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,x_range,y_range)
% a,b,c,d为平面的系数，x_range和y_range为平面的范围
[x,y] = meshgrid(x_range,y_range);
z = (-a*x - b*y - d)/c;

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,a,b,c,d)
% p1,p2,p3,p4,p5为五棱柱的五个顶点，a,b,c,d为平面的系数
% 求出五棱柱的n边的两个端点
p6 = [p1(1:2)+a*p1(3)/(p1(3)-p2(3)), 0];
p7 = [p2(1:2)+a*p2(3)/(p2(3)-p3(3)), 0];
p8 = [p3(1:2)+a*p3(3)/(p3(3)-p4(3)), 0];
p9 = [p4(1:2)+a*p4(3)/(p4(3)-p5(3)), 0];
p10 = [p5(1:2)+a*p5(3)/(p5(3)-p1(3)), 0];
% 判断是否与平面相交
flag1 = (p6(1)*b + p6(2)*c + d) * (p7(1)*b + p7(2)*c + d) <= 0;
flag2 = (p7(1)*b + p7(2)*c + d) * (p8(1)*b + p8(2)*c + d) <= 0;
flag3 = (p8(1)*b + p8(2)*c + d) * (p9(1)*b + p9(2)*c + d) <= 0;
flag4 = (p9(1)*b + p9(2)*c + d) * (p10(1)*b + p10(2)*c + d) <= 0;
flag5 = (p10(1)*b + p10(2)*c + d) * (p6(1)*b + p6(2)*c + d) <= 0;
flag = flag1 + flag2 + flag3 + flag4 + flag5;
% 计算相交曲线
if flag >= 2
    x = [];
    y = [];
    z = [];
else
    if flag1 == 1
        [x1,y1,z1] = line_plane_intersect(p6,p7,[a,b,c,d]);
        [x2,y2,z2] = line_plane_intersect(p7,p6,[a,b,c,d]);
        x = [x1,x2];
        y = [y1,y2];
        z = [z1,z2];
    elseif flag2 == 1
        [x1,y1,z1] = line_plane_intersect(p7,p8,[a,b,c,d]);
        [x2,y2,z2] = line_plane_intersect(p8,p7,[a,b,c,d]);
        x = [x1,x2];
        y = [y1,y2];
        z = [z1,z2];
    elseif flag3 == 1
        [x1,y1,z1] = line_plane_intersect(p8,p9,[a,b,c,d]);
        [x2,y2,z2] = line_plane_intersect(p9,p8,[a,b,c,d]);
        x = [x1,x2];
        y = [y1,y2];
        z = [z1,z2];
    elseif flag4 == 1
        [x1,y1,z1] = line_plane_intersect(p9,p10,[a,b,c,d]);
        [x2,y2,z2] = line_plane_intersect(p10,p9,[a,b,c,d]);
        x = [x1,x2];
        y = [y1,y2];
        z = [z1,z2];
    elseif flag5 == 1
        [x1,y1,z1] = line_plane_intersect(p10,p6,[a,b,c,d]);
        [x2,y2,z2] = line_plane_intersect(p6,p10,[a,b,c,d]);
        x = [x1,x2];
        y = [y1,y2];
        z = [z1,z2];
    else
        x = [];
        y = [];
        z = [];
    end
end

3. 绘制其中5种平面与五棱柱面相交的曲线

p1 = [0,0,0];
p2 = [1,1,1];
p3 = [2,2,1];
p4 = [3,1,0];
p5 = [4,0,0];
x_range = -5:0.1:5;
y_range = -5:0.1:5;
[a,b,c,d] = plane_coefficient(p1,p2,p3);
[x1,y1,z1] = intersect(p1,p2,p3,p4,p5,a,b,c,d);
[x2,y2,z2] = intersect(p1,p2,p3,p4,p5,a,b,c,-d);
[a,b,c,d] = plane_coefficient(p2,p3,p4);
[x3,y3,z3] = intersect(p1,p2,p3,p4,p5,a,b,c,d);
[x4,y4,z4] = intersect(p1,p2,p3,p4,p5,a,b,c,-d);
[a,b,c,d] = plane_coefficient(p3,p4,p5);
[x5,y5,z5] = intersect(p1,p2,p3,p4,p5,a,b,c,d);
[x6,y6,z6] = intersect(p1,p2,p3,p4,p5,a,b,c,-d);
[a,b,c,d] = plane_coefficient(p4,p5,p1);
[x7,y7,z7] = intersect(p1,p2,p3,p4,p5,a,b,c,d);
[x8,y8,z8] = intersect(p1,p2,p3,p4,p5,a,b,c,-d);
[a,b,c,d] = plane_coefficient(p5,p1,p2);
[x9,y9,z9] = intersect(p1,p2,p3,p4,p5,a,b,c,d);
[x10,y10,z10] = intersect(p1,p2,p3,p4,p5,a,b,c,-d);

figure()
subplot(2,3,1)
plot3(x1,y1,z1,'LineWidth',2)
title('平面1与五棱柱相交')
subplot(2,3,2)
plot3(x2,y2,z2,'LineWidth',2)
title('平面1与五棱柱不相交')
subplot(2,3,3)
plot3(x3,y3,z3,'LineWidth',2)
title('平面2与五棱柱相交')
subplot(2,3,4)
plot3(x4,y4,z4,'LineWidth',2)
title('平面2与五棱柱不相交')
subplot(2,3,5)
plot3(x5,y5,z5,'LineWidth',2)
title('平面3与五棱柱相交')
subplot(2,3,6)
plot3(x6,y6,z6,'LineWidth',2)
title('平面3与五棱柱不相交')