Merge pull request #13040 from szymag/trans_equations_translation

Add _translation_trans_equations method.

sympy/vector/coordsysrect.py

@@ -407,6 +407,30 @@ def _rotation_trans_equations(self, matrix):
 
         return trans_eq1, trans_eq2, trans_eq3
 
+    def _translation_trans_equations(self, inverse=False):
+        """
+        Returns the transformation equations obtained from translation
+        vector. Translation vector is defined as a linking vector of
+        origins of two coordinate systems.
+
+        """
+        if inverse:
+            sign = -1
+        else:
+            sign = 1
+
+        if self._parent is None:
+            return self.base_scalars()
+        else:
+            vec_component = self._origin.position_wrt(self._parent).components
+            vec_norm_projections = []
+            for i in self._parent.base_vectors():
+                try:
+                    vec_norm_projections.append(sign * vec_component[i])
+                except:
+                    vec_norm_projections.append(0)
+            return tuple([sum(i) for i in zip(vec_norm_projections, self.base_scalars())])
+
     @property
     def origin(self):
         return self._origin

sympy/vector/tests/test_coordsysrect.py

@@ -399,3 +399,17 @@ def test_rotation_trans_equations():
            (-sin(q0) * c.y + cos(q0) * c.x, sin(q0) * c.x + cos(q0) * c.y, c.z)
     assert c._rotation_trans_equations(c._inverse_rotation_matrix()) == \
            (sin(q0) * c.y + cos(q0) * c.x, -sin(q0) * c.x + cos(q0) * c.y, c.z)
+
+def test_translation_trans_equations():
+    from sympy import symbols
+    q0 = symbols('q0')
+    a = CoordSys3D('a')
+    assert a._translation_trans_equations() == (a.x, a.y, a.z)
+    b = a.locate_new('b', None)
+    assert b._translation_trans_equations() == (b.x, b.y, b.z)
+    assert b._translation_trans_equations(inverse=True) == (b.x, b.y, b.z)
+    c = a.locate_new('c', (a.i + a.j + a.k))
+    assert c._translation_trans_equations() == (c.x + 1, c.y + 1, c.z + 1)
+    d = a.locate_new('d', (a.i + a.j + Vector.zero))
+    assert d._translation_trans_equations() == (d.x + 1, d.y + 1, d.z)
+    assert d._translation_trans_equations(inverse=True) == (d.x - 1, d.y - 1, d.z)