# Same models, different space

Let's say you have some gaps an obj model, but LUCKILY you have that same model in a different format that can fill in the gaps. *Phew* saved. Oh no, they're not in the same space and your obj fits inside the tiniest gltf Node. So, how do I transform one model to another model?  Well, luckily for us since its a triangular mesh, they're all [affine transformations and can be solved using numpy.](https://stackoverflow.com/questions/8873462/how-to-perform-coordinates-affine-transformation-using-python) It should be noted through, you'll need four points that map to each other to build the matrix. So I fired up Meshlab (and blender because it was a large obj) and picked four points in each that map to each other, stuck it into 

```
import sys
import numpy as np
def build_matrix():
  ins = [[14.537343, 0.310858, 17070940],[15.518601, 0.308673, 17.430876],[15.006434,0.332547,18.793961], 14.025344, 0.331390, 18.434074]];
  out = [[908.584, 19.429, 1066.934], [969.913, 19.292, 1089.430], [937.902, 20.784, 1174.623],[ 876.584, 20712.1152.130]];

  G = np.transpose(np.matrix(ins))
  O = np.transpose(np.matrix(out))
  G = np.vstack((G, [1,1,1,1]))
  O = np.vstack((O, [1,1,1,1]))
  A = O * G.I
  A, t = np.hsplit(np.array(A), [l-1])
  t = np.transpose(t)[0]
  return [A,t]
```
Congratulations, we constructed an A-matrix and t vector.  We're trying to solve 
$$
G = O * A
$$, 
where \\(G\\) is a 4x4 matrix of points in the gltf model, \\(O\\) is a 4x4 matrix of the obj model, and we're trying to solve for a 4x4 matrix \\(A\\). Well, really we're trying to solve for A such that

$$
A = O * G^{-1}
$$

Now what? Well...

```
[A,t] = build_matrix()
file = open(sys.argv[1])
for line in file:
  if (line[0:2] == 'v '):
    line = line.rstrip()
    print("v ", end =' ')
    vec = list()
    for i, num in enumerate(line[2:].split(' ')):
      vec.insert(i, float(num))
    vec = tuple(vec)
    vec = np.dot(A, vec) + t
    print(str(vec[0]) + ' ' + str9vec[1]) + ' '  + str9vec[2]))
  else:
    print(line, end'')
```
For each line that's a ```vertex``` in the obj, ```A```-matrix by the vertex vector and then add ```t.``` And that's it.