在 Matlab 中模拟不能相互碰撞的随机步行者

Question

我编写了一个代码来模拟二维盒子中圆形粒子的运动。每当他们搬出盒子时，我都会把它们放在盒子里靠近墙壁的地方。我想在代码中添加粒子的直径（2R），这意味着当两个圆的中心之间的距离变得小于 2R 时，它们沿着连接它们的中心的线分开，使得圆心之间的距离变为等于 2R。

谁能建议一个防止粒子重叠的代码？

这是我的代码，其中不考虑重叠：

clear all
close all
l = 224; nn = 800; %number of particles
time = 1000; dd = 1;
x= l*rand(1,nn);
y= l*rand(1,nn);

for t = 1:time;
x= x + rand(1,nn)-0.5* ones(1,nn);
y=y+rand(1,nn)-0.5* ones (1,nn);
index = (x < 0); x(index) = abs(normrnd(0,1,1,nnz(index)));
index = (y < 0); y(index) = abs(normrnd(0,1,1,nnz(index)));
index = (x > l); x(index) = l-abs(normrnd(0,1,1,nnz(index)));
index = (y > l); y(index) = l-abs(normrnd(0,1,1,nnz(index)));
end

Answer 1

这是一些注释代码，可以满足您的需求。值得注意的是：

• psize 是一些为相互作用而定义的粒子大小。
• 使用pdist2 找到的点到点距离。
• 距离太近的点会彼此远离一定距离（dp 乘以它们当前的距离，如果dp=1/2 则它们的 x 和 y 距离加倍）直到没有冲突。

详见 cmets。

clear; close all;
l = 224; nn = 800; % number of particles
time = 100;
x = l*rand(1,nn); y = l*rand(1,nn);
psize = 2;         % Particle size for interaction
dp = 0.1;

figure; hold on; axis([0 l 0 l]);
for t = 1:time;
    % Random movement
    movement = 2*rand(2,nn)-1;
    x = x + movement(1,:);
    y = y + movement(2,:);
    index = (x < 0); x(index) = abs(normrnd(0,1,1,nnz(index)));
    index = (y < 0); y(index) = abs(normrnd(0,1,1,nnz(index)));
    index = (x > l); x(index) = l-abs(normrnd(0,1,1,nnz(index)));
    index = (y > l); y(index) = l-abs(normrnd(0,1,1,nnz(index)));

    % Particle interaction. Loop until there are no clashes. For
    % robustness, some max iteration counter should be added!
    numclash = 1;
    while numclash > 0
        dists = pdist2([x;y]', [x;y]');   % Distances between all particles
        dists(dists < psize) = NaN;       % Those too close are assigned NaN
        tooclose = isnan(tril(dists,-1)); % All NaNs identified by logical
        [clash1,clash2] = find(tooclose); % Get particles which are clashing
        numclash = numel(clash1);         % Get number of clashes
        % All points where there was a clash, move away from each other
        x(clash1) = x(clash1) + (x(clash1)-x(clash2))*dp;
        x(clash2) = x(clash2) - (x(clash1)-x(clash2))*dp;
        y(clash1) = y(clash1) + (y(clash1)-y(clash2))*dp;
        y(clash2) = y(clash2) - (y(clash1)-y(clash2))*dp;
    end

    % Plot to visualise results. Colour fade from dark to bright green over time
    scatter(x,y,'.','markeredgecolor',[0.1,t/time,0.4]);
    drawnow;
end
hold off

结果：

---

编辑：

为了更清晰的图表，您可以初始化一些颜色矩阵C = rand(nn,3); 并使用绘图

scatter(x,y,[],C*(t/time),'.'); % the (t/time) factor makes it fade from dark to light

这会给每个粒子一个不同的颜色，它们也会从暗淡到亮，而不是像以前那样从暗淡到亮。结果会是这样的：