计算两维空间线段最小距离的matlab程序

以下是一个计算两维空间线段最小距离的 Matlab 程序：

function [dist, p1, p2] = minDistLineSegments(l1, l2)
% Computes the minimum distance between two line segments in 2D space
% Inputs:
%   l1: a 2x2 matrix representing the endpoints of the first line segment
%   l2: a 2x2 matrix representing the endpoints of the second line segment
% Outputs:
%   dist: the minimum distance between the two line segments
%   p1: the closest point on the first line segment to the second line segment
%   p2: the closest point on the second line segment to the first line segment

% Compute directions and norms of line segments
d1 = l1(2,:) - l1(1,:);
d2 = l2(2,:) - l2(1,:);
norm1 = norm(d1);
norm2 = norm(d2);

% Compute unit direction vectors
if norm1 > 0
    u1 = d1 / norm1;
else
    u1 = [0 0];
end
if norm2 > 0
    u2 = d2 / norm2;
else
    u2 = [0 0];
end

% Compute vector between the two line segment endpoints
w = l1(1,:) - l2(1,:);

% Compute coefficients of system of equations to find closest points
a = dot(u1, u1);
b = dot(u1, u2);
c = dot(u2, u2);
d = dot(u1, w);
e = dot(u2, w);

% Compute determinant of system of equations
D = a*c - b^2;

% Compute parameters for closest points on each line segment
if D < 1e-6  % lines are nearly parallel
    s1 = 0;
    s2 = e/c;
else
    s1 = (b*e - c*d) / D;
    s2 = (a*e - b*d) / D;
end

% Compute closest points on each line segment
if s1 < 0
    p1 = l1(1,:);
elseif s1 > norm1
    p1 = l1(2,:);
else
    p1 = l1(1,:) + s1*u1;
end
if s2 < 0
    p2 = l2(1,:);
elseif s2 > norm2
    p2 = l2(2,:);
else
    p2 = l2(1,:) + s2*u2;
end

% Compute distance between closest points
dist = norm(p1 - p2);

你可以将 `l1` 和 `l2` 分别表示为 $2\times2$ 的矩阵，其中每一行代表一个点的 $(x,y)$ 坐标。例如，如果 `l1` 包含点 $(x_1, y_1)$ 和 $(x_2, y_2)$，则 `l1` 可以定义为：

l1 = [x1 y1; x2 y2];

调用此函数时，`dist` 将包含两个线段之间的最小距离，`p1` 将包含第一个线段上距离第二个线段最近的点，`p2` 将包含第二个线段上距离第一个线段最近的点。