5       ,  0.8660254 ]
[ 1.        ,  0.        ]
[ 2.        ,  0.        ]
def find_neighbors(pindex, triang):
    neighbors = list()
    for simplex in triang.vertices:
        if pindex in simplex:
            neighbors.extend([simplex[i] for i in range(len(simplex)) if simplex[i] != pindex])
            '''
            this is a one liner for if a simplex contains the point we`re interested in,
            extend the neighbors list by appending all the *other* point indices in the simplex
            '''
    #now we just have to strip out all the dulicate indices and return the neighbors list:
    return list(set(neighbors))
Is it possible to enforce edges (constrained delaunay triangulation) in scipy.spatial's Delaunay?

Is it possible to enforce edges (constrained delaunay triangulation) in scipy.spatial's Delaunay?


By : user3679786
Date : March 29 2020, 07:55 AM
Does that help What you are looking for is called constrained Delaunay triangulation, and unfortunately the scipy.spatial implementation does not support it.
As you pointed out, triangle does have that feature -- why not use it instead?
Is there a Python library to do constrained triangulations in 3D?

Is there a Python library to do constrained triangulations in 3D?


By : Jose Chavez
Date : March 29 2020, 07:55 AM
I wish this help you You may take a look at CGAL it has python-bindings.
One side note: If you need the surface triangulation (which seems to be a 2D problem), you may take each face, project it to 2D, triangulate it, and back to your 3D face.
Delaunay triangulation in 3D

Delaunay triangulation in 3D


By : bilal akkar
Date : March 29 2020, 07:55 AM
will help you You could try Bowyer-Watson algorithm but with tetrahedrons or you could try to lift the points to a paraboloid:https://math.stackexchange.com/questions/200536/3d-delaunay-triangulation-by-4d-paraboloids.
Is there an implementation of hyperbolic Delaunay triangulations?

Is there an implementation of hyperbolic Delaunay triangulations?


By : Jim
Date : March 29 2020, 07:55 AM
With these it helps The code that Marc mentions is computing periodic triangulations (along translations corresponding to the hyperbolic octagon), following the paper soon to be presented at SoCG'17 (see https://hal.inria.fr/hal-01411415 for a preliminary version).
We also have code that computes Delaunay triangulations in the hyperbolic plane, as presented in our JoCG paper (see http://jocg.org/index.php/jocg/article/view/141). The branch is currently private in github, but we will make it public soon. Some parts need polishing, though, and the documentation is not yet written.
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