matlab - 预期区域外的飞机

Question

主意

我试图绘制一个由两个向量分隔的平面，在matlab中使用交叉

代码

NM= [1 3; 2 4]                                 //matrix  
figure
hold on;
z = zeros(size(NM, 1), 1);                    //to use quiver3
quiver3(z, z, z, NM(:,1), NM(:,2), z, 0);     //vectors plotted
grid on
view(45, 45);
s=sum(NM);
p = 10*(rand(3,1) - 0.5);                     //  generation of points
O1=[NM(1,:) 0]                                // new vectors of length 3 ,
O2=[NM(2,:) 0]                                // to be used by cross
v3 = cross(O1,O2)                             //cross product to find the norm
[ x , y ] = meshgrid( p(1)+(-5:5) , p(2)+(-5:5) );   // points inside the plane
z = p(3) - (v3(1)*(x-p(1)) + v3(2)*(y-p(2)))/v3(3);  // plane equation
surf(x,y,z)                                   //the plane itself

输出是

问题
平面必须由矢量分隔，或者矢量必须在平面内而不是在平面外。

标签： matlabmatlab-figurelinear-algebra

Answer 1

矢量不会出现在平面内，因为您(0,0,0)在使平面经过随机选择的点时选择作为矢量的起点p。

当用 绘制时，您要么使平面经过，(0,0,0)要么p用作向量的起点quiver3()。

这是我选择第二个选项的解决方案：

vplane = [1 3 0; 2 4 0]';                                                   % (column) vectors defining the plane
vnormal = cross(vplane(:,1), vplane(:,2));                                  % normal defining the orientation of the plane

figure; hold on; grid on; view(45, 45);
rng(1313)                                                                   % seed for reproducible output
p = 10*(rand(3,1) - 0.5);                                                   % a point defining the position of the plane we want to plot with the given normal vector
P = repmat(p, 1, 2);                                                        % matrix with the given point repeated for easier use of quiver3()
quiver3(P(1,:), P(2,:), P(3,:), vplane(1,:), vplane(2,:), vplane(3,:), 0);  % arrows representing the vectors defining the plane
[x,y] = meshgrid( p(1)+(-5:5), p(2)+(-5:5) );                               % set of equally spaced points inside the plane
z = p(3) - (vnormal(1)*(x-p(1)) + vnormal(2)*(y-p(2))) / vnormal(3);        % plane equation
surf(x,y,z)                                                                 % plot the plane

结果如下：