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Lambert azimuthal equal-area (laea) projection

This commit is contained in:
Philip Eisenlohr 2021-12-28 10:19:17 +00:00 committed by Franz Roters
parent 2ea2930638
commit b2d0fd8ff5
2 changed files with 72 additions and 17 deletions
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70
python/damask/util.py
View File

@ -18,11 +18,11 @@ from . import version
__all__=[
'srepr',
'emph', 'deemph', 'warn', 'strikeout',
'run',
'run',
'natural_sort',
'show_progress',
'scale_to_coprime',
'project_stereographic',
'project_equal_angle', 'project_equal_area',
'hybrid_IA',
'execution_stamp',
'shapeshifter', 'shapeblender',
@ -267,13 +267,13 @@ def scale_to_coprime(v):
return m
def project_stereographic(vector,direction='z',normalize=True,keepdims=False):
def project_equal_angle(vector,direction='z',normalize=True,keepdims=False):
"""
Apply stereographic projection to vector.
Apply equal-angle projection to vector.
Parameters
----------
vector : numpy.ndarray of shape (...,3)
vector : numpy.ndarray, shape (...,3)
Vector coordinates to be projected.
direction : str
Projection direction 'x', 'y', or 'z'.
@ -281,32 +281,74 @@ def project_stereographic(vector,direction='z',normalize=True,keepdims=False):
normalize : bool
Ensure unit length of input vector. Defaults to True.
keepdims : bool
Maintain three-dimensional output coordinates.
Default two-dimensional output uses right-handed frame spanned by
Maintain three-dimensional output coordinates. Defaults to False.
Two-dimensional output uses right-handed frame spanned by
the next and next-next axis relative to the projection direction,
e.g. x-y when projecting along z and z-x when projecting along y.
Returns
-------
coordinates : numpy.ndarray of shape (...,2 | 3)
coordinates : numpy.ndarray, shape (...,2 | 3)
Projected coordinates.
Examples
--------
>>> import damask
>>> import numpy as np
>>> project_stereographic(np.ones(3))
>>> project_equal_angle(np.ones(3))
[0.3660254, 0.3660254]
>>> project_stereographic(np.ones(3),direction='x',normalize=False,keepdims=True)
>>> project_equal_angle(np.ones(3),direction='x',normalize=False,keepdims=True)
[0, 0.5, 0.5]
>>> project_stereographic([0,1,1],direction='y',normalize=True,keepdims=False)
>>> project_equal_angle([0,1,1],direction='y',normalize=True,keepdims=False)
[0.41421356, 0]
"""
shift = 'zyx'.index(direction)
v_ = np.roll(vector/np.linalg.norm(vector,axis=-1,keepdims=True) if normalize else vector,
shift,axis=-1)
return np.roll(np.block([v_[...,:2]/(1+np.abs(v_[...,2:3])),np.zeros_like(v_[...,2:3])]),
v = np.roll(vector/np.linalg.norm(vector,axis=-1,keepdims=True) if normalize else vector,
shift,axis=-1)
return np.roll(np.block([v[...,:2]/(1.0+np.abs(v[...,2:3])),np.zeros_like(v[...,2:3])]),
-shift if keepdims else 0,axis=-1)[...,:3 if keepdims else 2]
def project_equal_area(vector,direction='z',normalize=True,keepdims=False):
"""
Apply equal-area projection to vector.
Parameters
----------
vector : numpy.ndarray, shape (...,3)
Vector coordinates to be projected.
direction : str
Projection direction 'x', 'y', or 'z'.
Defaults to 'z'.
normalize : bool
Ensure unit length of input vector. Defaults to True.
keepdims : bool
Maintain three-dimensional output coordinates. Defaults to False.
Two-dimensional output uses right-handed frame spanned by
the next and next-next axis relative to the projection direction,
e.g. x-y when projecting along z and z-x when projecting along y.
Returns
-------
coordinates : numpy.ndarray, shape (...,2 | 3)
Projected coordinates.
Examples
--------
>>> import damask
>>> import numpy as np
>>> project_equal_area(np.ones(3))
[0.45970084, 0.45970084]
>>> project_equal_area(np.ones(3),direction='x',normalize=False,keepdims=True)
[0.0, 0.70710678, 0.70710678]
>>> project_equal_area([0,1,1],direction='y',normalize=True,keepdims=False)
[0.5411961, 0.0]
"""
shift = 'zyx'.index(direction)
v = np.roll(vector/np.linalg.norm(vector,axis=-1,keepdims=True) if normalize else vector,
shift,axis=-1)
return np.roll(np.block([v[...,:2]/np.sqrt(1.0+np.abs(v[...,2:3])),np.zeros_like(v[...,2:3])]),
-shift if keepdims else 0,axis=-1)[...,:3 if keepdims else 2]

19
python/tests/test_util.py
View File

@ -59,9 +59,22 @@ class TestUtil:
([1,1,0],'x',False,False,[0.5,0]),
([1,1,1],'y',True, True, [0.3660254, 0,0.3660254]),
])
def test_project_stereographic(self,point,direction,normalize,keepdims,answer):
assert np.allclose(util.project_stereographic(np.array(point),direction=direction,
normalize=normalize,keepdims=keepdims),answer)
def test_project_equal_angle(self,point,direction,normalize,keepdims,answer):
assert np.allclose(util.project_equal_angle(np.array(point),direction=direction,
normalize=normalize,keepdims=keepdims),answer)
@pytest.mark.parametrize('point,direction,normalize,keepdims,answer',
[
([1,0,0],'z',False,True, [1,0,0]),
([1,0,0],'z',True, False,[1,0]),
([0,1,1],'z',False,True, [0,0.70710678,0]),
([0,1,1],'y',True, False,[0.5411961,0]),
([1,1,0],'x',False,False,[0.70710678,0]),
([1,1,1],'y',True, True, [0.45970084,0,0.45970084]),
])
def test_project_equal_area(self,point,direction,normalize,keepdims,answer):
assert np.allclose(util.project_equal_area(np.array(point),direction=direction,
normalize=normalize,keepdims=keepdims),answer)
@pytest.mark.parametrize('fro,to,mode,answer',
[