Travis's answer works for line3d objects consisting of a single segment.
Here is a more general version for any line3d object.
If you haven't already, install more-itertools:
```
sage: %pip install more-itertools
```
Then define this length function:
```
def line3d_euclidean_length(L):
r"""
Return the euclidean length of this piecewise linear path.
INPUT:
- ``L`` a piecewise linear path, as a ``line3d`` graphics object.
"""
from more_itertools import pairwise
V = RDF^3
return sum((V(q) - V(p)).norm() for p, q in pairwise(L.points))
```
Use it as follows:
```
sage: A = line3d([(1, 0, 1), (1, 1, 1)])
sage: line3d_euclidean_length(A)
sage: 1.0
sage: B = line3d([(0, 0, 0), (1, 0, 0), (1, 1, 1)])
sage: line3d_euclidean_length(B)
2.414213562373095
```
As Travis suggests, one might also be interested in the combinatorial
length:
```
def line3d_combinatorial_length(L):
r"""
Return the combinatorial length of this piecewise linear path.
That is, the number of segments it consists of.
INPUT:
- ``L`` a piecewise linear path, as a ``line3d`` graphics object.
"""
return Integer(len(L.points) - 1)
```
Usage:
```
sage: line3d_combinatorial_length(A)
sage: line3d_combinatorial_length(B)
```
Following Travis's suggestion, one could add an option
to combine successive segments if they are collinear.
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