Bug in ArcLength?

Question

fixed in 10.1 (windows)

With Mathematica 10.0.2:

ArcLength[Line[{{0, 0}, {1, 0}, {2, 0}}]]
ArcLength[Line[{{0}, {1}, {2}}]]
(* 2 *)
(* 2 *)

However,

ArcLength[Line[{{0, 0}, {1, 0}, {2.0, 0}}]]
ArcLength[Line[{{0}, {1}, {2.0}}]]
(* 1. *)
(* 1. *)

Certainly looks like a bug, especially since ArcLength[{{0.0},{1},{2}}] = 2. — David G. Stork, Dec 16 '14 at 02:36
And ArcLength[Line[{{0, 0}, {1, 0}, {2.000001, 0}}]] is back to 2. again... — bill s, Dec 16 '14 at 03:05
Confirmed on 10.0.1 on Windows 7(64). This is quite horrible. — Yves Klett, Dec 16 '14 at 07:06
There are another problems with new geometric measure capabilities, read carefully e.g. answers to this question Finding length of intersection of two surfaces. The anser by RunnyKine had involved a wrong result before a few edits. — Artes, Dec 16 '14 at 09:43
The bug is actually in RegionMeasure. Try RegionMeasure[Line[{{0, 0}, {1, 0}, {2., 0}}], 1] and RegionMeasure[Line[{{0, 0}, {1, 0}, {2, 0}}], 1] — Rolf Mertig, Dec 16 '14 at 10:00

score 15 · Answer 1 · edited Aug 01 '17 at 01:57

15

Yes, this is a bug in the more general function RegionMeasure. I knew there were some edge cases in the handling of inexact numerics, but I was unaware of such a simple example. I will forward this bug internally.

Workarounds include using the parametric (2-argument) form of ArcLength, and using DiscretizeRegion to pre-process regions before sending them to ArcLength/RegionMeausure:

In[21]:= ArcLength[DiscretizeRegion@Line[{{0, 0}, {1, 0}, {2.0, 0}}]]

Out[21]= 2.

In[22]:= ArcLength[DiscretizeRegion@Line[{{0}, {1}, {2.0}}]]

Out[22]= 2.

edited Aug 01 '17 at 01:57

J. M.'s missing motivation

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answered Dec 16 '14 at 22:28

Itai Seggev

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This seems to be an issue with any Line composed of collinear segments and having inexact numbers for coordinates. – Michael E2 Feb 07 '15 at 18:07

score 1 · Answer 2 · answered Apr 02 '15 at 08:56

1

bug fixed in 10.1 (windows)

Mathematica graphics

code

ArcLength[Line[{{0, 0}, {1, 0}, {2, 0}}]]
ArcLength[Line[{{0}, {1}, {2}}]]
ArcLength[Line[{{0, 0}, {1, 0}, {2.0, 0}}]]
ArcLength[Line[{{0}, {1}, {2.0}}]]

answered Apr 02 '15 at 08:56

Nasser

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Bug in ArcLength?

2 Answers2

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