[PyVista] 绘制样条曲线和管状路径

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从numpy.array开始绘制纤维束路径/样条曲线的几种方式。

"""
Create a spline/polyline from a numpy array of XYZ vertices using
:func:`pyvista.Spline`.
"""

import numpy as np
import pyvista as pv

###############################################################################
# Create a dataset to plot


def make_points():
    """Helper to make XYZ points"""
    theta = np.linspace(-4 * np.pi, 4 * np.pi, 100)
    z = np.linspace(-2, 2, 100)
    r = z**2 + 1
    x = r * np.sin(theta)
    y = r * np.cos(theta)
    return np.column_stack((x, y, z))


points = make_points()

1. 方法一 （会出现不连续片段）

###############################################################################
# Now let's make a function that can create line cells on a
# :class:`pyvista.PolyData` mesh given that the points are in order for the
# segments they make.


def lines_from_points(points):
    """
    Given an array of points, make a line set.

    Parameters
    ----------
    points : np.ndarray
        Array of XYZ points. Shape is n-by-3.

    Returns
    -------
    poly : pyvista.PolyData
        PolyData with lines cells.
    """
    poly = pv.PolyData()
    poly.points = points
    # cells are a 2d numpy array of the point indices that make each cell
    # the first value in each row is the number of points in the cell,
    # followed by the first and the second point indices.
    cells = np.full((len(points) - 1, 3), 2, dtype=np.int_)
    cells[:, 1] = np.arange(0, len(points) - 1, dtype=np.int_)
    cells[:, 2] = np.arange(1, len(points), dtype=np.int_)
    poly.lines = cells
    return poly


line = lines_from_points(points)
line["scalars"] = np.arange(line.n_points)
tube = line.tube(radius=0.2)
tube.plot(smooth_shading=True)

2. 方法二 （较好）

###############################################################################
# That tube has sharp edges at each line segment. This can be mitigated by
# creating a single PolyLine cell for all of the points
def polyline_from_points(points):
    """
    Given an array of points, make a PolyLine.

    Parameters
    ----------
    points : np.ndarray
        Array of XYZ points. Shape is n-by-3.

    Returns
    -------
    poly : pyvista.PolyData
        PolyData with PolyLine cell.
    """
    poly = pv.PolyData()
    poly.points = points
    the_cell = np.arange(0, len(points), dtype=np.int_)
    the_cell = np.insert(the_cell, 0, len(points))
    poly.lines = the_cell
    return poly


polyline = polyline_from_points(points)
polyline["scalars"] = np.arange(polyline.n_points)
tube = polyline.tube(radius=0.2)
tube.plot(smooth_shading=True)

3. 方法三 (最佳)

###############################################################################
# You could also interpolate those points onto a parametric spline

# Create spline with 1000 interpolation points
spline = pv.Spline(points, 1000)

# add scalars to spline and plot it
spline["scalars"] = np.arange(spline.n_points)
tube = spline.tube(radius=0.1)
tube.plot(smooth_shading=True)

# The spline can also be plotted as a plain line
# generate same spline with 400 interpolation points
spline = pv.Spline(points, 400)
# plot without scalars
spline.plot(line_width=4, color="k")

# The radius of the tube can be modulated with scalars
spline["theta"] = 0.4 * np.arange(len(spline.points))
spline["radius"] = np.abs(np.sin(spline["theta"]))
tube = spline.tube(scalars="radius", absolute=True)
tube.plot(scalars="theta", smooth_shading=True)