计算三维空间线段最小距离的matlab程序
时间: 2023-08-04 07:19:37 浏览: 53
以下是计算三维空间线段最小距离的Matlab程序:
```
function d = minDist3DSegment(seg1, seg2)
% 计算三维空间线段最小距离
% seg1 和 seg2 分别为两个线段的端点坐标,每个端点坐标为一个三维向量
% 计算两个线段的向量
vec1 = seg1(2,:) - seg1(1,:);
vec2 = seg2(2,:) - seg2(1,:);
% 计算向量的点积和范数
dot1 = dot(vec1, vec1);
dot2 = dot(vec1, vec2);
dot3 = dot(vec2, vec2);
% 计算最短距离的参数值
t1 = (dot1 * dot2 - dot2 * dot3) / (dot1 * dot1 - dot2 * dot2);
t2 = (dot1 * t1 + dot2) / dot1;
% 计算最短距离的点
if t2 < 0
d = norm(seg2(1,:) - seg1(1,:));
elseif t2 > 1
d = norm(seg2(2,:) - seg1(2,:));
else
p = seg1(1,:) + t2 * vec1;
d = norm(seg2(1,:) - p);
end
end
```
这个程序使用向量的点积和范数来计算最短距离,并根据最短距离的参数值来确定最短距离的点。在程序中,如果最短距离的参数值小于0或大于1,则最短距离点在另一个线段的端点上,否则最短距离点在两个线段的交点上。
相关问题
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。
计算三维空间线段最小距离和最近点对坐标的Matlab程序
以下是计算三维空间线段最小距离和最近点对坐标的Matlab程序:
```
function [d, p1, p2] = minDist3DSegment(seg1, seg2)
% 计算三维空间线段最小距离和最近点对坐标
% seg1 和 seg2 分别为两个线段的端点坐标,每个端点坐标为一个三维向量
% 计算两个线段的向量
vec1 = seg1(2,:) - seg1(1,:);
vec2 = seg2(2,:) - seg2(1,:);
% 计算向量的点积和范数
dot1 = dot(vec1, vec1);
dot2 = dot(vec1, vec2);
dot3 = dot(vec2, vec2);
% 计算最短距离的参数值
t1 = (dot1 * dot2 - dot2 * dot3) / (dot1 * dot1 - dot2 * dot2);
t2 = (dot1 * t1 + dot2) / dot1;
% 计算最短距离的点
if t2 < 0
d = norm(seg2(1,:) - seg1(1,:));
p1 = seg1(1,:);
p2 = seg2(1,:);
elseif t2 > 1
d = norm(seg2(2,:) - seg1(2,:));
p1 = seg1(2,:);
p2 = seg2(2,:);
else
p1 = seg1(1,:) + t2 * vec1;
p2 = seg2(1,:);
d = norm(p1 - p2);
end
% 对比两个线段的两个端点,更新最短距离和最近点对坐标
[dist, point] = minDist3DPoint(p1, [seg2(1,:); seg2(2,:)]);
if dist < d
d = dist;
p2 = point;
end
[dist, point] = minDist3DPoint(p2, [seg1(1,:); seg1(2,:)]);
if dist < d
d = dist;
p1 = point;
end
end
function [d, p] = minDist3DPoint(p, seg)
% 计算三维空间点到线段的最短距离和最近点坐标
% p 为点的坐标,seg 为线段的端点坐标,每个端点坐标为一个三维向量
% 计算线段的向量和点到线段起点的向量
vec1 = seg(2,:) - seg(1,:);
vec2 = p - seg(1,:);
% 计算向量的点积和范数
dot1 = dot(vec1, vec1);
dot2 = dot(vec1, vec2);
% 计算最短距离的参数值
t = dot2 / dot1;
% 计算最短距离的点
if t < 0
d = norm(p - seg(1,:));
p = seg(1,:);
elseif t > 1
d = norm(p - seg(2,:));
p = seg(2,:);
else
p = seg(1,:) + t * vec1;
d = norm(p - p);
end
end
```
这个程序计算了两个线段之间的最短距离和最近点对坐标,并且在计算最短距离的同时,根据两个线段的端点计算了最短距离和最近点对坐标。程序中还定义了一个计算三维空间点到线段的最短距离和最近点坐标的子函数。