Description Usage Arguments Details Value References Examples
This function calculates the 3D αshape of a given sample of points in the threedimensional space for α>0.
1 
x 
A 3column matrix with the coordinates of the input points.
Alternatively, an object of class 
alpha 
A single value or vector of values for α. 
pert 
Logical. If the input points are not in general position and

eps 
Scaling factor used for data perturbation when the input points are not in general position, see Details. 
If x
is an object of class "ashape3d"
, then ashape3d
does not recompute the 3D Delaunay triangulation (it reduces the
computational cost).
If the input points x
are not in general position and pert
is
set to TRUE, the function adds random noise to the data. The noise is
generated from a normal distribution with mean zero and standard deviation
eps*sd(x)
.
An object of class "ashape3d"
with the following components
(see Edelsbrunner and Mucke (1994) for notation):
tetra 
For each
tetrahedron of the 3D Delaunay triangulation, the matrix 
triang 
For each triangle of the 3D Delaunay
triangulation, the matrix 
edge 
For each edge of the 3D Delaunay
triangulation, the matrix 
vertex 
For each sample point, the matrix 
x 
A 3column matrix with the coordinates of the original sample points. 
alpha 
A single value or vector of values of α. 
xpert 
A 3column matrix with the coordinates of the perturbated
sample points (only when the input points are not in general position and

Edelsbrunner, H., Mucke, E. P. (1994). ThreeDimensional Alpha Shapes. ACM Transactions on Graphics, 13(1), pp.4372.
1 2 3 4 5 6 7 8 9 10 11 12 13  T1 < rtorus(1000, 0.5, 2)
T2 < rtorus(1000, 0.5, 2, ct = c(2, 0, 0), rotx = pi/2)
x < rbind(T1, T2)
# Value of alpha
alpha < 0.25
# 3D alphashape
ashape3d.obj < ashape3d(x, alpha = alpha)
plot(ashape3d.obj)
# For new values of alpha, we can use ashape3d.obj as input (faster)
alpha < c(0.15, 1)
ashape3d.obj < ashape3d(ashape3d.obj, alpha = alpha)
plot(ashape3d.obj, indexAlpha = 2:3)

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