We Keep Coding

Is it possible to fill in a circular graph with a solid colour and save it as svg in matplotlib?

I wrote some code that creates randomised patches from graphs in matplotlib. Basically how it works is that you create a graph from nodes taken from a circle using the parametric equation for a circle and then you randomly displace the nodes along the vector of (0,0) to the node point on the circumference of the circle. That way you can be certain to avoid lines from crossing each other once the circle is drawn. In the end you just append the first (x,y) coordinate to the list of coordinates to close the circle.
What I want to do next is to find a way to fill that circular graph with a solid colour so that I can create a "stamp" that can be used to make randomised patches on a canvas that hopefully will not create crossing edges. I want to use this to make procedural risk maps in svg format, because a lot of those are uploaded with terrible edges using raster image formats using jpeg.
I am pretty sure that my information of the nodes should be sufficient to make that happen but I have no idea how to implement that. Can anyone help?
import numpy as np
import matplotlib.pyplot as plt
def node_circle(r=0.5,res=100):
# Create arrays (x and y coordinates) for the nodes on the circumference of a circle. Use parametric equation.
# x = r cos(t) y = r sin(t)
t = np.linspace(0,2*np.pi,res)
x = r*np.cos(t)
y = r*np.sin(t)
return t,x,y
def sgn(x,x_shift=-0.5,y_shift=1):
# A shifted sign function to use as a switching function
# in order to avoid shifts lower than -0.5 which is
# the radius of the circle.
return -0.5*(np.abs(x -x_shift)/(x -x_shift)) +y_shift
def displacer(x,y,low=-0.5,high=0.5,maxrad=0.5):
# Displaces the node points of the circle
shift = 0
shift_increment = 0
for i in range(len(x)):
shift_increment = np.random.uniform(low,high)
shift += shift_increment*sgn(maxrad)
x[i] += x[i]*shift
y[i] += y[i]*shift
x = np.append(x,x[0])
y = np.append(y,y[0])
return x,y
def plot():
# Actually visualises everything
fig, ax = plt.subplots(figsize=(4,4))
# np.random.seed(1)
ax.axis('off')
t,x,y = node_circle(res=100)
a = 0
x,y = displacer(x,y,low=-0.15,high=0.15)
ax.plot(x,y,'r-')
# ax.scatter(x,y,)
plt.show()
plot()

got it: the answer is to use matplotlib.Patches.Polygon
import numpy as np
import matplotlib.pyplot as plt
from matplotlib.patches import Polygon
def node_circle(r=0.5,res=100):
# Create arrays (x and y coordinates) for the nodes on the circumference of a circle. Use parametric equation.
# x = r cos(t) y = r sin(t)
t = np.linspace(0,2*np.pi,res)
x = r*np.cos(t)
y = r*np.sin(t)
return x,y
def sgn(x,x_shift=-0.5,y_shift=1):
# A shifted sign function to use as a switching function
# in order to avoid shifts lower than -0.5 which is
# the radius of the circle.
return -0.5*(np.abs(x -x_shift)/(x -x_shift)) +y_shift
def displacer(x,y,low=-0.5,high=0.5,maxrad=0.5):
# Displaces the node points of the circle
shift = 0
shift_increment = 0
for i in range(len(x)):
shift_increment = np.random.uniform(low,high)
shift += shift_increment*sgn(maxrad)
x[i] += x[i]*shift
y[i] += y[i]*shift
x = np.append(x,x[0])
y = np.append(y,y[0])
return x,y
def patch_distributor(M,N,res,grid='square'):
# Distribute Patches based on a specified pattern/grid.
if grid == 'square':
data = np.zeros(shape=(M,N,2,res+1))
for i in range(M):
for j in range(N):
x,y = displacer(*node_circle(res=res),low=-0.2,high=0.2)
data[i,j,0,:] = x
data[i,j,1,:] = y
return data
def plot(res):
# Actually visualises everything
fig, ax = plt.subplots(figsize=(4,4))
# np.random.seed(1)
ax.axis('off')
# x,y = node_circle(res=res)
# x,y = displacer(x,y,low=-0.15,high=0.15)
# xy = np.zeros((len(x),2))
# xy[:,0] = x
# xy[:,1] = y
patch_data = patch_distributor(10,10,res)
for i in range(patch_data.shape[0]):
for j in range(patch_data.shape[1]):
x,y = patch_data[i,j]
x += i*0.5
y += j*0.5
xy = np.zeros((len(x),2))
xy[:,0] = x
xy[:,1] = y
patch = Polygon(xy,fc='w',ec='k',lw=2,zorder=np.random.randint(2),antialiased=False)
ax.add_patch(patch)
ax.autoscale_view()
# ax.plot(x,y,'r-')
# ax.scatter(x,y,)
plt.savefig('lol.png')
plot(res=40)
# Displace circle along the line of (0,0) -> (cos(t),sin(t))
# Make the previous step influence the next to avoid jaggedness
# limit displacement level to an acceptable amount
# Random displaced cubic grid as placing points for stamps.

Plot arbitrary paths with constant width given in data coordinates

General aim
I am trying to write some plotting functionality that (at its core)
plots arbitrary paths with a constant width given in data coordinates
(i.e. unlike lines in matplotlib which have widths given in display coordinates).
Previous solutions
This answer achieves
the basic goal. However, this answer converts between display and data
coordinates and then uses a matplotlib line with adjusted
coordinates. The existing functionality in my code that I would like
to replace / extend inherits from matplotlib.patches.Polygon. Since
the rest of the code base makes extensive use of
matplotlib.patches.Polygon attributes and methods, I would like to
continue to inherit from that class.
Problem
My current implementation (code below) seems to come close. However,
the patch created by simple_test seems to be subtly thicker towards
the centre than it is at the start and end point, and I have no
explanation why that may be the case.
I suspect that the problem lies in the computation of the orthogonal vector.
As supporting evidence, I would like to point to the start and end points of the patch in the figure created by complicated_test, which do not seem exactly orthogonal to the path. However, the dot product of the orthonormal vector and the tangent vector is always zero, so I am not sure that what is going on here.
Output of simple_test:
Output of complicated_test:
Code
#!/usr/bin/env python
import numpy as np
import matplotlib.patches
import matplotlib.pyplot as plt
class CurvedPatch(matplotlib.patches.Polygon):
def __init__(self, path, width, *args, **kwargs):
vertices = self.get_vertices(path, width)
matplotlib.patches.Polygon.__init__(self, list(map(tuple, vertices)),
closed=True,
*args, **kwargs)
def get_vertices(self, path, width):
left = _get_parallel_path(path, -width/2)
right = _get_parallel_path(path, width/2)
full = np.concatenate([left, right[::-1]])
return full
def _get_parallel_path(path, delta):
# initialise output
offset = np.zeros_like(path)
# use the previous and the following point to
# determine the tangent at each point in the path;
for ii in range(1, len(path)-1):
offset[ii] += _get_shift(path[ii-1], path[ii+1], delta)
# handle start and end points
offset[0] = _get_shift(path[0], path[1], delta)
offset[-1] = _get_shift(path[-2], path[-1], delta)
return path + offset
def _get_shift(p1, p2, delta):
# unpack coordinates
x1, y1 = p1
x2, y2 = p2
# get orthogonal unit vector;
# adapted from https://stackoverflow.com/a/16890776/2912349
v = np.r_[x2-x1, y2-y1] # vector between points
v = v / np.linalg.norm(v) # unit vector
w = np.r_[-v[1], v[0]] # orthogonal vector
w = w / np.linalg.norm(w) # orthogonal unit vector
# check that vectors are indeed orthogonal
assert np.isclose(np.dot(v, w), 0.)
# rescale unit vector
dx, dy = delta * w
return dx, dy
def simple_test():
x = np.linspace(-1, 1, 1000)
y = np.sqrt(1. - x**2)
path = np.c_[x, y]
curve = CurvedPatch(path, 0.1, facecolor='red', alpha=0.5)
fig, ax = plt.subplots(1,1)
ax.add_artist(curve)
ax.plot(x, y) # plot path for reference
plt.show()
def complicated_test():
random_points = np.random.rand(10, 2)
# Adapted from https://stackoverflow.com/a/35007804/2912349
import scipy.interpolate as si
def scipy_bspline(cv, n=100, degree=3, periodic=False):
""" Calculate n samples on a bspline
cv : Array ov control vertices
n : Number of samples to return
degree: Curve degree
periodic: True - Curve is closed
"""
cv = np.asarray(cv)
count = cv.shape[0]
# Closed curve
if periodic:
kv = np.arange(-degree,count+degree+1)
factor, fraction = divmod(count+degree+1, count)
cv = np.roll(np.concatenate((cv,) * factor + (cv[:fraction],)),-1,axis=0)
degree = np.clip(degree,1,degree)
# Opened curve
else:
degree = np.clip(degree,1,count-1)
kv = np.clip(np.arange(count+degree+1)-degree,0,count-degree)
# Return samples
max_param = count - (degree * (1-periodic))
spl = si.BSpline(kv, cv, degree)
return spl(np.linspace(0,max_param,n))
x, y = scipy_bspline(random_points, n=1000).T
path = np.c_[x, y]
curve = CurvedPatch(path, 0.1, facecolor='red', alpha=0.5)
fig, ax = plt.subplots(1,1)
ax.add_artist(curve)
ax.plot(x, y) # plot path for reference
plt.show()
if __name__ == '__main__':
plt.ion()
simple_test()
complicated_test()

VTK cannot construct a proper closed surface with vtkClipClosedSurface

Here's a rough explanation of what I do in vtk:
Create a surface (a minimal surface, not too relevant what it is, the geometry is important though: the gyroid has two labyrinths that are completely shut off from each other).
use vtkClipClosedSurface to shut off one of the labyrinths so that I get an object that has no open surfaces anymore. A regular surface looks like this, with a closed surface it looks like this.
Here's my problem: For more complicated versions of my structure, I get this:
Can you see how on the top left it works fine and near the bottom right it stops creating surfaces? Sometimes I also get really weird triangles in that last part.
To my understanding vtkClipClosedSurface knows from the surface normals where to close a surface and where not. The thing is: The normals of my structure are fine and they all point in the right direction. If you take a closer look on the structure you will notice that the lower part is basically an inversion of the top part that changes gradually, all in one surface.
I tried to modify my structure before cutting with many things like vtkSmoothPolyDataFilter, vtkCleanPolyData or vtkPolyDataNormals. I even tried extracting the boundary surfaces with vtkFeatureEdges, which led to an even worse result. Even vtkFillHolesFilter didn't yield any acceptable results. My surface seems flawless and easy enough to create a boundary.
I have no idea what else to try. This happens for other structures, too. Fixing it with a CAD tool is out of question, because it is supposed to work out of box. Please help me!
Here's another example of a geometry that doesn't close the surface properly. This time I used vtkFillHolesFilter which results in surfaces on the inside of the structure, while they should only occupy the boundary of te object.
In case you need a more detailed rundown of my pipeline, here goes:
create surface using mayavi.mlab.contour3d
get the PolyData by extracting the actor.mapper.input
convert format from tvtk to regular vtk
vtkClipClosedSurface with a plane collection that cuts away part of the structure (errors occur when the plane collection is the same as the structure boundary)
visualize it
Edit: Okay, this did not receive enough attention, so I constructed a minimal, complete and verifiable working example that reproduces the behaviour:
import numpy as np
import vtk # VTK version 7.0
from mayavi import mlab # mayavi version 4.4.4
from mayavi.api import Engine, OffScreenEngine
from tvtk.api import tvtk
def schwarz_D(x, y, z, linear_term=0):
"""This is the function for the Schwarz Diamond level surface."""
return (np.sin(x) * np.sin(y) * np.sin(z) + np.sin(x) * np.cos(y) * np.cos(z) +
np.cos(x) * np.sin(y) * np.cos(z) + np.cos(x) * np.cos(y) * np.sin(z)) - linear_term * z
def plane_collection(xn, x, yn, y, zn, z):
"""Defines the 6 planes for cutting rectangular objects to the right size."""
plane1 = vtk.vtkPlane()
plane1.SetOrigin(x, 0, 0)
plane1.SetNormal(-1, 0, 0)
plane2 = vtk.vtkPlane()
plane2.SetOrigin(0, y, 0)
plane2.SetNormal(0, -1, 0)
plane3 = vtk.vtkPlane()
plane3.SetOrigin(0, 0, z)
plane3.SetNormal(0, 0, -1)
plane4 = vtk.vtkPlane()
plane4.SetOrigin(xn, 0, 0)
plane4.SetNormal(1, 0, 0)
plane5 = vtk.vtkPlane()
plane5.SetOrigin(0, yn, 0)
plane5.SetNormal(0, 1, 0)
plane6 = vtk.vtkPlane()
plane6.SetOrigin(0, 0, zn)
plane6.SetNormal(0, 0, 1)
plane_list = [plane4, plane1, plane5, plane2, plane6, plane3]
planes = vtk.vtkPlaneCollection()
for item in plane_list:
planes.AddItem(item)
return planes
[nx, ny, nz] = [2, 2, 8] # amount of unit cells
cell_size = 1
gradient_value = 0.04 # only values below 0.1 produce the desired geometry; this term is essential
x, y, z = np.mgrid[-cell_size*(nx + 1)/2:cell_size*(nx + 1)/2:100j,
-cell_size*(ny + 1)/2:cell_size*(ny + 1)/2:100j,
-cell_size*(nz + 1)/2:cell_size*(nz + 1)/2:100*2j] * np.pi / (cell_size/2)
# engine = Engine()
engine = OffScreenEngine() # do not start mayavi GUI
engine.start()
fig = mlab.figure(figure=None, engine=engine)
contour3d = mlab.contour3d(x, y, z, schwarz_D(x, y, z, gradient_value), figure=fig)
scene = engine.scenes[0]
actor = contour3d.actor.actors[0]
iso_surface = scene.children[0].children[0].children[0]
iso_surface.contour.minimum_contour = 0
iso_surface.contour.number_of_contours = 1
iso_surface.compute_normals = False
iso_surface.contour.auto_update_range = False
mlab.draw(fig)
# mlab.show() # enable if you want to see the mayavi GUI
polydata = tvtk.to_vtk(actor.mapper.input) # convert tvtkPolyData to vtkPolyData
# Move object to the coordinate center to make clipping easier later on.
center_coords = np.array(polydata.GetCenter())
center = vtk.vtkTransform()
center.Translate(-center_coords[0], -center_coords[1], -center_coords[2])
centerFilter = vtk.vtkTransformPolyDataFilter()
centerFilter.SetTransform(center)
centerFilter.SetInputData(polydata)
centerFilter.Update()
# Reverse normals in order to receive a closed surface after clipping
reverse = vtk.vtkReverseSense()
reverse.SetInputConnection(centerFilter.GetOutputPort())
reverse.ReverseNormalsOn()
reverse.ReverseCellsOn()
reverse.Update()
bounds = np.asarray(reverse.GetOutput().GetBounds())
clip = vtk.vtkClipClosedSurface()
clip.SetInputConnection(reverse.GetOutputPort())
clip.SetTolerance(10e-3)
# clip.TriangulationErrorDisplayOn() # enable to see errors for not watertight surfaces
clip.SetClippingPlanes(plane_collection(bounds[0] + cell_size/2, bounds[1] - cell_size/2,
bounds[2] + cell_size/2, bounds[3] - cell_size/2,
bounds[4] + cell_size/2, bounds[5] - cell_size/2))
clip.Update()
# Render the result
mapper = vtk.vtkPolyDataMapper()
mapper.SetInputConnection(clip.GetOutputPort())
actor = vtk.vtkActor()
actor.SetMapper(mapper)
renderer = vtk.vtkRenderer()
renderWindow = vtk.vtkRenderWindow()
renderWindow.AddRenderer(renderer)
renderWindowInteractor = vtk.vtkRenderWindowInteractor()
renderWindowInteractor.SetRenderWindow(renderWindow)
renderer.AddActor(actor)
renderWindow.Render()
renderWindowInteractor.Start()
This really is a short as it gets, I stripped as much as I could. The problem still persists and I can't figure out a solution.

Try using pymeshfix. I had a very similar problem with some low-res mandelbulbs I was generating.
You may also want ot check out pyvista, it's a nice python wrapper for vtk.

Great problem and thanks for the example.
I was able to get this to work in pyvista with some modifications:
import numpy as np
import pyvista as pv
def schwarz_D(x, y, z, linear_term=0):
"""This is the function for the Schwarz Diamond level surface."""
return (np.sin(x) * np.sin(y) * np.sin(z) + np.sin(x) * np.cos(y) * np.cos(z) +
np.cos(x) * np.sin(y) * np.cos(z) + np.cos(x) * np.cos(y) * np.sin(z)) - linear_term * z
# Create the grid
[nx, ny, nz] = [2, 2, 8] # amount of unit cells
cell_size = 1
gradient_value = 0.04 # only values below 0.1 produce the desired geometry; this term is essential
x, y, z = np.mgrid[-cell_size*(nx + 1)/2:cell_size*(nx + 1)/2:100j,
-cell_size*(ny + 1)/2:cell_size*(ny + 1)/2:100j,
-cell_size*(nz + 1)/2:cell_size*(nz + 1)/2:100*2j] * np.pi / (cell_size/2)
# make a grid and exclude cells below 0.1
grid = pv.StructuredGrid(x, y, z)
grid['scalars'] = schwarz_D(x, y, z, gradient_value).ravel(order='F')
contour = grid.clip_scalar(value=0.1)
# make a bunch of clips
# bounds = contour.bounds
# contour.clip(origin=(bounds[0] + cell_size/2, 0, 0), normal='-x', inplace=True)
# contour.clip(origin=(0, bounds[1] - cell_size/2, 0), normal='-y', inplace=True)
# contour.clip(origin=(0, 0, bounds[2] + cell_size/2), normal='-z', inplace=True)
# contour.clip(origin=(bounds[3] - cell_size/2, 0, 0), normal='x', inplace=True)
# contour.clip(origin=(0, bounds[4] + cell_size/2, 0), normal='y', inplace=True)
# contour.clip(origin=(0, 0, bounds[5] - cell_size/2), normal='z', inplace=True)
contour.plot(smooth_shading=True, color='w')
I'm not sure why you're using clipping planes, and I think that you would be better off simply limiting your x, y, and z ranges put into creating the grids. That way, you wouldn't have to clip the final mesh.

How to animate a BuiltinSurface in Mayavi mlab?

I'm attempting to animate the Earth rotating using Mayavi mlab. I've succeeded in the past by just rotating the camera around a BuiltinSurface representation of the Earth, but this becomes inconvenient when I need to plot many other objects (spacecraft, stars, etc) in the frame as well. The code below seems to "almost" work: on my Windows 10 machine, it runs for 8 iterations and then the animation freezes. How can I fix this code, or is there a better way to animate a BuiltinSurface in general?
import numpy as np
from mayavi import mlab
from mayavi.sources.builtin_surface import BuiltinSurface
from mayavi.modules.surface import Surface
from mayavi.filters.transform_data import TransformData
def rotMat3D(axis, angle, tol=1e-12):
"""Return the rotation matrix for 3D rotation by angle `angle` degrees about an
arbitrary axis `axis`.
"""
t = np.radians(angle)
x, y, z = axis
R = (np.cos(t))*np.eye(3) +\
(1-np.cos(t))*np.matrix(((x**2,x*y,x*z),(x*y,y**2,y*z),(z*x,z*y,z**2))) + \
np.sin(t)*np.matrix(((0,-z,y),(z,0,-x),(-y,x,0)))
R[np.abs(R)<tol]=0.0
return R
#mlab.show
#mlab.animate(delay=200)
def anim():
fig = mlab.figure()
engine = mlab.get_engine()
# Add a cylinder builtin source
cylinder_src = BuiltinSurface()
engine.add_source(cylinder_src)
cylinder_src.source = 'earth'
# Add transformation filter to rotate cylinder about an axis
transform_data_filter = TransformData()
engine.add_filter(transform_data_filter, cylinder_src)
Rt = np.eye(4)
Rt[0:3,0:3] = rotMat3D((0,0,1), 0) # in homogeneous coordinates
Rtl = list(Rt.flatten()) # transform the rotation matrix into a list
transform_data_filter.transform.matrix.__setstate__({'elements': Rtl})
transform_data_filter.widget.set_transform(transform_data_filter.transform)
transform_data_filter.filter.update()
transform_data_filter.widget.enabled = False # disable the rotation control further.
# Add surface module to the cylinder source
cyl_surface = Surface()
engine.add_filter(cyl_surface, transform_data_filter)
#add color property
#cyl_surface.actor.property.color = (1.0, 0.0, 0.0)
ind=1
while ind<90:
print ind
Rt[0:3,0:3] = rotMat3D((0,0,1), ind) # in homogeneous coordinates
Rtl = list(Rt.flatten()) # transform the rotation matrix into a list
transform_data_filter.transform.matrix.__setstate__({'elements': Rtl})
transform_data_filter.widget.set_transform(transform_data_filter.transform)
transform_data_filter.filter.update()
transform_data_filter.widget.enabled = False # disable the rotation control further.
# Add surface module to the cylinder source
cyl_surface = Surface()
engine.add_filter(cyl_surface, transform_data_filter)
# add color property
#cyl_surface.actor.property.color = (1.0, 0.0, 0.0)
yield
ind+=1
anim()

I haven't been able to figure out a way to use Mayavi to make this happen. However, Vpython appears to be much better suited to accomplish this task. I've posted an example section of code below to make a revolving Earth, along with a few other features.
from visual import *
def destroy():
for obj in scene.objects:
obj.visible = False
del obj
R = 6378. # radius of sphere
angle=0.
scene.range = 10000.
SunDirection=vector(.77,.77,0)
# scene.fov = 0.5
scene.center = (0,0,0)
scene.forward = (-1,0,-1)
scene.up = (0,0,1)
scene.lights=[distant_light(direction=SunDirection, color=color.gray(0.8)),
distant_light(direction=-SunDirection, color=color.gray(0.3))]
x=0
y=0
while True:
rate(10)
angle=angle+1.*pi/180.
destroy()
s = sphere(pos=(x,y,0), radius=R, material=materials.BlueMarble)
s.rotate(angle=90.*pi/180.,axis=(1,0,0)) # Always include this to rotate Earth into correct ECI x y z frame
s.rotate(angle=90.*pi/180.,axis=(0,0,1)) # Always include this to rotate Earth into correct ECI x y z frame
s.rotate(angle=angle, axis=(0,0,1)) # This rotation causes Earth to spin on its axis
xaxis = arrow(pos=(0,0,0), axis=vector(1,0,0)*7000, shaftwidth=100, color=color.red)
yaxis = arrow(pos=(0,0,0), axis=vector(0,1,0)*7000, shaftwidth=100, color=color.green)
zaxis = arrow(pos=(0,0,0), axis=vector(0,0,1)*7000, shaftwidth=100, color=color.blue)
ST = cone(pos=(0,8000,0),axis=(0,700,0),radius=700*tan(10*pi/180),color=color.blue,opacity=1)

Matplotlib custom projection: How to transform points

I am working with a custom projection of Matplotlib and don't understand how to do vector transformations within the projection (Note: The custom projection is a Lambert azimuthal equal-area projection with equatorial aspect).
In my example I want to transform a point that is dipping 30° to the North (meaning that the point is 60°N of the equator) into a point that dips 30° East (meaning that is lies 60° east of the prime meridian). I want to do this with the help of a vector transformation matrix, in order to do more complicated calculations with the program in the future. But I don't really understand how to get the length of the transformed vector right (or getting the correct longitude and latitude of that point).
I am also studying this example, but it uses a slightly different approach for the transformations:
https://github.com/joferkington/mplstereonet/blob/master/mplstereonet/stereonet_math.py
Testfile:
import matplotlib
import matplotlib.pyplot as plt
import numpy as np
from numpy import pi, sin, cos, sqrt, tan, arctan2, arccos
#Internal imports
import projection
def transformVector(geom, raxis, rot):
"""
Input:
geom: single point geometry (vector)
raxis: rotation axis as a vector (vector)
([0][1][2]) = (x,y,z) = (Longitude, Latitude, Down)
rot: rotation in radian
Returns:
Array: a vector that has been transformed
"""
sr = sin(rot)
cr = cos(rot)
omcr = 1.0 - cr
tf = np.array([
[cr + raxis[0]**2 * omcr,
-raxis[2] * sr + raxis[0] * raxis[1] * omcr,
raxis[1] * sr + raxis[0] * raxis[2] * omcr],
[raxis[2] * sr + raxis[1] * raxis[0] * omcr,
cr + raxis[1]**2 * omcr,
-raxis[0] * sr + raxis[1] * raxis[2] * omcr],
[-raxis[1] * sr + raxis[2] * raxis[0] * omcr,
raxis[0] * sr + raxis[2] * raxis[1] * omcr,
cr + raxis[2]**2 * omcr]])
ar = np.dot(geom, tf)
return ar
def sphericalToVector(inp_ar):
"""
Convert a spherical measurement into a vector in cartesian space
[0] = x (+) east (-) west
[1] = y (+) north (-) south
[2] = z (+) down
"""
ar = np.array([0.0, 0.0, 0.0])
ar[0] = sin(inp_ar[0]) * cos(inp_ar[1])
ar[1] = cos(inp_ar[0]) * cos(inp_ar[1])
ar[2] = sin(inp_ar[1])
return ar
def vectorToGeogr(vect):
"""
Returns:
Array with the components [0] longitude, [1] latitude
"""
ar = np.array([0.0, 0.0])
ar[0] = np.arctan2(vect[0], vect[2])
ar[1] = np.arctan2(vect[1], vect[2])
ar = ar * pi/2
return ar
def plotPoint(dip):
"""
Testfunction for converting, transforming and plotting a point
"""
plt.subplot(111, projection="lmbrt_equ_area_equ_aspect")
#Convert to radians
dip_rad = np.radians(dip)
#Set rotation to azimuth and convert dip to latitude on north-south axis
rot = dip_rad[0]
dip_lat = pi/2 - dip_rad[1]
plt.plot(0, dip_lat, "ro")
print(dip_lat, rot)
#Convert the dip into a vector along the north-south axis
#x = 0, y = dip
vect = sphericalToVector([0, dip_lat])
print(vect, np.linalg.norm(vect))
#Transfrom the dip to its proper azimuth
tvect = transformVector(vect, [0,0,1], rot)
print(tvect, np.linalg.norm(tvect))
#Transform the vector back to geographic coordinates
geo = vectorToGeogr(tvect)
print(geo)
plt.plot(geo[0], geo[1], "bo")
plt.grid(True)
plt.show()
datapoint = np.array([090.0,30])
plotPoint(datapoint)
Custom projection:
import matplotlib
from matplotlib.axes import Axes
from matplotlib.patches import Circle
from matplotlib.path import Path
from matplotlib.ticker import NullLocator, Formatter, FixedLocator
from matplotlib.transforms import Affine2D, BboxTransformTo, Transform
from matplotlib.projections import register_projection
import matplotlib.spines as mspines
import matplotlib.axis as maxis
import matplotlib.pyplot as plt
import numpy as np
from numpy import pi, sin, cos, sqrt, arctan2
# This example projection class is rather long, but it is designed to
# illustrate many features, not all of which will be used every time.
# It is also common to factor out a lot of these methods into common
# code used by a number of projections with similar characteristics
# (see geo.py).
class LambertAxes(Axes):
"""
A custom class for the Lambert azimuthal equal-area projection
with equatorial aspect. In geosciences this is also referre to
as a "Schmidt plot". For more information see:
http://pubs.er.usgs.gov/publication/pp1395
"""
# The projection must specify a name. This will be used be the
# user to select the projection, i.e. ``subplot(111,
# projection='lmbrt_equ_area_equ_aspect')``.
name = 'lmbrt_equ_area_equ_aspect'
def __init__(self, *args, **kwargs):
Axes.__init__(self, *args, **kwargs)
self.set_aspect(1, adjustable='box', anchor='C')
self.cla()
def _init_axis(self):
self.xaxis = maxis.XAxis(self)
self.yaxis = maxis.YAxis(self)
# Do not register xaxis or yaxis with spines -- as done in
# Axes._init_axis() -- until LambertAxes.xaxis.cla() works.
# self.spines['hammer'].register_axis(self.yaxis)
self._update_transScale()
def cla(self):
"""
Override to set up some reasonable defaults.
"""
# Don't forget to call the base class
Axes.cla(self)
# Set up a default grid spacing
self.set_longitude_grid(10)
self.set_latitude_grid(10)
self.set_longitude_grid_ends(80)
# Turn off minor ticking altogether
self.xaxis.set_minor_locator(NullLocator())
self.yaxis.set_minor_locator(NullLocator())
# Do not display ticks -- we only want gridlines and text
self.xaxis.set_ticks_position('none')
self.yaxis.set_ticks_position('none')
# The limits on this projection are fixed -- they are not to
# be changed by the user. This makes the math in the
# transformation itself easier, and since this is a toy
# example, the easier, the better.
Axes.set_xlim(self, -pi/2, pi/2)
Axes.set_ylim(self, -pi, pi)
def _set_lim_and_transforms(self):
"""
This is called once when the plot is created to set up all the
transforms for the data, text and grids.
"""
# There are three important coordinate spaces going on here:
#
# 1. Data space: The space of the data itself
#
# 2. Axes space: The unit rectangle (0, 0) to (1, 1)
# covering the entire plot area.
#
# 3. Display space: The coordinates of the resulting image,
# often in pixels or dpi/inch.
# This function makes heavy use of the Transform classes in
# ``lib/matplotlib/transforms.py.`` For more information, see
# the inline documentation there.
# The goal of the first two transformations is to get from the
# data space (in this case longitude and latitude) to axes
# space. It is separated into a non-affine and affine part so
# that the non-affine part does not have to be recomputed when
# a simple affine change to the figure has been made (such as
# resizing the window or changing the dpi).
# 1) The core transformation from data space into
# rectilinear space defined in the LambertEqualAreaTransform class.
self.transProjection = self.LambertEqualAreaTransform()
# 2) The above has an output range that is not in the unit
# rectangle, so scale and translate it so it fits correctly
# within the axes. The peculiar calculations of xscale and
# yscale are specific to a Aitoff-Hammer projection, so don't
# worry about them too much.
xscale = sqrt(2.0) * sin(0.5 * pi)
yscale = sqrt(2.0) * sin(0.5 * pi)
self.transAffine = Affine2D() \
.scale(0.5 / xscale, 0.5 / yscale) \
.translate(0.5, 0.5)
# 3) This is the transformation from axes space to display
# space.
self.transAxes = BboxTransformTo(self.bbox)
# Now put these 3 transforms together -- from data all the way
# to display coordinates. Using the '+' operator, these
# transforms will be applied "in order". The transforms are
# automatically simplified, if possible, by the underlying
# transformation framework.
self.transData = \
self.transProjection + \
self.transAffine + \
self.transAxes
# The main data transformation is set up. Now deal with
# gridlines and tick labels.
# Longitude gridlines and ticklabels. The input to these
# transforms are in display space in x and axes space in y.
# Therefore, the input values will be in range (-xmin, 0),
# (xmax, 1). The goal of these transforms is to go from that
# space to display space. The tick labels will be offset 4
# pixels from the equator.
self._xaxis_pretransform = \
Affine2D() \
.scale(1.0, pi) \
.translate(0.0, -pi)
self._xaxis_transform = \
self._xaxis_pretransform + \
self.transData
self._xaxis_text1_transform = \
Affine2D().scale(1.0, 0.0) + \
self.transData + \
Affine2D().translate(0.0, 4.0)
self._xaxis_text2_transform = \
Affine2D().scale(1.0, 0.0) + \
self.transData + \
Affine2D().translate(0.0, -4.0)
# Now set up the transforms for the latitude ticks. The input to
# these transforms are in axes space in x and display space in
# y. Therefore, the input values will be in range (0, -ymin),
# (1, ymax). The goal of these transforms is to go from that
# space to display space. The tick labels will be offset 4
# pixels from the edge of the axes ellipse.
yaxis_stretch = Affine2D().scale(pi * 2.0, 1.0).translate(-pi, 0.0)
yaxis_space = Affine2D().scale(1.0, 1.0)
self._yaxis_transform = \
yaxis_stretch + \
self.transData
yaxis_text_base = \
yaxis_stretch + \
self.transProjection + \
(yaxis_space + \
self.transAffine + \
self.transAxes)
self._yaxis_text1_transform = \
yaxis_text_base + \
Affine2D().translate(-8.0, 0.0)
self._yaxis_text2_transform = \
yaxis_text_base + \
Affine2D().translate(8.0, 0.0)
def get_xaxis_transform(self,which='grid'):
"""
Override this method to provide a transformation for the
x-axis grid and ticks.
"""
assert which in ['tick1','tick2','grid']
return self._xaxis_transform
def get_xaxis_text1_transform(self, pixelPad):
"""
Override this method to provide a transformation for the
x-axis tick labels.
Returns a tuple of the form (transform, valign, halign)
"""
return self._xaxis_text1_transform, 'bottom', 'center'
def get_xaxis_text2_transform(self, pixelPad):
"""
Override this method to provide a transformation for the
secondary x-axis tick labels.
Returns a tuple of the form (transform, valign, halign)
"""
return self._xaxis_text2_transform, 'top', 'center'
def get_yaxis_transform(self,which='grid'):
"""
Override this method to provide a transformation for the
y-axis grid and ticks.
"""
assert which in ['tick1','tick2','grid']
return self._yaxis_transform
def get_yaxis_text1_transform(self, pixelPad):
"""
Override this method to provide a transformation for the
y-axis tick labels.
Returns a tuple of the form (transform, valign, halign)
"""
return self._yaxis_text1_transform, 'center', 'right'
def get_yaxis_text2_transform(self, pixelPad):
"""
Override this method to provide a transformation for the
secondary y-axis tick labels.
Returns a tuple of the form (transform, valign, halign)
"""
return self._yaxis_text2_transform, 'center', 'left'
def _gen_axes_patch(self):
"""
Override this method to define the shape that is used for the
background of the plot. It should be a subclass of Patch.
In this case, it is a Circle (that may be warped by the axes
transform into an ellipse). Any data and gridlines will be
clipped to this shape.
"""
return Circle((0.5, 0.5), 0.5)
def _gen_axes_spines(self):
return {'lmbrt_equ_area_equ_aspect':mspines.Spine.circular_spine(self,
(0.5, 0.5), 0.5)}
# Prevent the user from applying scales to one or both of the
# axes. In this particular case, scaling the axes wouldn't make
# sense, so we don't allow it.
def set_xscale(self, *args, **kwargs):
if args[0] != 'linear':
raise NotImplementedError
Axes.set_xscale(self, *args, **kwargs)
def set_yscale(self, *args, **kwargs):
if args[0] != 'linear':
raise NotImplementedError
Axes.set_yscale(self, *args, **kwargs)
# Prevent the user from changing the axes limits. In our case, we
# want to display the whole sphere all the time, so we override
# set_xlim and set_ylim to ignore any input. This also applies to
# interactive panning and zooming in the GUI interfaces.
def set_xlim(self, *args, **kwargs):
Axes.set_xlim(self, -pi, pi)
Axes.set_ylim(self, -pi, pi)
set_ylim = set_xlim
def format_coord(self, lon, lat):
"""
Override this method to change how the values are displayed in
the status bar.
In this case, we want them to be displayed in degrees N/S/E/W.
"""
lon = np.degrees(lon)
lat = np.degrees(lat)
#if lat >= 0.0:
# ns = 'N'
#else:
# ns = 'S'
#if lon >= 0.0:
# ew = 'E'
#else:
# ew = 'W'
return "{0} / {1}".format(round(lon,1), round(lat,1))
class DegreeFormatter(Formatter):
"""
This is a custom formatter that converts the native unit of
radians into (truncated) degrees and adds a degree symbol.
"""
def __init__(self, round_to=1.0):
self._round_to = round_to
def __call__(self, x, pos=None):
degrees = (x / pi) * 180.0
degrees = round(degrees / self._round_to) * self._round_to
return "%d\u00b0" % degrees
def set_longitude_grid(self, degrees):
"""
Set the number of degrees between each longitude grid.
This is an example method that is specific to this projection
class -- it provides a more convenient interface to set the
ticking than set_xticks would.
"""
# Set up a FixedLocator at each of the points, evenly spaced
# by degrees.
number = (360.0 / degrees) + 1
self.xaxis.set_major_locator(
plt.FixedLocator(
np.linspace(-pi, pi, number, True)[1:-1]))
# Set the formatter to display the tick labels in degrees,
# rather than radians.
self.xaxis.set_major_formatter(self.DegreeFormatter(degrees))
def set_latitude_grid(self, degrees):
"""
Set the number of degrees between each longitude grid.
This is an example method that is specific to this projection
class -- it provides a more convenient interface than
set_yticks would.
"""
# Set up a FixedLocator at each of the points, evenly spaced
# by degrees.
number = (180.0 / degrees) + 1
self.yaxis.set_major_locator(
FixedLocator(
np.linspace(-pi / 2.0, pi / 2.0, number, True)[1:-1]))
# Set the formatter to display the tick labels in degrees,
# rather than radians.
self.yaxis.set_major_formatter(self.DegreeFormatter(degrees))
def set_longitude_grid_ends(self, degrees):
"""
Set the latitude(s) at which to stop drawing the longitude grids.
Often, in geographic projections, you wouldn't want to draw
longitude gridlines near the poles. This allows the user to
specify the degree at which to stop drawing longitude grids.
This is an example method that is specific to this projection
class -- it provides an interface to something that has no
analogy in the base Axes class.
"""
longitude_cap = degrees * (pi / 180.0)
# Change the xaxis gridlines transform so that it draws from
# -degrees to degrees, rather than -pi to pi.
self._xaxis_pretransform \
.clear() \
.scale(1.0, longitude_cap * 2.0) \
.translate(0.0, -longitude_cap)
def get_data_ratio(self):
"""
Return the aspect ratio of the data itself.
This method should be overridden by any Axes that have a
fixed data ratio.
"""
return 1.0
# Interactive panning and zooming is not supported with this projection,
# so we override all of the following methods to disable it.
def can_zoom(self):
"""
Return True if this axes support the zoom box
"""
return False
def start_pan(self, x, y, button):
pass
def end_pan(self):
pass
def drag_pan(self, button, key, x, y):
pass
class LambertEqualAreaTransform(Transform):
"""
The basic transformation class.
"""
input_dims = 2
output_dims = 2
is_separable = False
def transform_non_affine(self, ll):
"""
Override the transform_non_affine method to implement the custom
transform.
The input and output are Nx2 numpy arrays.
"""
xi = ll[:, 0:1]
yi = ll[:, 1:2]
k = 1 + np.absolute(cos(yi) * cos(xi))
k = 2 / k
if np.isposinf(k[0]) == True:
k[0] = 1e+15
if np.isneginf(k[0]) == True:
k[0] = -1e+15
if k[0] == 0:
k[0] = 1e-15
k = sqrt(k)
x = k * cos(yi) * sin(xi)
y = k * sin(yi)
return np.concatenate((x, y), 1)
# This is where things get interesting. With this projection,
# straight lines in data space become curves in display space.
# This is done by interpolating new values between the input
# values of the data. Since ``transform`` must not return a
# differently-sized array, any transform that requires
# changing the length of the data array must happen within
# ``transform_path``.
def transform_path_non_affine(self, path):
ipath = path.interpolated(path._interpolation_steps)
return Path(self.transform(ipath.vertices), ipath.codes)
transform_path_non_affine.__doc__ = \
Transform.transform_path_non_affine.__doc__
if matplotlib.__version__ < '1.2':
# Note: For compatibility with matplotlib v1.1 and older, you'll
# need to explicitly implement a ``transform`` method as well.
# Otherwise a ``NotImplementedError`` will be raised. This isn't
# necessary for v1.2 and newer, however.
transform = transform_non_affine
# Similarly, we need to explicitly override ``transform_path`` if
# compatibility with older matplotlib versions is needed. With v1.2
# and newer, only overriding the ``transform_path_non_affine``
# method is sufficient.
transform_path = transform_path_non_affine
transform_path.__doc__ = Transform.transform_path.__doc__
def inverted(self):
return LambertAxes.InvertedLambertEqualAreaTransform()
inverted.__doc__ = Transform.inverted.__doc__
class InvertedLambertEqualAreaTransform(Transform):
#This is not working yet !!!
input_dims = 2
output_dims = 2
is_separable = False
def transform_non_affine(self, xy):
x = xy[:, 0:1]
y = xy[:, 1:2]
#quarter_x = 0.25 * x
#half_y = 0.5 * y
#z = sqrt(1.0 - quarter_x*quarter_x - half_y*half_y)
#longitude = 2 * np.arctan((z*x) / (2.0 * (2.0*z*z - 1.0)))
r = sqrt(2)
p = sqrt(x**2 * y**2)
c = 2 * np.arcsin(p / (2 * r))
phi1 = pi/2
lbd0 = 0
#print(x,y)
if y[0] == 0:
lat = 0
else:
lat = np.arcsin(cos(c) * sin(phi1) + (y * sin(c) * cos(phi1 / p)))
#if phi == phi1:
# lon = lbd0 + np.arctan(x / (-y))
#elif phi == -phi1:
# lon = lbd0 + np.arctan(x / y)
#else:
# lon = lbd0 + np.arctan(x * sin(c) / (p * cos(phi1) * cos(c) - y * sin(phi1) * sin(c)))
if x[0] == 0:
lon = 0
else:
lon = lbd0 + np.arctan(x * sin(c) / (p * cos(phi1) * cos(c) - y * sin(phi1) * sin(c)))
return np.concatenate((lon, lat), 1)
transform_non_affine.__doc__ = Transform.transform_non_affine.__doc__
# As before, we need to implement the "transform" method for
# compatibility with matplotlib v1.1 and older.
if matplotlib.__version__ < '1.2':
transform = transform_non_affine
def inverted(self):
# The inverse of the inverse is the original transform... ;)
return LambertAxes.LambertEqualAreaTransform()
inverted.__doc__ = Transform.inverted.__doc__
# Now register the projection with matplotlib so the user can select
# it.
register_projection(LambertAxes)

It appears that the problem is in both your vectorToGeogr and spherical2vector functions. Based on the comments in those and the pole that you were rotating around, it looks (?) like you were intending to have the following relationship:
x : east-west (east-positive)
y : north-south (north-positive)
z : up-down (down-positive)
However, you had mixed in math in places that assumed mathematical coordinates:
x : towards the equator/prime-meridian intersection
y : towards the equator/90 intersection
z : towards the north pole
A quick-but-not-foolproof test is to try "round-tripping" any coordinate conversion functions. It doesn't guarantee that what you're doing is correct, but it guarantees that it's internally consistent. Your current version of things fails this test:
for lat in range(-90, 100, 10):
for lon in range(-180, 190, 10):
point = np.radians([lon, lat])
round_trip = vectorToGeogr(sphericalToVector(point))
assert np.allclose(point, round_trip)
As an aside, I highly reccomend getting at least a few tests up and running and using a test runner of some sort (py.test is my favorite). It will save you a lot of pain in the long run!
Quick side note:
Personally I prefer to separate "real-world" Cartesian space from the Cartesian space used in a stereonet.
It makes the math simpler, and converting between real-world and "stereonet" space is straight-forward (e.g. see the mplstereonet.xyz2stereonet and mplstereonet.stereonet2xyz functions. They're both in the file you linked to.). The examples in stereonet_math.py all use the second set of conventions. When you need to deal with "real" vectors, (e.g. the contour_normal_vectors.py example) they can be converted over with either xyz2stereonet (outputs lon, lat) or one of the various normal2<foo> functions (outputs plunge/bearing, strike/dip, etc).
However, if you do want to use "real-world" Cartesian coordinates internally, you'll need to change your conversion functions.
Your original sphericalToVector function:
def sphericalToVector(inp_ar):
ar = np.array([0.0, 0.0, 0.0])
ar[0] = sin(inp_ar[0]) * cos(inp_ar[1])
ar[1] = cos(inp_ar[0]) * cos(inp_ar[1])
ar[2] = sin(inp_ar[1])
return ar
Should be changed to:
def sphericalToVector(inp_ar):
ar = np.array([0.0, 0.0, 0.0])
ar[0] = -sin(inp_ar[1])
ar[1] = sin(inp_ar[0]) * cos(inp_ar[1])
ar[2] = cos(inp_ar[0]) * cos(inp_ar[1])
return ar
And your original vectorToGeogr function:
def vectorToGeogr(vect):
ar = np.array([0.0, 0.0])
ar[0] = np.arctan2(vect[0], vect[2])
ar[1] = np.arctan2(vect[1], vect[2])
ar = ar * pi/2
return ar
Should be changed to:
def vectorToGeogr(vect):
ar = np.array([0.0, 0.0])
ar[0] = np.arctan2(vect[1], vect[2])
ar[1] = np.arcsin(-vect[0] / np.linalg.norm(vect))
return ar
The modified version of your example is here: https://gist.github.com/joferkington/ddd90715421720033066 The only things changed are the functions above in test.py. As an example of the result: