如何在matlab中创建圆并在其中生成随机点

Question

你好我想问一个问题，如何在matlab中制作一个圆圈并标记其中心并在其中生成一定数量的随机点，例如50？我知道这个代码来制作一个圆圈

x = linspace(-sqrt(10),sqrt(10));
y1 = sqrt(10-x.^2);
y2 = -sqrt(10-x.^2);
plot(x,y1,x,y2)
axis equal
hold on

但我不知道如何在其中生成50个随机点 然后我想到了这个伪代码，但我不知道如何在matlab中编写它

01: FOR all nodes j
 02: FOR all nodes i except node j 
03: IF distance(j to center) < distance(j to  i) AND
 04: distance(i to cell center) < distance(j to  i) 
05: THEN there's a red link from node i to node j 
06: ELSEIF distance(j to cell center) < distance(j to  i)
 07: THEN there's a blue link from node i to node j 
08: ELSE there's no D2D link from node i and j;
 09: node i has a green link with the base station 
10: END if 
11: END inner for-loop

Answer 1

认为这就是你所需要的 -

%%// Plot the circle
x = linspace(-sqrt(10),sqrt(10));
y1 = sqrt(10-x.^2);
y2 = -sqrt(10-x.^2);
plot(x,y1,x,y2)
axis equal

%%// Choose from 1000 random point pairs
N = 1000; 
%%// Radius of circle
radius = sqrt(10); 

%%// Create a random point matrix Nx2
points_mat = [ radius*2*(rand(N,1)-0.5) radius*2*(rand(N,1)-0.5)];

%%// Select the first 50 pairs that lies inside circle
ind1 = find(sqrt( points_mat(:,1).^2 + points_mat(:,2).^2 )<radius);
points_mat=points_mat(ind1(1:50),:);

%%// Plot the 50 points on the circle
hold on
text(0,0,'x Center') %%// Center
text(points_mat(:,1),points_mat(:,2),'o') %%// 50 points

<强>剧情

Answer 2

我不知道matlab，所以我无法帮助你，但是如果你想在没有拒绝的情况下这样做，你可以在极坐标中生成点。如果rand()返回统一（0,1）随机数，则：

r = radius * sqrt(rand())
theta = 2 * Pi * rand()
x = r * cos(theta)
y = r * sin(theta)

将产生均匀分布在半径radius的圆内的值。注意计算r时的平方根，它调整距离圆心的距离分布，使得给定距离处的点数总是与面积成比例，因此是均匀的。对于球形均匀性，你需要立方根来保持与体积的比例，一般来说k ^th 根对于k维超球面。

Answer 3

这是另一种选择：

%// Set parameters
R = 0.5;   %// radius
C = [3 4]; %// center [x y]
N = 50;    %// number of points inside circle

%// generate circle boundary
t = linspace(0, 2*pi, 100);
x = R*cos(t) + C(1);
y = R*sin(t) + C(2);

%// generate random points inside it
th = 2*pi*rand(N,1);
r  = R*rand(N,1);

xR = r.*cos(th) + C(1);
yR = r.*sin(th) + C(2);

%// Plot everything
figure(1), clf, hold on
plot(x,y,'b')
plot(C(1),C(2),'r.', 'MarkerSize', 100)
plot(xR,yR,'k.')
axis equal

这就是为什么这可能有用：

%// Set parameters
R = 0.5;     N = 50;
C = [3 4];   M = 100;  %// points on boundary

%// generate all points at once
t  = linspace(0, 2*pi, M)';
th = 2*pi*rand(N,1);
r  = R*rand(N,1);
xR = [R*ones(M,1); r] .* cos([t; th]) + C(1);
yR = [R*ones(M,1); r] .* sin([t; th]) + C(2);

%// Plot everything
figure(1), clf, hold on
plot(xR(1:M),yR(1:M),'b')                %// circle boundary
plot(C(1),C(2),'r.', 'MarkerSize', 100)  %// center
plot(xR(M+1:end),yR(M+1:end),'k.')       %// random points
axis equal