平面与五角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、构建求解判断五角柱面n边与平面相交曲线的函数 3、绘制其中5种平面与五角柱面相交的曲线

1、构建平面函数的MATLAB代码：

function [x,y,z] = planeFunc(a,b,c,d,x_range,y_range)
% a,b,c,d分别是平面方程ax+by+cz+d=0中的系数
% x_range和y_range定义了平面在x和y方向上的取值范围
% 返回三维坐标系中的x,y,z值

[x,y] = meshgrid(x_range,y_range);
z = (-a*x - b*y - d)/c;
end

2、构建求解五角柱面与平面相交曲线的函数：

function [x,y,z] = intersectPentagonalPrismWithPlane(a,b,c,d,h,n,x_range,y_range)
% a,b,c,d分别是平面方程ax+by+cz+d=0中的系数
% h是五角柱的高
% n是五角柱的边数
% x_range和y_range定义了平面在x和y方向上的取值范围
% 返回三维坐标系中的x,y,z值

theta = pi/n;
r = h/(2*sin(theta));
[x_circ,y_circ] = circleFunc(r,n);
z_circ = linspace(-h/2,h/2,n+1);

z_plane = (-a*x_circ - b*y_circ - d)/c;
idx_above_plane = z_circ > max(z_plane);
idx_below_plane = z_circ < min(z_plane);

for i = 1:n
    if idx_above_plane(i) == 0 && idx_above_plane(i+1) == 1
        [x1,y1,z1] = linePlaneIntersection([x_circ(i),y_circ(i),z_circ(i)],...
            [x_circ(i+1),y_circ(i+1),z_circ(i+1)],[a,b,c,d]);
        [x2,y2,z2] = linePlaneIntersection([x_circ(i+1),y_circ(i+1),z_circ(i+1)],...
            [x_circ(i+2),y_circ(i+2),z_circ(i+2)],[a,b,c,d]);
        [x,y,z] = cylinderFunc([x1,x2],[y1,y2],z_range);
        break;
    elseif idx_below_plane(i) == 0 && idx_below_plane(i+1) == 1
        [x1,y1,z1] = linePlaneIntersection([x_circ(i),y_circ(i),z_circ(i)],...
            [x_circ(i+1),y_circ(i+1),z_circ(i+1)],[a,b,c,d]);
        [x2,y2,z2] = linePlaneIntersection([x_circ(i+1),y_circ(i+1),z_circ(i+1)],...
            [x_circ(i+2),y_circ(i+2),z_circ(i+2)],[a,b,c,d]);
        [x,y,z] = cylinderFunc([x1,x2],[y1,y2],z_range);
        break;
    elseif idx_above_plane(i) == 0 && idx_above_plane(i+1) == 0
        [x1,y1,z1] = linePlaneIntersection([x_circ(i),y_circ(i),z_circ(i)],...
            [x_circ(i+1),y_circ(i+1),z_circ(i+1)],[a,b,c,d]);
        [x2,y2,z2] = linePlaneIntersection([x_circ(i),y_circ(i),z_circ(i)],...
            [x_circ(i+1),y_circ(i+1),z_circ(i+1)],[a,b,c,d]);
        [x,y,z] = cylinderFunc([x1,x2],[y1,y2],z_range);
        break;
    elseif idx_below_plane(i) == 0 && idx_below_plane(i+1) == 0
        [x1,y1,z1] = linePlaneIntersection([x_circ(i),y_circ(i),z_circ(i)],...
            [x_circ(i+1),y_circ(i+1),z_circ(i+1)],[a,b,c,d]);
        [x2,y2,z2] = linePlaneIntersection([x_circ(i),y_circ(i),z_circ(i)],...
            [x_circ(i+1),y_circ(i+1),z_circ(i+1)],[a,b,c,d]);
        [x,y,z] = cylinderFunc([x1,x2],[y1,y2],z_range);
        break;
    end
end
end

function [x,y,z] = linePlaneIntersection(p1,p2,plane)
% p1,p2是直线上两个点的位置向量
% plane是一个包含平面方程系数的向量[a,b,c,d]，ax+by+cz+d=0
% 返回交点的坐标向量[x,y,z]

p1 = reshape(p1,1,3);
p2 = reshape(p2,1,3);
plane = reshape(plane,1,4);

n = plane(1:3);
d = plane(4);

t = -(n*p1' + d)/(n*(p2-p1)');
intersect = p1 + t*(p2-p1);

x = intersect(1);
y = intersect(2);
z = intersect(3);
end

function [x,y] = circleFunc(r,n)
% r是圆的半径
% n是圆的边数
% 返回圆上的点的坐标向量[x,y]

theta = linspace(0,2*pi,n+1);
x = r*cos(theta);
y = r*sin(theta);
end

function [x,y,z] = cylinderFunc(p1,p2,z_range)
% p1,p2是圆柱轴线上两点的位置向量
% z_range是圆柱在z方向上的取值范围
% 返回圆柱的三维坐标向量[x,y,z]

p1 = reshape(p1,1,3);
p2 = reshape(p2,1,3);

r = norm(p2-p1)/2;
theta = linspace(0,2*pi,50);
[x_circ,y_circ] = pol2cart(theta,r);

z = linspace(z_range(1),z_range(2),50);
[x_circ,y_circ,z_circ] = meshgrid(x_circ,y_circ,z);

z_axis = [p1;p2];
x_axis = repmat([1 0 0],size(z_axis,1),1);
y_axis = cross(x_axis,z_axis-p1);
y_axis = y_axis./vecnorm(y_axis,2,2);
x_axis = cross(y_axis,z_axis-p1);
x_axis = x_axis./vecnorm(x_axis,2,2);
rot_mat = [x_axis;y_axis;z_axis-p1];
rot_mat_inv = inv(rot_mat);
xyz_circ = [x_circ(:),y_circ(:),z_circ(:)];

xyz_circ_rot = xyz_circ*rot_mat;
xyz_circ_rot(:,3) = xyz_circ_rot(:,3) + norm(p1);
xyz_circ_rot(:,1:2) = xyz_circ_rot(:,1:2) + p1(1:2);
xyz_circ_rot = xyz_circ_rot*rot_mat_inv;

x = reshape(xyz_circ_rot(:,1),size(x_circ));
y = reshape(xyz_circ_rot(:,2),size(y_circ));
z = reshape(xyz_circ_rot(:,3),size(z_circ));
end

3、绘制其中5种平面与五角柱面相交的曲线：

% 平面1：x+y+z=0
a = 1;
b = 1;
c = 1;
d = 0;
[x_range,y_range] = meshgrid(-2:0.1:2,-2:0.1:2);
x = x_range(:);
y = y_range(:);
z = (-a*x - b*y - d)/c;
plot3(x,y,z,'.');

hold on;
h = 2;
n = 5;
z_range = [-h/2,h/2];
[x_circ,y_circ,z_circ] = cylinder(h,n);
surf(x_circ,y_circ,z_circ,'FaceAlpha',0.5);

[x,y,z] = intersectPentagonalPrismWithPlane(a,b,c,d,h,n,x_range,y_range);
plot3(x,y,z,'LineWidth',2,'Color','r');

xlim([-2,2]);
ylim([-2,2]);
zlim([-1,1]);
xlabel('x');
ylabel('y');
zlabel('z');
title('Intersection of Plane 1 with Pentagonal Prism');

% 平面2：x-y=0
a = 1;
b = -1;
c = 0;
d = 0;
[x_range,y_range] = meshgrid(-2:0.1:2,-2:0.1:2);
x = x_range(:);
y = y_range(:);
z = (-a*x - b*y - d)/c;
plot3(x,y,z,'.');

hold on;
h = 2;
n = 5;
z_range = [-h/2,h/2];
[x_circ,y_circ,z_circ] = cylinder(h,n);
surf(x_circ,y_circ,z_circ,'FaceAlpha',0.5);

[x,y,z] = intersectPentagonalPrismWithPlane(a,b,c,d,h,n,x_range,y_range);
plot3(x,y,z,'LineWidth',2,'Color','r');

xlim([-2,2]);
ylim([-2,2]);
zlim([-1,1]);
xlabel('x');
ylabel('y');
zlabel('z');
title('Intersection of Plane 2 with Pentagonal Prism');

% 平面3：z=0
a = 0;
b = 0;
c = 1;
d = 0;
[x_range,y_range] = meshgrid(-2:0.1:2,-2:0.1:2);
x = x_range(:);
y = y_range(:);
z = (-a*x - b*y - d)/c;
plot3(x,y,z,'.');

hold on;
h = 2;
n = 5;
z_range = [-h/2,h/2];
[x_circ,y_circ,z_circ] = cylinder(h,n);
surf(x_circ,y_circ,z_circ,'FaceAlpha',0.5);

[x,y,z] = intersectPentagonalPrismWithPlane(a,b,c,d,h,n,x_range,y_range);
plot3(x,y,z,'LineWidth',2,'Color','r');

xlim([-2,2]);
ylim([-2,2]);
zlim([-1,1]);
xlabel('x');
ylabel('y');
zlabel('z');
title('Intersection of Plane 3 with Pentagonal Prism');

% 平面4：x+z=0
a = 1;
b = 0;
c = 1;
d = 0;
[x_range,y_range] = meshgrid(-2:0.1:2,-2:0.1:2);
x = x_range(:);
y = y_range(:);
z = (-a*x - b*y - d)/c;
plot3(x,y,z,'.');

hold on;
h = 2;
n = 5;
z_range = [-h/2,h/2];
[x_circ,y_circ,z_circ] = cylinder(h,n);
surf(x_circ,y_circ,z_circ,'FaceAlpha',0.5);

[x,y,z] = intersectPentagonalPrismWithPlane(a,b,c,d,h,n,x_range,y_range);
plot3(x,y,z,'LineWidth',2,'Color','r');

xlim([-2,2]);
ylim([-2,2]);
zlim([-1,1]);
xlabel('x');
ylabel('y');
zlabel('z');
title('Intersection of Plane 4 with Pentagonal Prism');

% 平面5：y=0
a = 0;
b = 1;
c = 0;
d = 0;
[x_range,y_range] = meshgrid(-2:0.1:2,-2:0.1:2);
x = x_range(:);
y = y_range(:);
z = (-a*x - b*y - d)/c;
plot3(x,y,z,'.');

hold on;
h = 2;
n = 5;
z_range = [-h/2,h/2];
[x_circ,y_circ,z_circ] = cylinder(h,n);
surf(x_circ,y_circ,z_circ,'FaceAlpha',0.5);

[x,y,z] = intersectPentagonalPrismWithPlane(a,b,c,d,h,n,x_range,y_range);
plot3(x,y,z,'LineWidth',2,'Color','r');

xlim([-2,2]);
ylim([-2,2]);
zlim([-1,1]);
xlabel('x');
ylabel('y');
zlabel('z');
title('Intersection of Plane 5 with Pentagonal Prism');