Behavior of parallelVectors() function

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  kevin_o_toole_1 Onshape Employees, Developers, HDM Posts: 565

  December 2017 edited December 2017

  Hmm, this one's tricky. I think you found a bug, but even if that bug were fixed, parallelVectors wouldn't quite suit that use case.
  
  In the case you mentioned of parallelVectors(p - refPoint, refVector), I think a zero check outside the function *is* warranted. If (p - refPoint) is very close to (but not precisely) zero, it quite likely is pointing in some non-parallel direction. If we called that parallel, we'd lose some other important properties, like the property where parallelVectors(K*a, b) returns the same thing for any non-zero K. So for your case, a better check check would be something like:
  

  norm(cross(p - refPoint, refUnitVector)) < TOLERANCE.zeroLength.

  Alternatively, if you (perhaps rightfully) don't want to think about cross products, just do a zero check (via tolerantEquals) and a parallel check separately.
  
  For reference, our implementation is not far from that, but it measures an angular deviation rather than a linear one:
  

  <div>export function parallelVectors(vector1 is Vector, vector2 is Vector) returns boolean<br>{<br>&nbsp; &nbsp; const crossP2 = squaredNorm(cross(vector1, vector2));<br>&nbsp; &nbsp; const v1v2 = squaredNorm(vector1) * squaredNorm(vector2);<br>&nbsp; &nbsp; return crossP2 < v1v2 * TOLERANCE.zeroAngle * TOLERANCE.zeroAngle;<br>}<br></div>

  The bug I mentioned up top is that I think the < sign should be <=, so for the case where a vector is exactly zero should return true. However, tolerances are tricky, so the fixed version still wouldn't have the property you desire. You care about linear deviation from a parallel line, whereas parallelVectors() cares about angular deviation from parallel angle. These two concepts are two closely related but mathematically distinct once you throw tolerances into the mix!
  

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  konstantin_shiriazdanov Member Posts: 1,221 ✭✭✭✭✭

  December 2017

  ok, thanks @kevin_o_toole_1
  a little problem with all that built in tolerances is that they are not documented
  
  

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