LineScaledCoordinate problem for exact coordinates

Question

Bug introduced in 10.4 or earlier and persisting through 11.2

CASE:2326540

Solution: Wait and use N meanwhile.

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I've faced this problem writing an answer for Animate point go round a triangle.

For coordinates with exact values, instead of moving along a multi-line LineScaledCoordinate is mooving along extrapolated first segment.

It is not always the case but always for exact values. N is the fix.

Needs["GraphUtilities`"]
vertices = {{0, 0}, {1, 0}, {1, 2}, {2, 1}};
Slider[Dynamic@t]
Graphics[{
EdgeForm@Thick, FaceForm@None, Polygon@vertices
  ,
  AbsolutePointSize@12, Red, Dynamic[Point[LineScaledCoordinate[vertices, t]]]
  ,
  AbsolutePointSize@12, Blue, Dynamic[Point[LineScaledCoordinate[N@vertices, t]]]
  },
  PlotRange -> {{0, 4.5}, {0, 4.5}}, Frame -> True
 ]

Answer 1

Internally LineScaledCoordinate use

Position[d, _?(#1 >= t &)]

to detect a current segment. Here d is an accumulated list of distances (relative to the total length of segments). However, algebraic expressions are not atomic:

t = 0.5;
d = {0, 1/(3 + Sqrt[2]), 3/(3 + Sqrt[2]), 1};
Position[d, _?(#1 >= t &)]
Position[N@d, _?(#1 >= t &)]
(* {{2, 1, 1}, {2, 1, 2, 1}, {2, 1, 2, 2}, {2, 1, 2}, {2, 
  1}, {3, 1}, {3, 2, 1, 1}, {3, 2, 1, 2, 1}, {3, 2, 1, 2, 2}, {3, 2, 
  1, 2}, {3, 2, 1}, {3}, {4}} *)
(* {{3}, {4}} *)