I have two points on a tkinter canvas. I need a function to determine which cardinal direction a line drawn between them would be the closest to (N, NW, W SW, S etc.) (Direction matters)? How would I go about doing this? Please note that in a canvas, the top-left is (0,0).
I have tried:
def dot_product(self, v, w):
return v[0]*w[0]+v[1]*w[1]
def inner_angle(self, v, w):
cosx=self.dot_product(v,w)/(sqrt(v[0]**2+v[1]**2)*sqrt(w[0]**2+w[1]**2))
rad=acos(cosx)
return rad*180/pi
def getAngle(self, A, B):
inner=self.inner_angle(A,B)
det = A[0]*B[1]-A[1]*B[0]
if det<0:
return inner
else:
return 360-inner
and:
def getBearing(self, pointA, pointB):
if (type(pointA) != tuple) or (type(pointB) != tuple):
raise TypeError("Only tuples are supported as arguments")
lat1 = math.radians(pointA[0])
lat2 = math.radians(pointB[0])
diffLong = math.radians(pointB[1] - pointA[1])
x = math.sin(diffLong) * math.cos(lat2)
y = math.cos(lat1) * math.sin(lat2) - (math.sin(lat1) * math.cos(lat2) * math.cos(diffLong))
initial_bearing = math.atan2(x, y)
initial_bearing = math.degrees(initial_bearing)
compass_bearing = (initial_bearing + 360) % 360
return compass_bearing
(I used this function to get direction (The code is incomplete, it's more of an example))
def findDirection(self, p1, p2):
bearing = self.getBearing(p1, p2) # OR getAngle()
print(bearing)
index = [180, 0]
closest = min(index, key=lambda x:abs(x-bearing))
if closest == 10:
print(str(bearing) + " : UP")
elif closest == 360:
print(str(bearing) + " : DOWN")
elif closest == 0:
print(str(bearing) + " : RIGHT")
elif closest == 180:
print(str(bearing) + " : LEFT")
None of those work. The result doesn't seem to be consistent enough to use. Is there a better way to do it?
Here is my proposed approach to determine the closest compass direction to the one pointed at by a line segment [A, B] defined by its end points point_a and point_b:
point_awith points defined in screen coordinates (Y axis down), call
get_bearings(point_a, point_b)
If the points defined in standard cartesian coordinates (Y axis up), callassign_bearing_to_compass(point_a, point_b)
(The tests underneath the code show the results of using points in standard coordinates, and screen coordinates.)
import math
def _change_origin_of_point_b_to_point_a(point_a, point_b):
# uses standard Y axis orientation, not screen orientation
return (point_b[0] - point_a[0], point_b[1] - point_a[1])
def _calc_angle_segment_a_b_with_x_axis(point_a, point_b):
# uses standard Y axis orientation, not screen orientation
xa, ya = point_a
xb, yb = _change_origin_of_point_b_to_point_a(point_a, point_b)
return math.atan2(yb, xb)
def determine_bearing_in_degrees(point_a, point_b):
"""returns the angle in degrees that line segment [point_a, point_b)]
makes with the horizontal X axis
"""
# uses standard Y axis orientation, not screen orientation
return _calc_angle_segment_a_b_with_x_axis(point_a, point_b) * 180 / math.pi
def assign_bearing_to_compass(point_a, point_b):
"""returns the standard bearing of line segment [point_a, point_b)
"""
# uses standard Y axis orientation, not screen orientation
compass = {'W' : [157.5, -157.5],
'SW': [-157.5, -112.5],
'S' : [-112.5, -67.5],
'SE': [-67.5, -22.5],
'E' : [-22.5, 22.5],
"NE": [22.5, 67.5],
'N' : [67.5, 112.5],
'NW': [112.5, 157.5]}
bear = determine_bearing_in_degrees(point_a, point_b)
for direction, interval in compass.items():
low, high = interval
if bear >= low and bear < high:
return direction
return 'W'
def _convert_to_negative_Y_axis(compass_direction):
"""flips the compass_direction horizontally
"""
compass_conversion = {'E' : 'E',
'SE': 'NE',
'S' : 'N',
'SW': 'NW',
'W' : 'W',
"NW": 'SW',
'N' : 'S',
'NE': 'SE'}
return compass_conversion[compass_direction]
def get_bearings(point_a, point_b):
return _convert_to_negative_Y_axis(assign_bearing_to_compass(point_a, point_b))
(using the standard trigonometric circle quadrants)
point_a = (0, 0)
points_b = [(1, 0), (1, 3), (1, 2), (1, 1), (2, 1), (3, 1), (0, 1)]
print("point_a, point_b Y_up Y_down (in screen coordinates)")
for point_b in points_b:
print(point_a, ' ', point_b, ' ', assign_bearing_to_compass(point_a, point_b), ' ', get_bearings(point_a, point_b))
point_a, point_b Y_up Y_down (in screen coordinates)
(0, 0) (1, 0) E E
(0, 0) (1, 3) N S
(0, 0) (1, 2) NE SE
(0, 0) (1, 1) NE SE
(0, 0) (2, 1) NE SE
(0, 0) (3, 1) E E
(0, 0) (0, 1) N S
point_a = (0, 0)
points_b = [(-1, 0), (-1, 3), (-1, 2), (-1, 1), (-2, 1), (-3, 1), (0, 1)]
print("point_a, point_b Y_up Y_down (in screen coordinates)")
for point_b in points_b:
print(point_a, ' ', point_b, ' ', assign_bearing_to_compass(point_a, point_b), ' ', get_bearings(point_a, point_b))
point_a, point_b Y_up Y_down (in screen coordinates)
(0, 0) (-1, 0) W W
(0, 0) (-1, 3) N S
(0, 0) (-1, 2) NW SW
(0, 0) (-1, 1) NW SW
(0, 0) (-2, 1) NW SW
(0, 0) (-3, 1) W W
(0, 0) (0, 1) N S
point_a = (0, 0)
points_b = [(-1, 0), (-1, -3), (-1, -2), (-1, -1), (-2, -1), (-3, -1), (0, -1)]
print("point_a, point_b Y_up Y_down (in screen coordinates)")
for point_b in points_b:
print(point_a, ' ', point_b, ' ', assign_bearing_to_compass(point_a, point_b), ' ', get_bearings(point_a, point_b))
point_a, point_b Y_up Y_down (in screen coordinates)
(0, 0) (-1, 0) W W
(0, 0) (-1, -3) S N
(0, 0) (-1, -2) SW NW
(0, 0) (-1, -1) SW NW
(0, 0) (-2, -1) SW NW
(0, 0) (-3, -1) W W
(0, 0) (0, -1) S N
point_a = (0, 0)
points_b = [(1, 0), (1, -3), (1, -2), (1, -1), (2, -1), (3, -1), (0, -1)]
print("point_a, point_b Y_up Y_down (in screen coordinates)")
for point_b in points_b:
print(point_a, ' ', point_b, ' ', assign_bearing_to_compass(point_a, point_b), ' ', get_bearings(point_a, point_b))
point_a, point_b Y_up Y_down (in screen coordinates)
(0, 0) (1, 0) E E
(0, 0) (1, -3) S N
(0, 0) (1, -2) SE NE
(0, 0) (1, -1) SE NE
(0, 0) (2, -1) SE NE
(0, 0) (3, -1) E E
(0, 0) (0, -1) S N