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Posted 25 May 2007

# A C# Implementation of Douglas-Peucker Line Approximation Algorithm

, 6 Jun 2007 MIT
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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.

## Introduction

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.

## Background

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]))
{
lastPoint--;
}

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

List<Point> returnPoints = new List<Point>();
pointIndexsToKeep.Sort();
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;
//}
//else
//{
//    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

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 to save stack memory with great amount of points and tolerance near zero i prefer to reject recursion adevder18-Feb-17 1:22 adevder 18-Feb-17 1:22
 Nice veen_rp18-Apr-16 19:41 veen_rp 18-Apr-16 19:41
 If (first = last) Bug! Giovani Luigi14-Dec-15 12:44 Giovani Luigi 14-Dec-15 12:44
 DouglasPeuckerN() conversion? cbordeman11-Dec-15 17:42 cbordeman 11-Dec-15 17:42
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 BUG tolerance Member 1017584518-Feb-15 2:08 Member 10175845 18-Feb-15 2:08
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 About Tolerance kamlesh Prajapati8-Jan-14 23:55 kamlesh Prajapati 8-Jan-14 23:55
 Why do you create your own Point? leiyangge3-Jan-14 22:37 leiyangge 3-Jan-14 22:37
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 1 bug, + 1 potential bug gyuri1023-Apr-12 23:45 gyuri10 23-Apr-12 23:45
 Re: 1 bug, + 1 potential bug tplokas26-Mar-13 14:46 tplokas 26-Mar-13 14:46
 Useful,Thanks! masy19112-Mar-12 23:43 masy191 12-Mar-12 23:43
 Great Job! cdrake19-Dec-11 8:32 cdrake 19-Dec-11 8:32
 how calculate an epsilon value unravel-the-sky23-May-11 6:52 unravel-the-sky 23-May-11 6:52
 Some Issues with your implementation matthew minke15-Jul-10 11:57 matthew minke 15-Jul-10 11:57
 I have found some issues with your implementation of this code. here are the changes that i have made. ``` Double maxDistance = 0; Int32 indexFarthest = 0; if (lastPointIndex - firstPointIndex > 1)//ADDITION: need to have more than two points in the set we are looking through { for (Int32 index = firstPointIndex; index < lastPointIndex; index++) { Double distance = PerpendicularDistance(points[firstPointIndex], points[lastPointIndex], points[index]); if (distance > maxDistance) { maxDistance = distance; indexFarthest = index; } } if (maxDistance > Tolerance && indexFarthest != firstPointIndex)//CHANGE: condition was wrong. { //Add the largest point that exceeds the tolerance pointIndexsToKeep.Add(indexFarthest); Reduction(points, firstPointIndex, indexFarthest, ref pointIndexsToKeep); Reduction(points, indexFarthest, lastPointIndex, ref pointIndexsToKeep); } } ```
 Very useful thanks - Point number reduction (Max Distance relevant tolerance) [modified] kamyk3-Mar-10 23:05 kamyk 3-Mar-10 23:05
 Very useful thanks dylanhayes17-Nov-09 2:35 dylanhayes 17-Nov-09 2:35
 Thanks! Member 337866727-Mar-09 10:28 Member 3378667 27-Mar-09 10:28
 And other functions from Plot Graphic Library? agorby28-Apr-08 3:28 agorby 28-Apr-08 3:28
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