I have a 3x1 point vector representing the start point of some line, and a 3x1 point vector representing the end of some line. I would like to sample an arbitrary amount of points along the line connected by these two points.
np.linspace does exactly what I need but in 1 dimension. Is there a similar functionality that can be extended to 3 dimensions?
Thanks
My interpolation suggestion:
In [664]: p1=np.array([0,1,2])
In [665]: p2=np.array([10,9,8])
In [666]: l1 = np.linspace(0,1,11)
In [667]: l1
Out[667]: array([0. , 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1. ])
In [668]: p1+(p2-p1)*l1[:,None]
Out[668]:
array([[ 0. , 1. , 2. ],
[ 1. , 1.8, 2.6],
[ 2. , 2.6, 3.2],
[ 3. , 3.4, 3.8],
[ 4. , 4.2, 4.4],
[ 5. , 5. , 5. ],
[ 6. , 5.8, 5.6],
[ 7. , 6.6, 6.2],
[ 8. , 7.4, 6.8],
[ 9. , 8.2, 7.4],
[10. , 9. , 8. ]])
Equivalent with 3 linspace calls
In [671]: np.stack([np.linspace(i,j,11) for i,j in zip(p1,p2)],axis=1)
Out[671]:
array([[ 0. , 1. , 2. ],
[ 1. , 1.8, 2.6],
[ 2. , 2.6, 3.2],
[ 3. , 3.4, 3.8],
[ 4. , 4.2, 4.4],
[ 5. , 5. , 5. ],
[ 6. , 5.8, 5.6],
[ 7. , 6.6, 6.2],
[ 8. , 7.4, 6.8],
[ 9. , 8.2, 7.4],
[10. , 9. , 8. ]])
A variation on this is:
np.c_[tuple(slice(i,j,11j) for i,j in zip(p1,p2))]
Really the same calculation, just different syntax.
outer can be used instead:
p1+np.outer(l1,(p2-p1))
But even that uses broadcasting. p1 is (3,) and the outer is (11,3), the result is (11,3).
@Brad's approach handles end points differently
In [686]: np.append(p1[:, None], np.repeat((p2 - p1) / 10, [10, 10, 10]).reshape
...: (3, -1).cumsum(axis=1), axis=1)
Out[686]:
array([[ 0. , 1. , 2. , 3. , 4. , 5. , 6. , 7. , 8. , 9. , 10. ],
[ 1. , 0.8, 1.6, 2.4, 3.2, 4. , 4.8, 5.6, 6.4, 7.2, 8. ],
[ 2. , 0.6, 1.2, 1.8, 2.4, 3. , 3.6, 4.2, 4.8, 5.4, 6. ]])
In [687]: _.shape
Out[687]: (3, 11)