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.