[英]How to find the order of discrete point-set efficiently?
我在平面上有一系列离散点,但是,它们的顺序是分散的。 这是一个例子:
为了用平滑的曲线将它们连接起来,我写了一个findSmoothBoundary()
来实现平滑的边界。
function findSmoothBoundary(boundaryPointSet)
%initialize the current point
currentP = boundaryPointSet(1,:);
%Create a space smoothPointsSet to store the point
smoothPointsSet = NaN*ones(length(boundaryPointSet),2);
%delete the current point from the boundaryPointSet
boundaryPointSet(1,:) = [];
ptsNum = 1; %record the number of smoothPointsSet
smoothPointsSet(ptsNum,:) = currentP;
while ~isempty(boundaryPointSet)
%ultilize the built-in knnsearch() to
%achieve the nearest point of current point
nearestPidx = knnsearch(boundaryPointSet,currentP);
currentP = boundaryPointSet(nearestPidx,:);
ptsNum = ptsNum + 1;
smoothPointsSet(ptsNum,:) = currentP;
%delete the nearest point from boundaryPointSet
boundaryPointSet(nearestPidx,:) = [];
end
%visualize the smooth boundary
plot(smoothPointsSet(:,1),smoothPointsSet(:,2))
axis equal
end
虽然findSmoothBoundary()
可以正确地找到平滑边界,但它的效率要低得多(关于数据,请看这里)
所以我想知道:
theta = linspace(0,2*pi,1000)';
boundaryPointSet= [2*sin(theta),cos(theta)];
tic;
findSmoothBoundary(boundaryPointSet)
toc;
%Elapsed time is 4.570719 seconds.
这个答案并不完美,因为我必须做出一些假设才能使其发挥作用。 但是,对于绝大多数情况,它应该按预期工作。 此外,从你在评论中给出的链接来看,我认为这些假设至少是弱的,如果没有通过定义验证:
1.点形成单个连通区域
2.你的点的质心位于这些点的凸包中
如果这些假设得到尊重,您可以执行以下操作(完整代码在最后):
第 1 步:计算点的质心
Means=mean(boundaryPointSet);
第 2 步:更改变量以将原点设置为质心
boundaryPointSet(:,1)=boundaryPointSet(:,1)-Means(1);
boundaryPointSet(:,2)=boundaryPointSet(:,2)-Means(2);
Step3:将坐标转换为极坐标
[Angles,Radius]=cart2pol(boundaryPointSet(:,1),boundaryPointSet(:,2));
Step4:对Angle
进行排序并使用这种排序对Radius
进行排序
[newAngles,ids]=sort(Angles);
newRadius=Radius(ids);
Step5:回到笛卡尔坐标,重新添加质心坐标:
[X,Y]=pol2cart(newAngles,newRadius);
X=X+Means(1);
Y=Y+means(2);
%%% Find smooth boundary
fid=fopen('SmoothBoundary.txt');
A=textscan(fid,'%f %f','delimiter',',');
boundaryPointSet=cell2mat(A);
boundaryPointSet(any(isnan(boundaryPointSet),2),:)=[];
idx=randperm(size(boundaryPointSet,1));
boundaryPointSet=boundaryPointSet(idx,:);
tic
plot(boundaryPointSet(:,1),boundaryPointSet(:,2))
%% Find mean value of all parameters
Means=mean(boundaryPointSet);
%% Center values around Mean point
boundaryPointSet(:,1)=boundaryPointSet(:,1)-Means(1);
boundaryPointSet(:,2)=boundaryPointSet(:,2)-Means(2);
%% Get polar coordinates of your points
[Angles,Radius]=cart2pol(boundaryPointSet(:,1),boundaryPointSet(:,2));
[newAngles,ids]=sort(Angles);
newRadius=Radius(ids);
[X,Y]=pol2cart(newAngles,newRadius);
X=X+Means(1);
Y=Y+means(2);
toc
figure
plot(X,Y);
注意:由于您的值已经在您的输入文件中排序,我不得不通过排列它们来弄乱它
边界
经过的时间是 0.131808 秒。
混乱的输入:
输出:
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