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streamtubes.py
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# -*- coding: utf-8 -*-
"""
Created on Fri Aug 21 15:30:44 2020
@author: artmenlope
"""
import numpy as np
import matplotlib
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
from mpl_toolkits.mplot3d.art3d import Poly3DCollection
from scipy.spatial.transform import Rotation as R
def polygonYZ(r, x0, y0, z0, n=8):
"""
Generate a polygon in the yz plane. n is the number of sides.
n+1 points to generate a closed line.
Input:
r : Float. The radius of the circle where the vertices
of the polygon will be laying.
x0, y0, z0 : Floats. 3D coordinates of the center of the polygon.
n : Number of vertices of the polygon.
Output:
Array containing the coordinates of the vertices of the polygon.
"""
angles = np.arange(0,2*np.pi+2*np.pi/n,2*np.pi/n)
xs = x0 + np.zeros(n+1)
ys = y0 + r*np.cos(angles)
zs = z0 + r*np.sin(angles)
return np.array([xs, ys, zs])
def calc_angles(centers):
"""
Given the centers of the polygon collection calculates the rotation
vectors required by scipy.spatial.transform.Rotation.from_rotvec().
These rotation vectors are calculated in order to rotate the polygons
(or streamtube's sections) in a way that the orientation of the plane
of each section is aligned with the direction of the streamtube's path.
Input:
centers : Numpy array of shape (n, 3), where n would be the number
of sections, containing in each row the coordinates of
each streamtube section's center.
Output:
rot_vecs : Numpy array of shape (, )
"""
vec0 = centers[1]-centers[0] #first vec
vecL = centers[-1]-centers[-2] #Last vec.
vecsi = centers[2:]-centers[:-2]
vecs = np.vstack((vec0, np.vstack((vecsi, vecL))))
vecs = (vecs.T/np.linalg.norm(vecs, axis=1)).T
##################
xaxis_vec = np.array([1,0,0])
rot_axis_0 = np.cross(xaxis_vec, vecs[0])
rot_axis_i = np.cross(xaxis_vec, vecs[1:-1])
rot_axis_L = np.cross(xaxis_vec, vecs[-1])
rot_axis_set = np.vstack((rot_axis_0, np.vstack((rot_axis_i, rot_axis_L))))
rot_angle_0 = np.arccos(np.dot(xaxis_vec, vecs[0].T))
rot_angle_i = np.arccos(np.dot(xaxis_vec, vecs[1:-1].T))
rot_angle_L = np.arccos(np.dot(xaxis_vec, vecs[-1].T))
rot_angles = np.hstack((rot_angle_0, rot_angle_i, rot_angle_L))
rot_vecs = (rot_angles * rot_axis_set.T).T
##################
return rot_vecs
def make_sections(x, y, z, r, num_sides=10):
"""
The sections are first oriented along the x axis.
"""
centers = np.stack((x, y, z), axis=1)
num_centers = centers.shape[0]
sections = np.array([polygonYZ(r[i], *centers[i], n=num_sides) for i in range(num_centers)])
rot_vecs = calc_angles(centers)
rotated_sections = []
for i in range(num_centers):
rotation_i = R.from_rotvec(rot_vecs[i])
rot_section_i = (rotation_i.apply(sections[i].T-centers[i])+centers[i]).T
rotated_sections.append(rot_section_i)
return np.array(rotated_sections)
def plot_streamtube(ax, x, y, z, r, num_sides=10,
color="black", alpha=0.2, linewidths=0.5,
cmap_name=None, vmin=None, vmax=None):
centers = np.stack((x, y, z), axis=1)
num_centers = centers.shape[0]
sections = make_sections(x, y, z, r, num_sides=num_sides)
if cmap_name is None:
verts = []
for i in range(num_centers-1):
x1, y1, z1 = sections[i]
x2, y2, z2 = sections[i+1]
for j in range(num_sides):
verts = [(x1[j ], y1[j ], z1[j ]), (x1[j+1], y1[j+1], z1[j+1]),
(x2[j+1], y2[j+1], z2[j+1]), (x2[j ], y2[j ], z2[j ])]
ax.add_collection3d(Poly3DCollection([verts],
alpha=alpha,
linewidths=linewidths,
color=color))
else:
if vmin is None and vmax is None:
cmap = plt.cm.get_cmap(cmap_name)
verts = []
for i in range(num_centers-1):
x1, y1, z1 = sections[i]
x2, y2, z2 = sections[i+1]
for j in range(num_sides):
verts = [(x1[j ], y1[j ], z1[j ]), (x1[j+1], y1[j+1], z1[j+1]),
(x2[j+1], y2[j+1], z2[j+1]), (x2[j ], y2[j ], z2[j ])]
ax.add_collection3d(Poly3DCollection([verts],
alpha=alpha,
linewidths=linewidths,
color=cmap(r[i])))
else:
cmap = plt.cm.get_cmap(cmap_name)
norm = matplotlib.colors.Normalize(vmin=vmin, vmax=vmax)
verts = []
for i in range(num_centers-1):
x1, y1, z1 = sections[i]
x2, y2, z2 = sections[i+1]
color_i = cmap(norm(r[i]))
for j in range(num_sides):
verts = [(x1[j ], y1[j ], z1[j ]), (x1[j+1], y1[j+1], z1[j+1]),
(x2[j+1], y2[j+1], z2[j+1]), (x2[j ], y2[j ], z2[j ])]
ax.add_collection3d(Poly3DCollection([verts],
alpha=alpha,
linewidths=linewidths,
color=color_i))