Dear Mikel,

The BoxRatios is nothing to worry about. It only concerns the representation. If you have a look at the line where I calculate the length of the curve:

ArcLength@DiscretizeGraphics@BSplineCurve[points]

there is no mention of the box ratios. So that is not a problem. You might want to look at the documentation of ArcLength and DiscretizeGraphics to study the available options.

Cheers,

Marco

Dear Mikel,

the result is actually not a plane. What happens it that the third coordinate is 5-6 orders of magnitude smaller than the other two components. This is why, when you plot it, It can be mistaken for a plane.

If you use

Graphics3D[{BSplineCurve[points]}, BoxRatios -> {1, 1, 1}, ImageSize -> Medium]

you see what is going on.

You can then also use your function

Graphics3D[{BSplineCurve[points], Green, Line[points], Red, Point[points]}, BoxRatios -> {1, 1, 1}, ImageSize -> Medium]

to achieve the same effect.

The Length might then be:

ArcLength@DiscretizeGraphics@BSplineCurve[points]
 (*165671.*)

The length will, of course depend on the degree of the spline. Here is a little table to show that:

Insert[Grid[Join[{{"Degree", "Length"}}, Table[{deg, NumberForm[
      ArcLength@DiscretizeGraphics[BSplineCurve[points, SplineDegree -> deg]], 16]}, {deg, 1, 8}]]], 
      {Background -> {None, {GrayLevel[0.7], {White}}}, Dividers -> {Black, {2 -> Black}}, Frame -> True, Spacings -> {2, {2, {0.7}, 2}}}, 2]

Here's a little plot of that:

ListLinePlot[
 Table[{deg, ArcLength@DiscretizeGraphics[BSplineCurve[points, SplineDegree -> deg]]}, {deg, 1, 30}], AxesLabel -> {"degree", "length"}]

Cheers,

Marco