Merge pull request #1332 from smichr/geom

geometry: perpendicular segment and orthocenter corrections

sympy/geometry/line.py

@@ -399,7 +399,7 @@ def perpendicular_line(self, p):
 
         """
         d1, d2 = (self.p1 - self.p2).args
-        if d2 == 0: # If an horizontal line
+        if d2 == 0: # If a horizontal line
             if p.y == self.p1.y: # if p is on this linear entity
                 return Line(p, p + Point(0, 1))
             else:
@@ -412,6 +412,10 @@ def perpendicular_line(self, p):
     def perpendicular_segment(self, p):
         """Create a perpendicular line segment from `p` to this line.
 
+        The enpoints of the segment are ``p`` and the closest point in
+        the line containing self. (If self is not a line, the point might
+        not be in self.)
+
         Parameters
         ==========
 
@@ -443,12 +447,14 @@ def perpendicular_segment(self, p):
         True
         >>> p3 in s1
         True
+        >>> l1.perpendicular_segment(Point(4, 0))
+        Segment(Point(2, 2), Point(4, 0))
 
         """
         if p in self:
             return p
         pl = self.perpendicular_line(p)
-        p2 = self.intersection(pl)[0]
+        p2 = Line(self).intersection(pl)[0]
         return Segment(p, p2)
 
     @property

sympy/geometry/polygon.py

@@ -1824,8 +1824,9 @@ def is_right(self):
     def altitudes(self):
         """The altitudes of the triangle.
 
-        An altitude of a triangle is a straight line through a vertex and
-        perpendicular to the opposite side.
+        An altitude of a triangle is a segment through a vertex,
+        perpendicular to the opposite side, with length being the
+        height of the vertex measured from the line containing the side.
 
         Returns
         =======
@@ -1884,7 +1885,7 @@ def orthocenter(self):
         """
         a = self.altitudes
         v = self.vertices
-        return a[v[0]].intersection(a[v[1]])[0]
+        return Line(a[v[0]]).intersection(Line(a[v[1]]))[0]
 
     @property
     def circumcenter(self):

sympy/geometry/tests/test_geometry.py

@@ -776,6 +776,14 @@ def test_polygon():
     assert altitudes[p2] == s1[0]
     assert altitudes[p3] == s1[2]
     assert t1.orthocenter == p1
+    t = S('''Triangle(
+    Point(100080156402737/5000000000000, 79782624633431/500000000000),
+    Point(39223884078253/2000000000000, 156345163124289/1000000000000),
+    Point(31241359188437/1250000000000, 338338270939941/1000000000000000))''')
+    assert t.orthocenter == S('''Point(-780660869050599840216997'''
+    '''79471538701955848721853/80368430960602242240789074233100000000000000,'''
+    '''20151573611150265741278060334545897615974257/16073686192120448448157'''
+    '''8148466200000000000)''')
 
     # Ensure
     assert len(intersection(*bisectors.values())) == 1