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
时间: 2023-07-15 08:13:40 浏览: 74
以下是实现以上要求的 MATLAB 代码:
1. 构建平面函数
```matlab
function [x,y,z] = plane(a, b, c, d, alpha, beta, gamma)
% 构建平面函数
% 输入参数:a,b,c,d为平面方程系数,alpha,beta,gamma为平面旋转角度
% 输出参数:x,y,z为平面上的点坐标
% 构建平面上的点坐标矩阵
[X,Y] = meshgrid(-10:0.1:10, -10:0.1:10);
Z = (-a*X - b*Y - d) / c;
% 平面旋转
R_x = [1 0 0; 0 cosd(alpha) -sind(alpha); 0 sind(alpha) cosd(alpha)];
R_y = [cosd(beta) 0 sind(beta); 0 1 0; -sind(beta) 0 cosd(beta)];
R_z = [cosd(gamma) -sind(gamma) 0; sind(gamma) cosd(gamma) 0; 0 0 1];
R = R_x * R_y * R_z;
xyz = [X(:), Y(:), Z(:)] * R';
x = reshape(xyz(:,1), size(X));
y = reshape(xyz(:,2), size(Y));
z = reshape(xyz(:,3), size(Z));
end
```
2. 构建五角柱面与平面相交曲线函数
```matlab
function [x,y,z] = intersect_pentagonal_prism_plane(a, b, c, d, alpha, beta, gamma, n)
% 构建五角柱面与平面相交曲线函数
% 输入参数:a,b,c,d为平面方程系数,alpha,beta,gamma为平面旋转角度,n为五角柱边数
% 输出参数:x,y,z为相交曲线上的点坐标
% 构建五角柱面顶点坐标
theta = 0:2*pi/n:2*pi*(n-1)/n;
x_top = cos(theta);
y_top = sin(theta);
z_top = 1/2*ones(1,n);
% 构建五角柱面底面坐标
x_bottom = cos(theta);
y_bottom = sin(theta);
z_bottom = -1/2*ones(1,n);
% 构建五角柱面侧面坐标
x_side = [cos(theta); cos(theta)];
y_side = [sin(theta); sin(theta)];
z_side = [ones(1,n)/2; -ones(1,n)/2];
% 求解相交曲线
[X,Y] = meshgrid(-10:0.1:10, -10:0.1:10);
Z = (-a*X - b*Y - d) / c;
R_x = [1 0 0; 0 cosd(alpha) -sind(alpha); 0 sind(alpha) cosd(alpha)];
R_y = [cosd(beta) 0 sind(beta); 0 1 0; -sind(beta) 0 cosd(beta)];
R_z = [cosd(gamma) -sind(gamma) 0; sind(gamma) cosd(gamma) 0; 0 0 1];
R = R_x * R_y * R_z;
xyz = [X(:), Y(:), Z(:)] * R';
% 判断点是否在五角柱面内
x = xyz(:,1);
y = xyz(:,2);
z = xyz(:,3);
in_top = inpolygon(x, y, x_top, y_top);
in_bottom = inpolygon(x, y, x_bottom, y_bottom);
in_side = inpolygon(x, y, x_side, y_side);
% 求解相交曲线坐标
idx = find((in_top | in_bottom) & ~in_side);
x = x(idx);
y = y(idx);
z = z(idx);
end
```
3. 绘制五种平面与五角柱面相交曲线
```matlab
% 绘制平面1与五角柱面相交曲线
figure(1);
[x,y,z] = intersect_pentagonal_prism_plane(1, 2, 3, 4, 0, 30, 0, 5);
plot3(x, y, z, 'r');
hold on;
[x,y,z] = intersect_pentagonal_prism_plane(1, 2, 3, 4, 0, 210, 0, 5);
plot3(x, y, z, 'b');
hold on;
[x,y,z] = intersect_pentagonal_prism_plane(1, 2, 3, 4, 0, 150, 0, 5);
plot3(x, y, z, 'g');
hold on;
[x,y,z] = intersect_pentagonal_prism_plane(1, 2, 3, 4, 0, 330, 0, 5);
plot3(x, y, z, 'm');
hold on;
[x,y,z] = intersect_pentagonal_prism_plane(1, 2, 3, 4, 0, 270, 0, 5);
plot3(x, y, z, 'k');
hold off;
xlabel('X');
ylabel('Y');
zlabel('Z');
title('Five planes intersecting with a pentagonal prism');
% 绘制平面2与五角柱面相交曲线
figure(2);
[x,y,z] = intersect_pentagonal_prism_plane(2, -1, 3, -4, 30, 0, 0, 5);
plot3(x, y, z, 'r');
hold on;
[x,y,z] = intersect_pentagonal_prism_plane(2, -1, 3, -4, 210, 0, 0, 5);
plot3(x, y, z, 'b');
hold on;
[x,y,z] = intersect_pentagonal_prism_plane(2, -1, 3, -4, 150, 0, 0, 5);
plot3(x, y, z, 'g');
hold on;
[x,y,z] = intersect_pentagonal_prism_plane(2, -1, 3, -4, 330, 0, 0, 5);
plot3(x, y, z, 'm');
hold on;
[x,y,z] = intersect_pentagonal_prism_plane(2, -1, 3, -4, 270, 0, 0, 5);
plot3(x, y, z, 'k');
hold off;
xlabel('X');
ylabel('Y');
zlabel('Z');
title('Five planes intersecting with a pentagonal prism');
% 绘制平面3与五角柱面相交曲线
figure(3);
[x,y,z] = intersect_pentagonal_prism_plane(-2, 1, 3, -4, 0, 30, 0, 5);
plot3(x, y, z, 'r');
hold on;
[x,y,z] = intersect_pentagonal_prism_plane(-2, 1, 3, -4, 0, 210, 0, 5);
plot3(x, y, z, 'b');
hold on;
[x,y,z] = intersect_pentagonal_prism_plane(-2, 1, 3, -4, 0, 150, 0, 5);
plot3(x, y, z, 'g');
hold on;
[x,y,z] = intersect_pentagonal_prism_plane(-2, 1, 3, -4, 0, 330, 0, 5);
plot3(x, y, z, 'm');
hold on;
[x,y,z] = intersect_pentagonal_prism_plane(-2, 1, 3, -4, 0, 270, 0, 5);
plot3(x, y, z, 'k');
hold off;
xlabel('X');
ylabel('Y');
zlabel('Z');
title('Five planes intersecting with a pentagonal prism');
% 绘制平面4与五角柱面相交曲线
figure(4);
[x,y,z] = intersect_pentagonal_prism_plane(1, 2, -3, 4, 0, 30, 0, 5);
plot3(x, y, z, 'r');
hold on;
[x,y,z] = intersect_pentagonal_prism_plane(1, 2, -3, 4, 0, 210, 0, 5);
plot3(x, y, z, 'b');
hold on;
[x,y,z] = intersect_pentagonal_prism_plane(1, 2, -3, 4, 0, 150, 0, 5);
plot3(x, y, z, 'g');
hold on;
[x,y,z] = intersect_pentagonal_prism_plane(1, 2, -3, 4, 0, 330, 0, 5);
plot3(x, y, z, 'm');
hold on;
[x,y,z] = intersect_pentagonal_prism_plane(1, 2, -3, 4, 0, 270, 0, 5);
plot3(x, y, z, 'k');
hold off;
xlabel('X');
ylabel('Y');
zlabel('Z');
title('Five planes intersecting with a pentagonal prism');
% 绘制平面5与五角柱面相交曲线
figure(5);
[x,y,z] = intersect_pentagonal_prism_plane(2, -1, -3, -4, 30, 0, 0, 5);
plot3(x, y, z, 'r');
hold on;
[x,y,z] = intersect_pentagonal_prism_plane(2, -1, -3, -4, 210, 0, 0, 5);
plot3(x, y, z, 'b');
hold on;
[x,y,z] = intersect_pentagonal_prism_plane(2, -1, -3, -4, 150, 0, 0, 5);
plot3(x, y, z, 'g');
hold on;
[x,y,z] = intersect_pentagonal_prism_plane(2, -1, -3, -4, 330, 0, 0, 5);
plot3(x, y, z, 'm');
hold on;
[x,y,z] = intersect_pentagonal_prism_plane(2, -1, -3, -4, 270, 0, 0, 5);
plot3(x, y, z, 'k');
hold off;
xlabel('X');
ylabel('Y');
zlabel('Z');
title('Five planes intersecting with a pentagonal prism');
```
运行以上代码可以得到五种平面与五角柱面相交曲线的三维图像。