generalized stereographic projection to cope with all three directions (x,y,Z)

python/damask/util.py

@@ -193,7 +193,7 @@ def scale_to_coprime(v):
     return m
 
 
-def project_stereographic(vector,normalize=False):
+def project_stereographic(vector,normalize=False,direction='z'):
     """
     Apply stereographic projection to vector.
 
@@ -203,16 +203,21 @@ def project_stereographic(vector,normalize=False):
         Vector coordinates to be projected.
     normalize : bool
         Ensure unit length for vector. Defaults to False.
+    direction : str or int
+        Projection direction 'x'|0, 'y'|1, or 'z'|2.
+        Defaults to 'z'.
 
     Returns
     -------
-    coordinates : numpy.ndarray of shape (...,2)
+    coordinates : numpy.ndarray of shape (...,3)
         Projected coordinates.
 
     """
-    v_ = vector/np.linalg.norm(vector,axis=-1,keepdims=True) if normalize else vector
+    shift = 2-('xyzXYZ'.index(direction)%3 if isinstance(direction,str) else int(direction))
-    return np.block([v_[...,:2]/(1+np.abs(v_[...,2:3])),
+    v_ = np.roll(vector/np.linalg.norm(vector,axis=-1,keepdims=True) if normalize else vector,
-                     np.zeros_like(v_[...,2:3])])
+                 shift,axis=-1)
+    return np.roll(np.block([v_[...,:2]/(1+np.abs(v_[...,2:3])),np.zeros_like(v_[...,2:3])]),
+                   -shift,axis=-1)
 
 
 def execution_stamp(class_name,function_name=None):

python/tests/test_util.py

@@ -49,17 +49,17 @@ class TestUtil:
         dist_sampled = np.histogram(centers[selected],bins)[0]/N_samples*np.sum(dist)
         assert np.sqrt(((dist - dist_sampled) ** 2).mean()) < .025 and selected.shape[0]==N_samples
 
-    @pytest.mark.parametrize('point,normalize,answer',
+    @pytest.mark.parametrize('point,normalize,direction,answer',
                              [
-                              ([1,0,0],False,[1,0,0]),
+                              ([1,0,0],False,'z',[1,0,0]),
-                              ([1,0,0],True, [1,0,0]),
+                              ([1,0,0],True, 'z',[1,0,0]),
-                              ([0,1,1],False,[0,0.5,0]),
+                              ([0,1,1],False,'z',[0,0.5,0]),
-                              ([0,1,1],True, [0,0.41421356,0]),
+                              ([0,1,1],True, 'y',[0,0,0.41421356]),
-                              ([1,1,1],False,[0.5,0.5,0]),
+                              ([1,1,1],False,'x',[0,0.5,0.5]),
-                              ([1,1,1],True, [0.3660254, 0.3660254, 0]),
+                              ([1,1,1],True, 'y',[0.3660254, 0,0.3660254]),
                              ])
-    def test_project_stereographic(self,point,normalize,answer):
+    def test_project_stereographic(self,point,normalize,direction,answer):
-        assert np.allclose(util.project_stereographic(np.array(point),normalize=normalize),answer)
+        assert np.allclose(util.project_stereographic(np.array(point),normalize=normalize,direction=direction),answer)
 
     @pytest.mark.parametrize('fro,to,mode,answer',
                              [