Question

I would like to implement the Ramer–Douglas–Peucker_algorithm in C++.

The pseudo code looks like this:

function DouglasPeucker(PointList[], epsilon)
 //Find the point with the maximum distance
 dmax = 0
 index = 0
 for i = 2 to (length(PointList) - 1)
  d = OrthogonalDistance(PointList[i], Line(PointList[1], PointList[end])) 
  if d > dmax
   index = i
   dmax = d
  end
 end

 //If max distance is greater than epsilon, recursively simplify
 if dmax >= epsilon
  //Recursive call
  recResults1[] = DouglasPeucker(PointList[1...index], epsilon)
  recResults2[] = DouglasPeucker(PointList[index...end], epsilon)

  // Build the result list
  ResultList[] = {recResults1[1...end-1] recResults2[1...end]}
 else
  ResultList[] = {PointList[1], PointList[end]}
 end

 //Return the result
 return ResultList[]
end

Here is my understanding so far.
It is a recursive function taking in an array of points and a distance threshold.

Then it iterates through the current points to find the point with the maximum distance.

I got a bit lost with the Orthographical Distance function. How do I compute this? I’ve never seen a distance function take a line segment as a parameter.

I think aside from this I should be alright, I will just use std::vectors for the arrays. I think I will use std::copy and then push or pop according to what the algorithm says.

Thanks

Answer 1

The OrthogonalDistance is shown in this picture:

So it’s the distance from your point and the point on the line which is the projection of that point on the line.

The distance from a point to a line is usally something like this:

_{(source: fauser.edu)}

where x0 and y0 are the coordinates of the external point and a, b, c are the coefficient of the equation of your line.

That’s what I remember from school, long time ago.