Click here to Skip to main content
13,248,562 members (76,241 online)
Click here to Skip to main content
Add your own
alternative version


55 bookmarked
Posted 25 May 2007

A C# Implementation of Douglas-Peucker Line Approximation Algorithm

, 6 Jun 2007
Rate this:
Please Sign up or sign in to vote.
DP Line approximation algorithm is a well-known method to approximate 2D lines. It is quite fast, O(nlog_2(n)) for a n-points line and can drastically compress a data curve. Here, a fully OOP implementation is given.


I have found multiple implementations of the Douglas-Peucker algorithm but not in any .NET language, so I decided to port it over. Jonathan de Halleux has a wonderful explanation here.


I needed to reduce polygons size to display on a map based on zoom levels.

Using the Code

The code included is complete and should run out of the box in Visual Studio 2005. If it does not, please let me know.

/// <summary>
/// Uses the Douglas Peucker algorithm to reduce the number of points.
/// </summary>
/// <param name="Points">The points.</param>
/// <param name="Tolerance">The tolerance.</param>
/// <returns></returns>
public static List<Point> DouglasPeuckerReduction
    (List<Point> Points, Double Tolerance)
    if (Points == null || Points.Count < 3)
    return Points;

    Int32 firstPoint = 0;
    Int32 lastPoint = Points.Count - 1;
    List<Int32> pointIndexsToKeep = new List<Int32>();

    //Add the first and last index to the keepers

    //The first and the last point cannot be the same
    while (Points[firstPoint].Equals(Points[lastPoint]))

    DouglasPeuckerReduction(Points, firstPoint, lastPoint, 
    Tolerance, ref pointIndexsToKeep);

    List<Point> returnPoints = new List<Point>();
    foreach (Int32 index in pointIndexsToKeep)

    return returnPoints;
/// <summary>
/// Douglases the peucker reduction.
/// </summary>
/// <param name="points">The points.</param>
/// <param name="firstPoint">The first point.</param>
/// <param name="lastPoint">The last point.</param>
/// <param name="tolerance">The tolerance.</param>
/// <param name="pointIndexsToKeep">The point index to keep.</param>
private static void DouglasPeuckerReduction(List<Point> 
    points, Int32 firstPoint, Int32 lastPoint, Double tolerance, 
    ref List<Int32> pointIndexsToKeep)
    Double maxDistance = 0;
    Int32 indexFarthest = 0;
    for (Int32 index = firstPoint; index < lastPoint; index++)
        Double distance = PerpendicularDistance
            (points[firstPoint], points[lastPoint], points[index]);
        if (distance > maxDistance)
            maxDistance = distance;
            indexFarthest = index;

    if (maxDistance > tolerance && indexFarthest != 0)
        //Add the largest point that exceeds the tolerance
        DouglasPeuckerReduction(points, firstPoint, 
        indexFarthest, tolerance, ref pointIndexsToKeep);
        DouglasPeuckerReduction(points, indexFarthest, 
        lastPoint, tolerance, ref pointIndexsToKeep);

/// <summary>
/// The distance of a point from a line made from point1 and point2.
/// </summary>
/// <param name="pt1">The PT1.</param>
/// <param name="pt2">The PT2.</param>
/// <param name="p">The p.</param>
/// <returns></returns>
public static Double PerpendicularDistance
    (Point Point1, Point Point2, Point Point)
    //Area = |(1/2)(x1y2 + x2y3 + x3y1 - x2y1 - x3y2 - x1y3)|   *Area of triangle
    //Base = v((x1-x2)²+(x1-x2)²)                               *Base of Triangle*
    //Area = .5*Base*H                                          *Solve for height
    //Height = Area/.5/Base

    Double area = Math.Abs(.5 * (Point1.X * Point2.Y + Point2.X * 
    Point.Y + Point.X * Point1.Y - Point2.X * Point1.Y - Point.X * 
    Point2.Y - Point1.X * Point.Y));
    Double bottom = Math.Sqrt(Math.Pow(Point1.X - Point2.X, 2) + 
    Math.Pow(Point1.Y - Point2.Y, 2));
    Double height = area / bottom * 2;

    return height;
    //Another option
    //Double A = Point.X - Point1.X;
    //Double B = Point.Y - Point1.Y;
    //Double C = Point2.X - Point1.X;
    //Double D = Point2.Y - Point1.Y;
    //Double dot = A * C + B * D;
    //Double len_sq = C * C + D * D;
    //Double param = dot / len_sq;
    //Double xx, yy;
    //if (param < 0)
    //    xx = Point1.X;
    //    yy = Point1.Y;
    //else if (param > 1)
    //    xx = Point2.X;
    //    yy = Point2.Y;
    //    xx = Point1.X + param * C;
    //    yy = Point1.Y + param * D;
    //Double d = DistanceBetweenOn2DPlane(Point, new Point(xx, yy));

Points of Interest

The code is not overly complicated. It was fun to port this algorithm, since all I feel I do nowadays is hold business' hands to help them try and solve business problems that there is no consensus on.


  • Beta 1


This article, along with any associated source code and files, is licensed under The MIT License


About the Author

Web Developer
United States United States
No Biography provided

You may also be interested in...

Comments and Discussions

Questionrejecting recursion + distance calc acceleration Pin
adevder19-Feb-17 0:12
memberadevder19-Feb-17 0:12 
AnswerRe: rejecting recursion + distance calc acceleration Pin
TerrySpiderman21-Mar-17 3:05
professionalTerrySpiderman21-Mar-17 3:05 
Questionto save stack memory with great amount of points and tolerance near zero i prefer to reject recursion Pin
adevder18-Feb-17 1:22
memberadevder18-Feb-17 1:22 
PraiseNice Pin
veen_rp18-Apr-16 19:41
professionalveen_rp18-Apr-16 19:41 
BugIf (first = last) Bug! Pin
Giovani Luigi14-Dec-15 12:44
memberGiovani Luigi14-Dec-15 12:44 
QuestionDouglasPeuckerN() conversion? Pin
cbordeman11-Dec-15 17:42
membercbordeman11-Dec-15 17:42 
AnswerRe: DouglasPeuckerN() conversion? Pin
lorsco0127-Apr-17 7:44
memberlorsco0127-Apr-17 7:44 
GeneralUseful Pin
Dineshkumar_MCA22-Apr-15 2:18
professionalDineshkumar_MCA22-Apr-15 2:18 
QuestionBUG tolerance Pin
Member 1017584518-Feb-15 2:08
memberMember 1017584518-Feb-15 2:08 
QuestionThanks + pruned code Pin
Stoyan Haralampiev23-Oct-14 3:30
memberStoyan Haralampiev23-Oct-14 3:30 
QuestionUsing this algorithm on data from database Pin
Saket Surya2-Jun-14 3:38
memberSaket Surya2-Jun-14 3:38 
QuestionPoint projected on the line but behind the segment? Bug? Pin
Sergiy Tkachuk25-Mar-14 14:31
memberSergiy Tkachuk25-Mar-14 14:31 
QuestionAbout Tolerance Pin
kamlesh Prajapati8-Jan-14 23:55
groupkamlesh Prajapati8-Jan-14 23:55 
QuestionWhy do you create your own Point? Pin
leiyangge3-Jan-14 22:37
memberleiyangge3-Jan-14 22:37 
QuestionLicense Pin
Diego Catalano14-Dec-13 2:42
memberDiego Catalano14-Dec-13 2:42 
Question1 bug, + 1 potential bug Pin
gyuri1023-Apr-12 23:45
membergyuri1023-Apr-12 23:45 
AnswerRe: 1 bug, + 1 potential bug Pin
tplokas26-Mar-13 14:46
membertplokas26-Mar-13 14:46 
QuestionUseful,Thanks! Pin
masy19112-Mar-12 23:43
membermasy19112-Mar-12 23:43 
QuestionGreat Job! Pin
cdrake19-Dec-11 8:32
membercdrake19-Dec-11 8:32 
Generalhow calculate an epsilon value Pin
unravel-the-sky23-May-11 6:52
memberunravel-the-sky23-May-11 6:52 
GeneralSome Issues with your implementation Pin
matthew minke15-Jul-10 11:57
membermatthew minke15-Jul-10 11:57 
GeneralVery useful thanks - Point number reduction (Max Distance relevant tolerance) [modified] Pin
kamyk3-Mar-10 23:05
memberkamyk3-Mar-10 23:05 
GeneralVery useful thanks Pin
dylanhayes17-Nov-09 2:35
memberdylanhayes17-Nov-09 2:35 
I have used this and it does a nice job of reducing a series of lat/longs for display on maps.

A couple of points for people looking to use the code:

I spent ages trying to hunt down a stack over flow error, before realising that the algo was crashing when passed a tolerance of 0. I'd suggest a simple sanity check of the arguments that get passed is a useful addition.

If you want to reduce the number of points to a useful number for display on Google maps or Bing maps (more than 2000 points in a polyline is slow!), it's quite useful to add a little bit of code to work out a tolerance value to get the right reduction. You could do that with either looking at the point count and picking a relevant tolerance, or interatively running the algo with progressively higher tolerances until the number of points returned was small enough.
GeneralThanks! Pin
Member 337866727-Mar-09 10:28
memberMember 337866727-Mar-09 10:28 
QuestionAnd other functions from Plot Graphic Library? Pin
agorby28-Apr-08 3:28
memberagorby28-Apr-08 3:28 

General General    News News    Suggestion Suggestion    Question Question    Bug Bug    Answer Answer    Joke Joke    Praise Praise    Rant Rant    Admin Admin   

Use Ctrl+Left/Right to switch messages, Ctrl+Up/Down to switch threads, Ctrl+Shift+Left/Right to switch pages.

Permalink | Advertise | Privacy | Terms of Use | Mobile
Web01 | 2.8.171114.1 | Last Updated 6 Jun 2007
Article Copyright 2007 by CraigSelbert
Everything else Copyright © CodeProject, 1999-2017
Layout: fixed | fluid