How to detect if a point lies on a polyline

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How to detect if a point lies on a polyline (Views: 711)

Problem/Question/Abstract:

I would like to know if a point is in a polyline (not polygon). Any code?

Answer:

The main procedure is called ExploreLine. In this procedure Fst and Lst may be two consecutively points in the polyline. Srch is the point searched.

{ ... }
const {global}
  BigM = 1000000;

function Pend(Pi, Pf: TPoint): Real;
begin
  if (Pf.X = Pi.X) then
    Result := BigM {for a vertical line}
  else
    Result := (Pf.Y - Pi.Y) / (Pf.X - Pi.X);
end;

function Dist(Pi, Pf: TPoint): Real;
begin
  Result := sqrt(sqr(Pi.Y - Pf.Y) + sqr(Pi.X - Pf.X))
end;

function CalcPoint(Pi, Pf: TPoint; d: Word): TPoint;
var
  k, m: Real; { k=d / (1 + m2)˝ }
begin
  m := Pend(Pi, Pf);
  k := d / (Sqrt(1 + Sqr(m)));
  if ((Pf.X - Pi.X) < 0) then
  begin
    Result.X := Pi.X - Round(k);
    Result.Y := Pi.Y - Round(m * k);
  end
  else
  begin
    Result.X := Pi.X + Round(k);
    Result.Y := Pi.Y + Round(m * k);
  end;
end;

function ExploreLine(Srch, Fst, Lst: TPoint): Boolean;
var
  p: Word;
  Any: TPoint;
  lim, dis: Real;
begin
  lim := Dist(Lst, Fst);
  p := 1;
  Any := Fst;
  repeat
    Result := TestPoint(Srch, Any);
    dis := Dist(Any, Fst);
    Any := CalcPoint(Fst, Lst, Rad * p);
    Inc(p);
  until
    (Result)rr(dis >= lim);
end;

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