三角形状のサーフェスを作成する

ドロネーの三角形分割により，点群から曲面を作成します．

注釈

PyVistaのフィルターを使って三角形分割を行います： delaunay_2d ．

import numpy as np
import pyvista as pv

単純な三角形分割

まず，サーフェス用のポイントをいくつか作成します．

# Define a simple Gaussian surface
n = 20
x = np.linspace(-200, 200, num=n) + np.random.uniform(-5, 5, size=n)
y = np.linspace(-200, 200, num=n) + np.random.uniform(-5, 5, size=n)
xx, yy = np.meshgrid(x, y)
A, b = 100, 100
zz = A * np.exp(-0.5 * ((xx / b) ** 2.0 + (yy / b) ** 2.0))

# Get the points as a 2D NumPy array (N by 3)
points = np.c_[xx.reshape(-1), yy.reshape(-1), zz.reshape(-1)]
points[0:5, :]

array([[-201.43742213, -197.97875194,    1.85250564],
       [-178.4553    , -197.97875194,    2.86645527],
       [-158.91155129, -197.97875194,    3.98583497],
       [-132.09767414, -197.97875194,    5.88791002],
       [-119.36154425, -197.97875194,    6.91043068]])

次に，これらの点を使って，点群PyVistaデータオブジェクトを作成します．これは pyvista.PolyData オブジェクトに包含されることになります．

# simply pass the numpy points to the PolyData constructor
cloud = pv.PolyData(points)
cloud.plot(point_size=15)

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点のPyVistaデータ構造ができたので，三角形分割を実行して，つまらない離散点を接続された曲面に変えることができます． pyvista.UnstructuredGridFilters.delaunay_2d() を参照してください．

help(cloud.delaunay_2d)

Help on method delaunay_2d in module pyvista.core.filters.poly_data:

delaunay_2d(tol=1e-05, alpha=0.0, offset=1.0, bound=False, inplace=False, edge_source=None, progress_bar=False) method of pyvista.core.pointset.PolyData instance
    Apply a 2D Delaunay filter along the best fitting plane.

    This filter can be used to generate a 2d surface from a set of
    points on a plane.  If you want to create a surface from a
    point cloud, see :func:`pyvista.PolyDataFilters.reconstruct_surface`.

    Parameters
    ----------
    tol : float, default: 1e-05
        Specify a tolerance to control discarding of closely
        spaced points. This tolerance is specified as a fraction
        of the diagonal length of the bounding box of the points.

    alpha : float, default: 0.0
        Specify alpha (or distance) value to control output of
        this filter. For a non-zero alpha value, only edges or
        triangles contained within a sphere centered at mesh
        vertices will be output. Otherwise, only triangles will be
        output.

    offset : float, default: 1.0
        Specify a multiplier to control the size of the initial,
        bounding Delaunay triangulation.

    bound : bool, default: False
        Boolean controls whether bounding triangulation points
        and associated triangles are included in the
        output. These are introduced as an initial triangulation
        to begin the triangulation process. This feature is nice
        for debugging output.

    inplace : bool, default: False
        If ``True``, overwrite this mesh with the triangulated
        mesh.

    edge_source : pyvista.PolyData, optional
        Specify the source object used to specify constrained
        edges and loops. If set, and lines/polygons are defined, a
        constrained triangulation is created. The lines/polygons
        are assumed to reference points in the input point set
        (i.e. point ids are identical in the input and
        source).

    progress_bar : bool, default: False
        Display a progress bar to indicate progress.

    Returns
    -------
    pyvista.PolyData
        Mesh from the 2D delaunay filter.

    Examples
    --------
    First, generate 30 points on circle and plot them.

    >>> import pyvista as pv
    >>> points = pv.Polygon(n_sides=30).points
    >>> circle = pv.PolyData(points)
    >>> circle.plot(show_edges=True, point_size=15)

    Use :func:`delaunay_2d` to fill the interior of the circle.

    >>> filled_circle = circle.delaunay_2d()
    >>> filled_circle.plot(show_edges=True, line_width=5)

    Use the ``edge_source`` parameter to create a constrained delaunay
    triangulation and plot it.

    >>> squar = pv.Polygon(n_sides=4, radius=8, fill=False)
    >>> squar = squar.rotate_z(45, inplace=False)
    >>> circ0 = pv.Polygon(center=(2, 3, 0), n_sides=30, radius=1)
    >>> circ1 = pv.Polygon(center=(-2, -3, 0), n_sides=30, radius=1)
    >>> comb = circ0 + circ1 + squar
    >>> tess = comb.delaunay_2d(edge_source=comb)
    >>> tess.plot(cpos='xy', show_edges=True)

    See :ref:`triangulated_surface` for more examples using this filter.

delaunay_2d フィルタを適用します．

surf = cloud.delaunay_2d()

# And plot it with edges shown
surf.plot(show_edges=True)

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クリーンエッジと三角形分割

# Create the points to triangulate
x = np.arange(10, dtype=float)
xx, yy, zz = np.meshgrid(x, x, [0])
points = np.column_stack((xx.ravel(order="F"), yy.ravel(order="F"), zz.ravel(order="F")))
# Perturb the points
points[:, 0] += np.random.rand(len(points)) * 0.3
points[:, 1] += np.random.rand(len(points)) * 0.3

# Create the point cloud mesh to triangulate from the coordinates
cloud = pv.PolyData(points)
cloud

PolyData	Information
N Cells	100
N Points	100
N Strips	0
X Bounds	1.886e-02, 9.259e+00
Y Bounds	1.054e-02, 9.233e+00
Z Bounds	0.000e+00, 0.000e+00
N Arrays	0

cloud.plot(cpos="xy")

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これらの点に対して三角測量を実行します

surf = cloud.delaunay_2d()
surf.plot(cpos="xy", show_edges=True)

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外側のエッジの一部は拘束されておらず，三角形分割によって不要な三角形が追加されていることに注意してください．私たちは alpha パラメータでそれを緩和します．

surf = cloud.delaunay_2d(alpha=1.0)
surf.plot(cpos="xy", show_edges=True)

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