Is Point between Points?

[thomthom]

Given three points A, B and C which are co-linear, what is the best practice way to determine if C is between A and B?

I searched the net and there appear to be various solutions, but there is the question of dealing with precision errors...

[thomthom]

I hacked together this:

def self.point_between(a, b, c)
  v1 = c.vector_to(a)
  v2 = c.vector_to(b)
  return true if !v1.valid? || !v2.valid?
  !v1.samedirection?(v2)
end

How bad is that?

[TIG]

RickW did something...
point1.between?(point2,point3)
???
Not sure where it is ...

[cjthompson]

Do you know why just comparing the individual X,Y and Zs won't work?

[thomthom]

@cjthompson said:

Do you know why just comparing the individual X,Y and Zs won't work?

Like how?

I'm curious in terms of performance and accuracy.

[TIG]

Here's one of several examples that are around

class Geom;;Point3d
  def between?(pt1, pt2, cond)
    # original idea by RickW
    # self is the point3d to test
    # cond if true returns true if self is at and end point, pt1 or pt2
    # cond if false does not include for self on an end point, pt1 or pt2
    # returns true if self is on the line between pt1 and pt2
    # returns false if not.
    d1 = self.distance(pt1) + self.distance(pt2)
    d2 = pt1.distance(pt2) + 0.0
    if (d1 <= d2) || (d1-d2 < 1e-10)
      if cond
        return true 
      else
        return true if self != pt1 && self != pt2
      end#if
    end#if
    return false
  end#def
end#class

[thomthom]

1e-10 - is that the tolerance?

I refined my previous hack. I have tried this method in hopes that the tolerance in the methods used makes for a result that matches how SU works. But I'm not all too sure. And I have not benchmarked it.

# Checks if point C is between line segment AB.
# Uses Sketchup methods to match it's accuracy. (Reliable?)
# Compares the vectors from C to A and B. Assumes Zero vector means that C
# is on the same point as A or B, which counts as 'between'.
def self.point_between(a, b, c)
  v1 = c.vector_to(a)
  v2 = c.vector_to(b)
  return true unless v1.valid? && v2.valid?
  v1.samedirection?(v2.reverse!)
end

[thomthom]

Btw, here is one of the links I looked at while reading up on this: http://stackoverflow.com/questions/328107/how-can-you-determine-a-point-is-between-two-other-points-on-a-line-segment

[cjthompson]

@TIG
You should probably convert d1 and d2 to float before comparing them:
0.0001.inch == 0.001.inch #=> true

BTW, do you have to determine whether the point is on the line, or is it just assumed?

[cjthompson]

something like this:

def pointBetween(a,b,c)
	array = [[a.x.to_f,b.x.to_f],[a.y.to_f,b.y.to_f],[a.z.to_f,b.z.to_f]]
	x = c.x.to_f.between?(*array[0].sort)
	y = c.y.to_f.between?(*array[1].sort)
	z = c.z.to_f.between?(*array[2].sort)
	return x && y && z
end

I'm not saying it will work, I'm just wondering whether it will or not.