CODEWITHSUNDEEP
matrixpython-2.7rotationtranslation
Mr. Polywhirl
Mr. Polywhirl

Reputation: 48600

Python: Transformation Matrix

Is this the correct way to co-compute translation and rotation, or is there a better way? At the moment my code translates and then rotates, could that pose a problem?

Code

from math import cos, sin, radians

def trig(angle):
  r = radians(angle)
  return cos(r), sin(r)

def matrix(rotation=(0,0,0), translation=(0,0,0)):
  xC, xS = trig(rotation[0])
  yC, yS = trig(rotation[1])
  zC, zS = trig(rotation[2])
  dX = translation[0]
  dY = translation[1]
  dZ = translation[2]
  return [[yC*xC, -zC*xS+zS*yS*xC, zS*xS+zC*yS*xC, dX],
    [yC*xS, zC*xC+zS*yS*xS, -zS*xC+zC*yS*xS, dY],
    [-yS, zS*yC, zC*yC, dZ],
    [0, 0, 0, 1]]

def transform(point=(0,0,0), vector=(0,0,0)):
  p = [0,0,0]
  for r in range(3):
    p[r] += vector[r][3]
    for c in range(3):
      p[r] += point[c] * vector[r][c]
  return p

if __name__ == '__main__':
  point = (7, 12, 8)
  rotation = (0, -45, 0)
  translation = (0, 0, 5)
  matrix = matrix(rotation, translation)
  print (transform(point, matrix))

Output

root@ubuntu:~$ python rotate.py 
[-0.707106781186547, 12.0, 15.606601717798213]

Upvotes: 4

Views: 38722

Answers (2)

Hugh Ward
Hugh Ward

Reputation: 121

As this is a highly viewed post I thought it would be useful to lead people to the SciPy Rotation Class which I found very useful for rotations, and would have been a good solution for the question, had it been around at the time.

Upvotes: 2

Hadi Farah
Hadi Farah

Reputation: 1162

well your matrix function is fine I got it working but for output I used this:

#def transform(point, vector):
#  p = [0,0,0]
#  for r in range(0,3):
#    p[r] += vector[r][3]
#    print p
#    for c in range(3):
#        p[r] += point[c] * vector[r][c]
#  return p

def transform(point, TransformArray):
  p = np.array([0,0,0,1])
  for i in range (0,len(point)-1):
      p[i] = point[i]
  p=np.dot(TransformArray,np.transpose(p))
  for i in range (0,len(point)-1):
      point[i]=p[i]
  return point

the theory behind it if instead of performing manual changes let the matrices sort it out. Here is where you can find the literature to better understand what I did: http://www.inf.ed.ac.uk/teaching/courses/cg/lectures/cg3_2013.pdf

And yes the way you perform your matrix function defines the way you perform the order of your transformations. There are 3 major transformations: Scaling, Translation, and Rotation. More on that in the link I sent.

Though matrix function works it seems you have the x and z rotations swapped by mistake now I could now follow any of your matrix indices so I rewrote it as such:

def matrix(rotation, translation):
  xC, xS = trig(rotation[0])
  yC, yS = trig(rotation[1])
  zC, zS = trig(rotation[2])
  dX = translation[0]
  dY = translation[1]
  dZ = translation[2]
  Translate_matrix = np.array([[1, 0, 0, dX],
                               [0, 1, 0, dY],
                               [0, 0, 1, dZ],
                               [0, 0, 0, 1]])
  Rotate_X_matrix = np.array([[1, 0, 0, 0],
                              [0, xC, -xS, 0],
                              [0, xS, xC, 0],
                              [0, 0, 0, 1]])
  Rotate_Y_matrix = np.array([[yC, 0, yS, 0],
                              [0, 1, 0, 0],
                              [-yS, 0, yC, 0],
                              [0, 0, 0, 1]])
  Rotate_Z_matrix = np.array([[zC, -zS, 0, 0],
                              [zS, zC, 0, 0],
                              [0, 0, 1, 0],
                              [0, 0, 0, 1]])
  return np.dot(Rotate_Z_matrix,np.dot(Rotate_Y_matrix,np.dot(Rotate_X_matrix,Translate_matrix)))

As you can see the sequence of transforms in my return will change the output: since the last is the translation it will translate the point first then rotate in X , then rotate in Y and finally in Z. Hope this helps cheers bud.

Upvotes: 3

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