I tried to calculate the angle ABC between points A, B and C. I know the math are pretty basic but I don't understand why my function give the wrong result. First, here is the code (a contains a list [x, y, z])
def angle(a, b, c):
# Create vectors from points
ba = [a[0] - b[0], a[1] - b[1], a[2] - b[2]]
bc = [c[0] - b[0], c[1] - b[1], c[2] - b[2]]
# Normalize vector
nba = sqrt(ba[0]**2 + ba[1]**2 + ba[2]**2)
ba = [ba[0]/nba, ba[1]/nba, ba[2]/nba]
nbc = sqrt(bc[0]**2 + bc[1]**2 + bc[2]**2)
bc = [bc[0]/nbc, bc[1]/nbc, bc[2]/nbc]
# Calculate scalar from normalized vectors
scal = ba[0]*bc[0] + ba[1]*bc[1] + ba[2]*bc[2]
# calculate the angle in radian
angle = acos(scal)
This function gives wrong result. In fact, it gives the good result if I change the second vector from bc to cb:
cb = [b[0]-c[0], b[1]-c[1], b[2]-c[2]]
I don't understand why, as if I follow math, my first solution should work well and give the good result...
Firstly, your code is very non-pythonic. Here is a suggestion:
from math import sqrt, acos
def angle(a, b, c):
# Create vectors from points
ba = [ aa-bb for aa,bb in zip(a,b) ]
bc = [ cc-bb for cc,bb in zip(c,b) ]
# Normalize vector
nba = sqrt ( sum ( (x**2.0 for x in ba) ) )
ba = [ x/nba for x in ba ]
nbc = sqrt ( sum ( (x**2.0 for x in bc) ) )
bc = [ x/nbc for x in bc ]
# Calculate scalar from normalized vectors
scalar = sum ( (aa*bb for aa,bb in zip(ba,bc)) )
# calculate the angle in radian
angle = acos(scalar)
return angle
Secondly, your code is probably returning the correct angle, but maybe not the angle you expected.
Assuming this scenario:
A-----C
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B
The angle you're calculating is the bottom angle at B, not the top-left angle at A which is usually what people want when they pass three vectors (a,b,c) into a function that returns angles.