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Posted 25 May 2007

A C# Implementation of Douglas-Peucker Line Approximation Algorithm

, 6 Jun 2007
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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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 Very useful thanks - Point number reduction (Max Distance relevant tolerance) [modified] kamyk3-Mar-10 22:05 kamyk 3-Mar-10 22:05
 Very useful thanks dylanhayes17-Nov-09 1:35 dylanhayes 17-Nov-09 1:35
 Thanks! Member 337866727-Mar-09 9:28 Member 3378667 27-Mar-09 9:28
 And other functions from Plot Graphic Library? agorby28-Apr-08 2:28 agorby 28-Apr-08 2:28
 perpendicular Alex Bespalov22-Dec-07 20:23 Alex Bespalov 22-Dec-07 20:23
 perpendicular Alex Bespalov22-Dec-07 20:21 Alex Bespalov 22-Dec-07 20:21
 Do you know offhand if the result of this algorithm is the same/different.... sherifffruitfly6-Jun-07 11:28 sherifffruitfly 6-Jun-07 11:28
 Re: Do you know offhand if the result of this algorithm is the same/different.... CraigSelbert6-Jun-07 15:27 CraigSelbert 6-Jun-07 15:27
 I do not know. I was just wanting to port varius c and c++ versions to c#, being that I could not find one. From what I just read about your post, I would hazard to say that yea thwy would give the same result.
 Code question DocJim4-Jun-07 8:46 DocJim 4-Jun-07 8:46
 Re: Code question CraigSelbert6-Jun-07 8:30 CraigSelbert 6-Jun-07 8:30
 Neat...Yeah...New algorithm jconwell25-May-07 4:50 jconwell 25-May-07 4:50
 Re: Neat...Yeah...New algorithm CraigSelbert25-May-07 15:40 CraigSelbert 25-May-07 15:40
 Take a look here D_Guidi25-May-07 3:32 D_Guidi 25-May-07 3:32
 Re: Take a look here CraigSelbert25-May-07 15:49 CraigSelbert 25-May-07 15:49
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