public static List <T> SimplifyByArea <T>(List <T> points, SimplificationParamters parameters /*, double threshold, bool retain3Points = false*/) where T : IPoint
{
if (points == null || points.Count == 0)
{
return(null);
}
else if (points.Count == 2)
{
return(points);
}
List <T> result = new List <T>();
result.Add(points.First());
for (int i = 0; i < points.Count - 2; i++)
{
var area = SpatialUtility.GetUnsignedTriangleArea(points[i], points[i + 1], points[i + 2]);
if (area > parameters.AreaThreshold /* threshold*/)
{
result.Add(points[i + 1]);
}
}
if (parameters.Retain3Points && result.Count == 1)
{
result.Add(points[points.Count() / 2]);
}
result.Add(points.Last());
return(result);
}
/// <summary>
///
/// </summary>
/// <param name="points"></param>
/// <param name="threshold">Must be between 0 and 1</param>
/// <returns></returns>
public static List <T> SimplifyByAngle <T>(List <T> points, SimplificationParamters paramters /*double threshold, bool retain3Points = false*/) where T : IPoint
{
if (points == null || points.Count == 0)
{
return(null);
}
else if (points.Count == 2)
{
return(points);
}
List <Tuple <int, double> > angles = new List <Tuple <int, double> >();
for (int i = 0; i < points.Count - 2; i++)
{
var angle = SpatialUtility.GetSquareCosineOfAngle(points[i], points[i + 1], points[i + 2]);
angles.Add(new Tuple <int, double>(i + 1, angle));
}
//When i.Item2 ~ 1 it means points are on a line
var filter1 = angles.Where(i => i.Item2 < paramters.AngleThreshold).Select(i => i.Item1).ToList();
filter1.Insert(0, 0);
filter1.Add(points.Count - 1);
var result = filter1.Select(i => points[i]).ToList();
return(result);
}
// ref: https://doi.org/10.3138/FM57-6770-U75U-7727
public static List <T> SimplifyByDouglasPeucker <T>(List <T> pointList, SimplificationParamters parameters /*, double threshold, bool retain3Points = false*/) where T : IPoint
{
var result = new List <T>();
if (pointList == null || pointList.Count < 2)
{
return(result);
}
if (pointList.Count == 2)
{
return(pointList);
}
//to handle lines with the same start and end
if (pointList.First().Equals(pointList.Last()))
{
//return DivideForDouglasPeucker(pointList, threshold, pointList.Count / 2);
return(DivideForDouglasPeucker(pointList, parameters, pointList.Count / 2));
}
var numberOfPoints = pointList.Count;
//
double maxSemiPerpendicularDistance = 0;
int maxIndex = 0;
//1399.06.23
//در این جا برای سرعت بیشتر مقدار فاصله استفاه
//نمیشود بلکه توان دوم آن استفاده میشود. این
//روش باعث میشود در محاسبات از تابع جزر استفاده
//نشود
//double effectiveThreshold = threshold * threshold;
double effectiveThreshold = parameters.DistanceThreshold.Value /** parameters.DistanceThreshold.Value*/;
for (int i = 1; i < numberOfPoints - 1; i++)
{
var semiPerpendicularDistance = SpatialUtility.GetPointToLineSegmentDistance(pointList[0], pointList[numberOfPoints - 1], pointList[i]);
if (semiPerpendicularDistance > maxSemiPerpendicularDistance)
{
maxIndex = i;
maxSemiPerpendicularDistance = semiPerpendicularDistance;
}
}
if (maxSemiPerpendicularDistance > effectiveThreshold)
{
return(DivideForDouglasPeucker(pointList, parameters, maxIndex));
}
else
{
return(new List <T> {
pointList[0], pointList[numberOfPoints - 1]
});
}
}
/// <summary>
/// Additive Angle + Area Check
/// </summary>
/// <param name="points"></param>
/// <param name="anglethreshold">Must be between 0 and 1</param>
/// <returns></returns>
public static List <T> AdditiveSimplifyByAngleArea <T>(List <T> points, SimplificationParamters paramters /*double angleThreshold, double areaThreshold, bool retain3Points = false*/) where T : IPoint
{
if (points == null || points.Count == 0)
{
return(null);
}
else if (points.Count == 2)
{
return(points);
}
List <int> filtered = new List <int>();
filtered.Add(0);
int firstIndex = 0, secondIndex = 1, thirdIndex = 2;
double tempArea = 0;
while (thirdIndex < points.Count)
{
var angle = SpatialUtility.GetSquareCosineOfAngle(points[firstIndex], points[secondIndex], points[thirdIndex]);
var area = SpatialUtility.GetUnsignedTriangleArea(points[firstIndex], points[secondIndex], points[thirdIndex]);
tempArea += area;
//if (Math.Abs(angle) < threshold)
//{
if ((angle < 0 || angle < paramters.AngleThreshold.Value) || tempArea > paramters.AreaThreshold.Value)
{
filtered.Add(secondIndex);
firstIndex = secondIndex;
tempArea = 0;
}
secondIndex = thirdIndex;
thirdIndex = thirdIndex + 1;
}
if (paramters.Retain3Points && filtered.Count == 1)
{
filtered.Add(points.Count() / 2);
}
filtered.Add(points.Count - 1);
var result = filtered.Select(i => points[i]).ToList();
return(result);
}
public static List <T> AdditiveSimplifyByArea <T>(List <T> points, SimplificationParamters parameters /*, double threshold, bool retain3Points = false*/) where T : IPoint
{
if (points == null || points.Count == 0)
{
return(null);
}
else if (points.Count == 2)
{
return(points);
}
List <T> result = new List <T>();
result.Add(points.First());
int firstIndex = 0, secondIndex = 1, thirdIndex = 2;
double tempArea = 0;
while (thirdIndex < points.Count)
{
//1399.07.10
//var area = SpatialUtility.CalculateSignedTriangleArea(points[firstIndex], points[secondIndex], points[thirdIndex]);
//tempArea += area;
//if (Math.Abs(tempArea) > threshold)
var area = SpatialUtility.GetUnsignedTriangleArea(points[firstIndex], points[secondIndex], points[thirdIndex]);
tempArea += area;
if (tempArea > parameters.AreaThreshold /*threshold*/)
{
tempArea = 0;
result.Add(points[secondIndex]);
firstIndex = secondIndex;
}
secondIndex = thirdIndex;
thirdIndex = thirdIndex + 1;
}
if (parameters.Retain3Points && result.Count == 1)
{
result.Add(points[points.Count() / 2]);
}
result.Add(points.Last());
//var result = filtered.Select(i => points[i]).ToList();
return(result);
}
public static List <T> AdditiveSimplifyByAreaPlus <T>(List <T> points, SimplificationParamters paramters /*double threshold, bool retain3Points = false*/) where T : IPoint
{
if (points == null || points.Count == 0)
{
return(null);
}
else if (points.Count == 2)
{
return(points);
}
List <int> filtered = new List <int>();
filtered.Add(0);
int firstIndex = 0, secondIndex = 1, thirdIndex = 2;
var totalAreaCoef = SpatialUtility.IsClockwise(points) ? 1 : -1;
double tempArea = 0;
while (thirdIndex < points.Count)
{
var area = SpatialUtility.GetSignedTriangleArea(points[firstIndex], points[secondIndex], points[thirdIndex]);
var areaCheck2 = SpatialUtility.GetUnsignedTriangleArea(points[firstIndex], points[(int)((firstIndex + thirdIndex) / 2.0)], points[thirdIndex]);
tempArea += area;
if (Math.Abs(tempArea) > paramters.AreaThreshold || areaCheck2 > paramters.AreaThreshold || (area * totalAreaCoef > 0))
{
tempArea = 0;
filtered.Add(secondIndex);
firstIndex = secondIndex;
}
secondIndex = thirdIndex;
thirdIndex = thirdIndex + 1;
}
if (filtered.Count == 1)
{
filtered.Add(points.Count() / 2);
}
filtered.Add(points.Count - 1);
var result = filtered.Select(i => points[i]).ToList();
return(result);
}
// http://psimpl.sourceforge.net/reumann-witkam.html
public static List <T> SimplifyByReumannWitkam <T>(List <T> pointList, SimplificationParamters parameters) where T : IPoint
{
var result = new List <T>();
if (pointList == null || pointList.Count < 2)
{
return(result);
}
if (pointList.Count == 2)
{
return(pointList);
}
var numberOfPoints = pointList.Count;
//1399.06.23
//در این جا برای سرعت بیشتر مقدار فاصله استفاه
//نمیشود بلکه توان دوم آن استفاده میشود. این
//روش باعث میشود در محاسبات از تابع جزر استفاده
//نشود
//double effectiveThreshold = threshold * threshold;
double effectiveThreshold = parameters.DistanceThreshold.Value /** parameters.DistanceThreshold.Value*/;
result.Add(pointList[0]);
int startIndex = 0;
int middleIndex = 1;
for (int i = 2; i < numberOfPoints; i++)
{
var semiPerpendicularDistance = SpatialUtility.GetPointToLineSegmentDistance(pointList[startIndex], pointList[middleIndex], pointList[i]);
if (semiPerpendicularDistance > effectiveThreshold)
{
result.Add(pointList[i - 1]);
startIndex = i - 1;
middleIndex = i;
}
}
if (parameters.Retain3Points && result.Count == 1)
{
result.Add(pointList[pointList.Count() / 2]);
}
result.Add(pointList.Last());
return(result);
}
public static List <T> AdditiveSimplifyByDistance <T>(List <T> points, SimplificationParamters parameters /*double threshold, bool retain3Points = false*/) where T : IPoint
{
if (points == null || points.Count == 0)
{
return(null);
}
else if (points.Count == 2)
{
return(points);
}
List <int> filtered = new List <int>();
filtered.Add(0);
int firstIndex = 0, secondIndex = 1;
var temp = 0.0;
while (secondIndex < points.Count)
{
var semiDistance = SpatialUtility.GetSquareDistance(points[firstIndex], points[secondIndex]);
temp += semiDistance;
if (temp > parameters.DistanceThreshold.Value)
{
temp = 0;
filtered.Add(secondIndex);
firstIndex = secondIndex;
}
secondIndex++;
}
if (parameters.Retain3Points && filtered.Count == 1)
{
filtered.Add(points.Count() / 2);
}
filtered.Add(points.Count - 1);
var result = filtered.Select(i => points[i]).ToList();
return(result);
}
private static List <T> DivideForDouglasPeucker <T>(List <T> pointList, SimplificationParamters paramters, int divideIndex) where T : IPoint
{
var result = new List <T>();
var leftList = pointList.Take(divideIndex + 1).ToList();
result = SimplifyByDouglasPeucker(leftList, paramters);
var rightList = pointList.Skip(divideIndex).ToList();
var rightResult = SimplifyByDouglasPeucker(rightList, paramters);
result.AddRange(rightResult.Skip(1));
return(result);
}
// 1400.05.20
public static List <T> SimplifyByBeforeOpeningWindow <T>(List <T> points, SimplificationParamters parameters /*, double threshold, bool retain3Points = false*/) where T : IPoint
{
if (points == null || points.Count == 0)
{
return(null);
}
else if (points.Count == 2)
{
return(points);
}
List <T> result = new List <T>();
result.Add(points.First());
// 1400.05.20
//در این جا برای سرعت بیشتر مقدار فاصله استفاه
//نمیشود بلکه توان دوم آن استفاده میشود. این
//روش باعث میشود در محاسبات از تابع جزر استفاده
//نشود
double effectiveThreshold = parameters.DistanceThreshold.Value /* * parameters.DistanceThreshold.Value*/;
int startIndex = 0, middleIndex = 1, endIndex = 2;
while (endIndex < points.Count)
{
while (middleIndex < endIndex)
{
var semiDistance = SpatialUtility.GetPointToLineSegmentDistance(points[startIndex], points[endIndex], points[middleIndex]);
if (semiDistance > effectiveThreshold)
{
result.Add(points[endIndex - 1]);
startIndex = endIndex - 1;
middleIndex = startIndex + 1;
// after breaking it will increment by 1 6 lines below
endIndex = middleIndex;
break;
}
middleIndex++;
}
endIndex++;
middleIndex = startIndex + 1;
}
if (parameters.Retain3Points && result.Count == 1)
{
result.Add(points[points.Count() / 2]);
}
if (result.Last().DistanceTo(points.Last()) != 0)
{
result.Add(points.Last());
}
return(result);
}
// 1400.05.11
// http://psimpl.sourceforge.net/perpendicular-distance.html
// Ekdemir, S., Efficient Implementation of Polyline Simplification for Large Datasets and Usability Evaluation.
// Master’s thesis, Uppsala University, Department of Information Technology, 2011
public static List <T> SimplifyByPerpendicularDistance <T>(List <T> points, SimplificationParamters parameters /*, double threshold, bool retain3Points = false*/) where T : IPoint
{
if (points == null || points.Count == 0)
{
return(null);
}
else if (points.Count == 2)
{
return(points);
}
List <T> result = new List <T>();
result.Add(points.First());
// 1400.06.05
// استفاده از مقدار توان دوم در مقایسه مشکلساز
// نخواهد بود چون در هر حال تابع توان دوم هم
// اکیدا صعودی است و توان دوم هیچ مقداری از توان
// دوم مقدار کمتر از خودش، بیشتر نخواهد شد. اما
// برای اینکه مقایسه سرعت درست انجام شود
// استفاده از توان دوم متوقف شد.
// 1400.05.11
//در این جا برای سرعت بیشتر مقدار فاصله استفاه
//نمیشود بلکه توان دوم آن استفاده میشود. این
//روش باعث میشود در محاسبات از تابع جزر استفاده
//نشود
//double effectiveThreshold = threshold * threshold;
double effectiveThreshold = parameters.DistanceThreshold.Value /** parameters.DistanceThreshold.Value*/;
for (int i = 0; i < points.Count - 2; i++)
{
var perpendicularDistance = SpatialUtility.GetPointToLineSegmentDistance(points[i], points[i + 2], points[i + 1]);
if (perpendicularDistance > effectiveThreshold)
{
result.Add(points[i + 1]);
}
// 1400.06.05
// نقطه حذف شده به عنوان نقطه شروع استفاده نمیشود
// این روش در بهترین حالت ۵۰ درصد فشرده سازی ایجاد
// می کند
else
{
result.Add(points[i + 2]);
i++;
}
}
if (parameters.Retain3Points && result.Count == 1)
{
result.Add(points[points.Count() / 2]);
}
if (result.Last().DistanceTo(points.Last()) != 0)
{
result.Add(points.Last());
}
return(result);
}
// ref: Lang, T., 1969, Rules for robot draughtsmen. Geographical Magazine, vol.62, No.1, pp.50-51
// link:
// AreaThreshold is used
public static List <T> SimplifyByLang <T>(List <T> pointList, SimplificationParamters parameters /*, double threshold, int? lookAhead, bool retain3Points = false*/) where T : IPoint
{
var result = new List <T>();
if (pointList == null || pointList.Count < 2)
{
return(result);
}
if (pointList.Count == 2)
{
return(pointList);
}
if (parameters.LookAhead == null)
{
parameters.LookAhead = Math.Max(3, pointList.Count / 10);
}
var numberOfPoints = pointList.Count;
//
//1399.07.09
//در این جا برای سرعت بیشتر مقدار فاصله استفاه
//نمیشود بلکه توان دوم آن استفاده میشود. این
//روش باعث میشود در محاسبات از تابع جذر استفاده
//نشود
//double effectiveThreshold = threshold * threshold;
double effectiveThreshold = parameters.AreaThreshold.Value /** parameters.AreaThreshold.Value*/;
int startIndex = 0;
result.Add(pointList[0]);
int endIndex = Math.Min(numberOfPoints - 1, parameters.LookAhead.Value);
while (true)
{
if (startIndex == endIndex)
{
break;
}
if (endIndex - startIndex == 1)
{
result.Add(pointList[endIndex]);
startIndex = endIndex;
endIndex = Math.Min(numberOfPoints - 1, endIndex + parameters.LookAhead.Value);
continue;
}
if (AnyPerpendicularDistanceExceedTolerance(pointList.Skip(startIndex).Take(endIndex - startIndex + 1).ToList(), effectiveThreshold))
{
endIndex--;
}
else
{
result.Add(pointList[endIndex]);
startIndex = endIndex;
endIndex = Math.Min(numberOfPoints - 1, endIndex + parameters.LookAhead.Value);
}
}
if (parameters.Retain3Points && result.Count == 2)
{
result.Insert(1, pointList[pointList.Count / 2]);
}
return(result);
}
// ref: https://www.tandfonline.com/doi/abs/10.1179/000870493786962263
public static List <T> SimplifyByVisvalingam <T>(List <T> pointList, SimplificationParamters parameters, bool isRing /*, double threshold, bool isRing, bool retain3Points = false*/) where T : IPoint
{
if (pointList == null || pointList.Count <= 3)
{
return(pointList);
}
var areas = SpatialUtility.GetPrimitiveAreas(pointList, isRing);
List <T> pList = pointList.ToList();
//var areas2 = SpatialUtility.GetPrimitiveAreas(pointList, isRing);
//List<T> pList2 = pointList.ToList();
while (areas.Count > 0)
{
//if (!areas.SequenceEqual(areas2))
//{
//}
//if (!pList.SequenceEqual(pList2))
//{
//}
var minArea = Statistics.Statistics.GetMin(areas);
if (minArea > parameters.AreaThreshold)
{
break;
}
var pointCount = pList.Count;
var areaCount = areas.Count;
//double a1=0, a2=0;
//remove min areas
for (int i = areas.Count - 1; i >= 0; i--)
{
if (areas[i] == minArea)
{
if (isRing || i > 0)
{
// (i-1, i, i+2): i+2 is used insted of i+1 because i+1 is going to be removed
var firstIndex = i - 1 < 0 ? pointCount - 1 : i - 1;
areas[firstIndex] = SpatialUtility.GetUnsignedTriangleArea(pList[firstIndex], pList[i], pList[(i + 2) % pointCount]);
//a1 = areas[firstIndex];
}
if (isRing || i < areas.Count - 1)
{
// (i, i+2, i+3): i is used insted of i+1 because i+1 is going to be removed
areas[(i + 1) % areaCount] = SpatialUtility.GetUnsignedTriangleArea(pList[i], pList[(i + 2) % pointCount], pList[(i + 3) % pointCount]);
//a2 = areas[(i + 1) % areaCount];
}
////recalculate adjacent areas
//if (i > 0)
//{
// areas[i - 1] = SpatialUtility.GetUnsignedTriangleArea(pList[i - 1], pList[i], pList[i + 2]);
//}
//if (i < areas.Count - 1)
//{
// areas[i] = SpatialUtility.GetUnsignedTriangleArea(pList[i], pList[i + 1], pList[i + 2]);
//}
pList.RemoveAt((i + 1) % pointCount);
areas.RemoveAt(i);
break;
}
}
//for (int i = areas2.Count - 1; i >= 0; i--)
//{
// if (areas2[i] == minArea)
// {
// pList2.RemoveAt((i + 1));
// areas2.RemoveAt(i);
// ////recalculate adjacent areas
// if (i > 0)
// {
// areas2[i - 1] = SpatialUtility.GetUnsignedTriangleArea(pList2[i - 1], pList2[i], pList2[i + 1]);
// if (areas2[i - 1] != a1)
// {
// }
// }
// if (i < areas2.Count - 1)
// {
// areas2[i] = SpatialUtility.GetUnsignedTriangleArea(pList2[i], pList2[i + 1], pList2[i + 2]);
// if (areas2[i] != a2)
// {
// }
// }
// break;
// }
//}
}
if (parameters.Retain3Points && pList.Count == 2)
{
pList.Insert(1, pointList[pointList.Count() / 2]);
}
return(pList.ToList());
}