道格拉斯-普克抽稀算法 曲线平滑

 switch(m_SmoothMode)

        {

        case 0: //三点线性            
            for(i=2+offsetpos;i<datanum-2;i++)

            {

                m_pfDataArray[i] = (m_pfDataArray[i-1]+m_pfDataArray[i]+m_pfDataArray[i+1])/3;

            }

            break;

        case 1://五点二次滤波         
            for(i=2+offsetpos;i<datanum-2;i++)

            {

                m_pfDataArray[i] = (12*(m_pfDataArray[i-1]+m_pfDataArray[i+1])

                    -3*(m_pfDataArray[i-2]+m_pfDataArray[i+2])

                    +17*m_pfDataArray[i])/35;

            }

            break;

        case 2://三点钟形滤波       
            for(i=2+offsetpos;i<datanum-2;i++)

            {

                m_pfDataArray[i] = (short)(0.212f*m_pfDataArray[i-1]+0.576f*m_pfDataArray[i]

                +0.212f*m_pfDataArray[i+1]);

            }

            break;

        case 3://五点钟形滤波       
            for(i=2+offsetpos;i<datanum-2;i++)

            {

                m_pfDataArray[i] = (short)(0.11f*(m_pfDataArray[i-2]+m_pfDataArray[i+2])

                    +0.24f*(m_pfDataArray[i-1]+m_pfDataArray[i+1])

                    +0.3f*m_pfDataArray[i]);

            }

            break;

        case 4://三点汉明滤波         
            for(i=2+offsetpos;i<datanum-2;i++)

            {

                m_pfDataArray[i] = (short)(0.07f*m_pfDataArray[i-1]+0.86f*m_pfDataArray[i]

                +0.07f*m_pfDataArray[i+1]);

            }

            break;

        default://五点汉明滤波         
            for(i=2+offsetpos;i<datanum-2;i++)

            {

                m_pfDataArray[i] = (short)(0.04f*(m_pfDataArray[i-2]+m_pfDataArray[i+2])

                    +0.24f*(m_pfDataArray[i-1]+m_pfDataArray[i+1])

                    +0.44f*m_pfDataArray[i]);

            }

            break;

        }

道格拉斯-普克抽稀算法

道格拉斯-普克抽稀算法，是用来对大量冗余的图形数据点进行压缩以提取必要的数据点。该算法实现抽稀的过程是：先将一条曲线首尾点虚连一条直线，求其余各点到该直线的距离，取其最大者与规定的临界值相比较，若小于临界值，则将直线两端间各点全部舍去，否则将离该直线距离最大的点保留，并将原线条分成两部分，对每部分线条再实施该抽稀过程，直到结束。抽稀结果点数随选取限差临界值的增大而减少，应用时应根据精度来选取限差临界值，以获得最好的效果。

 

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以下转载自：垂距法与道格拉斯-普克法删除冗余顶点效率的比较

                                     彭认灿 ,董 　 箭 ,郑义东 ,李改肖

                               (大连舰艇学院 海洋测绘工程系 ,辽宁 大连 116018)

道格拉斯- 普克法可描述为:将一条曲线首末顶点虚连一条直线 ,求出其余各顶点到该直线的距离 ,选其最大者与规定的限差相比较 ,若小于等于限差 ,则将直线两端间各点全部删去;若大于限差 ,则离该直线距离最大的顶点保留 ,并以此为界 ,把曲线分为两部分
,对这两部分重复使用上述方法 ,直至最终无法作进一步的压缩为止 (见图 3)。



道格拉斯 2 普克法有一个十分突出的优点 ,即它是一个整体算法 ,在一般情况下可保留较大弯曲形态上的特征点。经道格拉斯-普克法压缩后得到的图形如图 4所示。由于该算法可准确删除小弯曲上的定点 ,故能从体上有效地保持线要素的形态特征。正是因为道格拉斯-普克法具有这样突出的优点 ,所以已经在线要素地自动制图中得到了较广泛的应用。但道格拉斯- 普克法较垂距法复杂 ,且通常编程实现时需要采用递归方 ,有一定的难度。



----------------------------------------------------------转载end

此算法可以在获取手写笔顺的特征点时应用。

C++代码

//=================================================================================================================

double PerpendicularDistance(CPoint Point1, CPoint Point2, CPoint 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 = abs(0.5 * (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 = sqrt(pow(Point1.x - Point2.x, 2) + pow(Point1.y - Point2.y, 2));

    double height = area / bottom * 2;

    return height;

}

void DouglasPeuckerReduction(vector<CPoint>points, int firstPoint, int lastPoint, double tolerance, list<int> &pointIndexsToKeep)

{

    double maxDistance = 0;

    int indexFarthest = 0;

    

    for (int 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.push_back(indexFarthest);

    

        DouglasPeuckerReduction(points, firstPoint, 

        indexFarthest, tolerance, pointIndexsToKeep);

        

        DouglasPeuckerReduction(points, indexFarthest, 

        lastPoint, tolerance, pointIndexsToKeep);

    }

}

vector<CPoint> DouglasPeucker(vector<CPoint> &Points, double Tolerance)

{

    if (Points.empty() || (Points.size() < 3))

    return Points;

    int firstPoint = 0;

    int lastPoint = Points.size() - 1;

    list<int> pointIndexsToKeep ;

    //Add the first and last index to the keepers

    pointIndexsToKeep.push_back(firstPoint);

    pointIndexsToKeep.push_back(lastPoint);

    //The first and the last point cannot be the same

    while (Points[firstPoint]==(Points[lastPoint]))

    {

        lastPoint--;

    }

    DouglasPeuckerReduction(Points, firstPoint, lastPoint, 

    Tolerance, pointIndexsToKeep);

    vector<CPoint> returnPoints ;

    pointIndexsToKeep.sort();

list<int>::iterator theIterator;

    for( theIterator = pointIndexsToKeep.begin(); theIterator != pointIndexsToKeep.end(); theIterator++ )

    {

        returnPoints.push_back(Points[*theIterator]);

    }

    return returnPoints;

}

//==============================

matlab算法：

function curve = dp(pnts)
%dp点抽稀算法
clc;
close all;
clear all;

x = 1:0.01: 2;
num = size(x,2);

pnts = 2*sin(8*pi*x) ; % + rand(1,num)*0.8;
pnts = x .* sin(8*pi*x) + rand(1,num)*0.5;
figure; plot( x, pnts,'-.'); title('pnts');

head = [x(1), pnts(1)] ;
tail = [x(end), pnts(end)] ;

%距离阈值
dist_th = 0.1;

hold on;
max_dist = 0;
max_dist_i = 0;
%把起始点和终止点加进去
curve = [head; tail];
pnt_index = [1, num];

while(1)
%目前抽稀后的曲线上的点数
curve_num = size(curve,1);

%标记是否添加了新点，若有，表明还要继续处理
add_new_pnt = 0;
% 对区间头尾连线，然后计算各点到这条直线的距离
for nx = 1:curve_num-1
cur_pnt = curve(nx,:);
%下一个抽稀了的曲线上的点
next_pnt = curve(nx+1,:);
pnt_d = next_pnt - cur_pnt ;

th = atan2(pnt_d(2), pnt_d(1));
angle = th*180/pi;
%直线方程
% y = kx + b
k = tan(th);
b = cur_pnt(2) - k*cur_pnt(1);
k2 = k*k;
deno = sqrt(1 + k *k) ;

max_dist = 0;
pnt_index(nx);
pnt_index(nx+1);

%对这一区间的点计算到直线的距离
for i= pnt_index(nx) : pnt_index(nx+1)
dist = abs(pnts(i) - k*x(i) - b)/deno ;

if(dist> max_dist)
max_dist = dist;
max_dist_i = i;
end
end
max_dist;
max_dist_i;

far_pnt = [x(max_dist_i), pnts(max_dist_i)];

%最远的点加进去
if(max_dist > dist_th)
curve = [curve(1:nx,:); far_pnt; curve(nx+1:end,:)];
pnt_index = [pnt_index(1:nx), max_dist_i, pnt_index(nx+1:end)];
%标记添加了新点，可能还要继续处理
add_new_pnt = 1;
end
end
close all ;
figure; plot( x, pnts,'-.'); title('pnts');
hold on;
plot(curve(:,1), curve(:,2), '-g*');
drawnow;

%如果各点到直线距离都没有超过阈值则退出
%处理完毕了，ok了，退出
if(0 == add_new_pnt)
break;
end
end