/// <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
pointIndexsToKeep.Add(firstPoint);
pointIndexsToKeep.Add(lastPoint);
//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)
{
returnPoints.Add(Points[index]);
}
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
pointIndexsToKeep.Add(indexFarthest);
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));
}
