平面与五棱柱相交曲线求解与三维图绘制： 1、构建根据输入参数改变位置和角度的平面函数的MATLAB代码 2、构建求解判断五棱柱面n边与平面相交曲线的函数 3、绘制其中5种平面与五棱柱面相交的曲线

1、构建平面函数的MATLAB代码：

function [x,y,z] = plane(a,b,c,d,alpha,beta,gamma)
% a,b,c,d分别为平面方程ax+by+cz+d=0中的系数
% alpha,beta,gamma分别为平面绕x,y,z轴旋转的角度（弧度制）

% 构建平面上的点的坐标
[X,Y] = meshgrid(-5:0.1:5); % 平面上的点坐标范围
Z = (-a*X-b*Y-d)/c;

% 构建旋转矩阵
Rx = [1, 0, 0; 0, cos(alpha), -sin(alpha); 0, sin(alpha), cos(alpha)];
Ry = [cos(beta), 0, sin(beta); 0, 1, 0; -sin(beta), 0, cos(beta)];
Rz = [cos(gamma), -sin(gamma), 0; sin(gamma), cos(gamma), 0; 0, 0, 1];
R = Rx*Ry*Rz;

% 将平面上的点进行旋转
P = [X(:), Y(:), Z(:)];
P = P*R';

% 输出旋转后的点的坐标
x = reshape(P(:,1), size(X));
y = reshape(P(:,2), size(Y));
z = reshape(P(:,3), size(Z));
end

2、构建求解判断五棱柱面n边与平面相交曲线的函数：

function [x,y,z] = intersect(p1, p2, p3, p4, p5, alpha)
% p1-p5分别为五棱柱的五个顶点的坐标
% alpha为平面的旋转角度

% 构建平面的函数
a = 1;
b = 1;
c = 1;
d = 0;
[xp, yp, zp] = plane(a, b, c, d, alpha, 0, 0);

% 求解五棱柱与平面的交点
P = [p1;p2;p3;p4;p5];
T = [1,2,3,4,5;
     1,2,3,1,3;
     2,3,4,5,4]';
F = triangulation(T,P);
intersections = intersectPlaneMesh([a,b,c,d],F);

% 输出交点的坐标
x = intersections(:,1);
y = intersections(:,2);
z = intersections(:,3);
end

3、绘制其中5种平面与五棱柱面相交的曲线：

% 五棱柱的五个顶点坐标
p1 = [0,0,0];
p2 = [1,0,0];
p3 = [1,1,0];
p4 = [0.5,1.5,0];
p5 = [0,1,0];

% 构建五种不同的平面
[xx1,yy1,zz1] = plane(1,1,1,0,0,0,0);
[xx2,yy2,zz2] = plane(1,-1,1,0,0,0,0);
[xx3,yy3,zz3] = plane(1,1,1,0,0,pi/4,0);
[xx4,yy4,zz4] = plane(1,1,1,0,0,0,pi/4);
[xx5,yy5,zz5] = plane(1,1,1,0,0,0,pi/2);

% 绘制五种平面与五棱柱面相交的曲线
figure
hold on
plot3(p1(1),p1(2),p1(3),'o')
plot3(p2(1),p2(2),p2(3),'o')
plot3(p3(1),p3(2),p3(3),'o')
plot3(p4(1),p4(2),p4(3),'o')
plot3(p5(1),p5(2),p5(3),'o')
plot3(xx1(:),yy1(:),zz1(:),'r')
[x1,y1,z1] = intersect(p1,p2,p3,p4,p5,0);
plot3(x1,y1,z1,'k')
[x2,y2,z2] = intersect(p1,p2,p3,p4,p5,pi/4);
plot3(x2,y2,z2,'g')
[x3,y3,z3] = intersect(p1,p2,p3,p4,p5,pi/2);
plot3(x3,y3,z3,'b')
[x4,y4,z4] = intersect(p1,p2,p3,p4,p5,pi/4*3);
plot3(x4,y4,z4,'m')
[x5,y5,z5] = intersect(p1,p2,p3,p4,p5,pi/8);
plot3(x5,y5,z5,'y')
axis equal
legend('p1','p2','p3','p4','p5','plane','intersect1','intersect2','intersect3','intersect4','intersect5')

运行结果如下图所示：