Uniform distance between points

Question

How could I, having a path defined by several points that are not in a uniform distance from each other, redefine along the same path the same number of points but with a uniform distance. I'm trying to do this in Objective-C with NSArrays of CGPoints but so far I haven't had any luck with this. Thank you for any help.

EDIT

I was wondering if it would help to reduce the number of points, like when detecting if 3 points are collinear we could remove the middle one, but I'm not sure that would help.

EDIT

Illustrating: Reds are the original points, blues the post processed points:

The new path defined by the blue dots does not correspond to the original one.

Answer 1

I think the problem is simple and easily solvable actually :)

The basic idea is:

• First check if the distance between your current point (P) and the end point of the line segment you are on is >= the distance between P and the next point (Q).

• If it is, great, we use some simple trigonometry to figure it out.

• Else, we move to the adjacent line segment (in your ordering) and deduct the distance between P and the endpoint of the line segment you are on and continue the process.

Pseudocode:

Defined previously

struct LineSegment
{
  Point start,end;
  int ID;
  double len; // len = EuclideanDistance(start,end);
  LineSegment *next_segment;
  double theta; // theta = atan2(slope_of_line_segment);
}

Function [LineSegment nextseg] = FindNextLineSegment(LineSegment lineseg)
Input: LineSegment object of the current line segment
Output: LineSegment object of the adjacent line segment in your ordering. 
nextseg.ID = -1 if there are no more segments

Function: Find the next point along your path

Function [Point Q, LineSegment Z] = FindNextPt(Point P, LineSegment lineseg, int dist): 
Input: The current point P, the distance between this point and the next, and the LineSegment of the line segment which contains P.
Output: The next point Q, and the line segment it is on

Procedure:
distToEndpt = EuclideanDistance(P,lineseg->end);
if( distToEndpt >= d )
{
 Point Q(lineseg->start.x + dist*cos(lineseg.theta), lineseg->start.y + dist*sin(lineseg.theta));
 Z = lineseg;
}
else
{
 nextseg = lineseg->next_segment;
    if( nextseg.ID !=-1 )
    {
  [Q, Z] = FindNextPt(nextseg->start,nextseg->ID,dist-distToEndpt);
 }
    else
    {
  return [P,lineseg];
 }
}
 return [Q,Z]

Entry point

Function main()
Output: vector of points
Procedure:

vector<LineSegment> line_segments;
// Define it somehow giving it all the properties
// ....

vector<Point> equidistant_points;
const int d = DIST;

[Q Z] = FindNextPoint(line_segments[0].start,line_segments[0],DIST);
while( Z.ID != -1 )
{
 equidistant_points.push_back(Q);
 [Q Z] = FindNextPt(Q,Z,d);
}