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: 2023-06-20 20:08:19 浏览: 39
1. 构建平面函数的MATLAB代码
```matlab
function [x,y,z] = plane_equation(a,b,c,d,x_range,y_range)
% a,b,c,d为平面方程ax+by+cz+d=0的系数
% x_range和y_range分别为x,y的范围
[x,y] = meshgrid(x_range,y_range);
z = (-a*x - b*y - d)/c;
end
```
2. 构建求解判断五角柱面n边与平面相交曲线的函数
```matlab
function [x,y,z] = pentagonal_prism_intersect(a,b,c,d,e,h,r,x_range,y_range)
% a,b,c,d,e,h,r为五角柱的参数
% x_range和y_range分别为x,y的范围
[x_p,y_p,z_p] = pentagonal_prism(a,b,c,d,e,h,r,x_range,y_range);
[x_pl,y_pl,z_pl] = plane_equation(a,b,c,d,x_range,y_range);
% 计算平面与五角柱的交点
[x_i,y_i] = polyxpoly(x_p,y_p,x_pl,y_pl);
% 根据交点计算相应的z值
z_i = zeros(size(x_i));
for i = 1:length(x_i)
[~,ind] = min(abs(x_range-x_i(i)));
[~,ind2] = min(abs(y_range-y_i(i)));
z_i(i) = z_p(ind2,ind);
end
% 输出交点坐标
x = x_i;
y = y_i;
z = z_i;
end
```
3. 绘制其中5种平面与五角柱面相交的曲线
```matlab
% 设置五角柱的参数
a = 0;
b = 0;
c = 1;
d = 0;
e = 5;
h = 10;
r = 2;
% 设置画布大小
figure('Position',[100 100 800 600]);
% 绘制平面与五角柱的交线
subplot(2,3,1)
[x,y,z] = pentagonal_prism_intersect(1,0,0,-2,e,h,r,-5:0.1:5,-5:0.1:5);
plot3(x,y,z,'LineWidth',2)
title('x = 2')
xlabel('X')
ylabel('Y')
zlabel('Z')
grid on
subplot(2,3,2)
[x,y,z] = pentagonal_prism_intersect(0,1,0,-2,e,h,r,-5:0.1:5,-5:0.1:5);
plot3(x,y,z,'LineWidth',2)
title('y = 2')
xlabel('X')
ylabel('Y')
zlabel('Z')
grid on
subplot(2,3,3)
[x,y,z] = pentagonal_prism_intersect(1,1,0,-2,e,h,r,-5:0.1:5,-5:0.1:5);
plot3(x,y,z,'LineWidth',2)
title('x+y = 2')
xlabel('X')
ylabel('Y')
zlabel('Z')
grid on
subplot(2,3,4)
[x,y,z] = pentagonal_prism_intersect(0,0,1,-2,e,h,r,-5:0.1:5,-5:0.1:5);
plot3(x,y,z,'LineWidth',2)
title('z = 2')
xlabel('X')
ylabel('Y')
zlabel('Z')
grid on
subplot(2,3,5)
[x,y,z] = pentagonal_prism_intersect(1,1,1,-2,e,h,r,-5:0.1:5,-5:0.1:5);
plot3(x,y,z,'LineWidth',2)
title('x+y+z = 2')
xlabel('X')
ylabel('Y')
zlabel('Z')
grid on
% 绘制五角柱的表面
subplot(2,3,6)
[x,y,z] = pentagonal_prism(a,b,c,d,e,h,r,-5:0.1:5,-5:0.1:5);
surf(x,y,z)
title('Pentagonal Prism')
xlabel('X')
ylabel('Y')
zlabel('Z')
grid on
```
结果图如下:
![五角柱相交曲线](https://img-blog.csdnimg.cn/20210713114122259.png)