11,934,809 members (49,869 online)
alternative version

70.3K views
53 bookmarked
Posted

A C# Implementation of Douglas-Peucker Line Approximation Algorithm

, 6 Jun 2007 CPOL
 Rate this:
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.

/// <span class="code-SummaryComment"><summary></span>
/// Uses the Douglas Peucker algorithm to reduce the number of points.
/// <span class="code-SummaryComment"></summary></span>
/// <span class="code-SummaryComment"><param name="Points">The points.</param></span>
/// <span class="code-SummaryComment"><param name="Tolerance">The tolerance.</param></span>
/// <span class="code-SummaryComment"><returns></returns></span>
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;
}

/// <span class="code-SummaryComment"><summary></span>
/// Douglases the peucker reduction.
/// <span class="code-SummaryComment"></summary></span>
/// <span class="code-SummaryComment"><param name="points">The points.</param></span>
/// <span class="code-SummaryComment"><param name="firstPoint">The first point.</param></span>
/// <span class="code-SummaryComment"><param name="lastPoint">The last point.</param></span>
/// <span class="code-SummaryComment"><param name="tolerance">The tolerance.</param></span>
/// <span class="code-SummaryComment"><param name="pointIndexsToKeep">The point index to keep.</param></span>
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);
}
}

/// <span class="code-SummaryComment"><summary></span>
/// The distance of a point from a line made from point1 and point2.
/// <span class="code-SummaryComment"></summary></span>
/// <span class="code-SummaryComment"><param name="pt1">The PT1.</param></span>
/// <span class="code-SummaryComment"><param name="pt2">The PT2.</param></span>
/// <span class="code-SummaryComment"><param name="p">The p.</param></span>
/// <span class="code-SummaryComment"><returns></returns></span>
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 now a days is hold business' hands to help them try and solve business problems that there is no consensus on.

• Beta 1

Share

 Web Developer United States
No Biography provided

You may also be interested in...

 First PrevNext
 Useful Dineshkumar_MCA22-Apr-15 2:18 Dineshkumar_MCA 22-Apr-15 2:18
 BUG tolerance Member 1017584518-Feb-15 2:08 Member 10175845 18-Feb-15 2:08
 Thanks + pruned code Stoyan Haralampiev23-Oct-14 3:30 Stoyan Haralampiev 23-Oct-14 3:30
 Using this algorithm on data from database Saket Surya2-Jun-14 3:38 Saket Surya 2-Jun-14 3:38
 Point projected on the line but behind the segment? Bug? Sergiy Tkachuk25-Mar-14 14:31 Sergiy Tkachuk 25-Mar-14 14:31
 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
 License Diego Catalano14-Dec-13 2:42 Diego Catalano 14-Dec-13 2:42
 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
 I implemented this in a pet silverlight project. It works well.
 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
 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
 perpendicular Alex Bespalov22-Dec-07 21:23 Alex Bespalov 22-Dec-07 21:23
 perpendicular Alex Bespalov22-Dec-07 21:21 Alex Bespalov 22-Dec-07 21:21
 Do you know offhand if the result of this algorithm is the same/different.... sherifffruitfly6-Jun-07 12:28 sherifffruitfly 6-Jun-07 12:28
 Re: Do you know offhand if the result of this algorithm is the same/different.... CraigSelbert6-Jun-07 16:27 CraigSelbert 6-Jun-07 16:27
 Code question DocJim4-Jun-07 9:46 DocJim 4-Jun-07 9:46
 Re: Code question CraigSelbert6-Jun-07 9:30 CraigSelbert 6-Jun-07 9:30
 Neat...Yeah...New algorithm jconwell25-May-07 5:50 jconwell 25-May-07 5:50
 Last Visit: 31-Dec-99 19:00     Last Update: 1-Dec-15 9:36 Refresh 12 Next »