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

以下是实现上述需求的MATLAB代码：

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：

function [x,y,z] = plane_function(a, b, c, d, alpha, beta, gamma, x0, y0, z0, n)
    % a,b,c,d为平面方程ax+by+cz+d=0中的系数
    % alpha,beta,gamma为平面的欧拉角（旋转角度）
    % x0,y0,z0为平面的平移距离
    % n为平面上离散点的个数，用于绘制曲线
    x = linspace(-1, 1, n);
    y = linspace(-1, 1, n);
    [X, Y] = meshgrid(x, y);
    Z = (-a*X - b*Y - d)/c;
    R = [cos(beta)*cos(gamma), -cos(alpha)*sin(gamma)+sin(alpha)*sin(beta)*cos(gamma), sin(alpha)*sin(gamma)+cos(alpha)*sin(beta)*cos(gamma);
         cos(beta)*sin(gamma), cos(alpha)*cos(gamma)+sin(alpha)*sin(beta)*sin(gamma), -sin(alpha)*cos(gamma)+cos(alpha)*sin(beta)*sin(gamma);
         -sin(beta), sin(alpha)*cos(beta), cos(alpha)*cos(beta)];
    P = [X(:) Y(:) Z(:)]';
    P = R*P + repmat([x0; y0; z0], 1, n*n);
    x = reshape(P(1,:), n, n);
    y = reshape(P(2,:), n, n);
    z = reshape(P(3,:), n, n);
end

2、构建求解判断五角柱面n边与平面相交曲线的函数：

function [x,y,z] = intersect_function(n, h, r, a, b, c, d)
    % n为五角柱的边数
    % h为五角柱的高度
    % r为五角柱底面半径
    % a,b,c,d为平面方程ax+by+cz+d=0中的系数
    X = [];
    Y = [];
    Z = [];
    for i = 1:n
        x1 = r*cos(2*pi/n*(i-1));
        y1 = r*sin(2*pi/n*(i-1));
        x2 = r*cos(2*pi/n*i);
        y2 = r*sin(2*pi/n*i);
        % 底面五边形的顶点
        X1 = [x1, x2, 0, -x2, -x1];
        Y1 = [y1, y2, r, y2, y1];
        Z1 = [0, 0, 0, 0, 0];
        % 顶面五边形的顶点
        X2 = [x1, x2, 0, -x2, -x1];
        Y2 = [y1, y2, -r, y2, y1];
        Z2 = [h, h, h, h, h];
        % 连接底面五边形和顶面五边形的侧面上的四边形的顶点
        X3 = [x1, x2, x2, x1];
        Y3 = [y1, y2, y2, y1];
        Z3 = [0, 0, h, h];
        X = [X, X1, X2, X3];
        Y = [Y, Y1, Y2, Y3];
        Z = [Z, Z1, Z2, Z3];
    end
    % 将五角柱变换成与平面在同一坐标系下的位置和角度
    [X, Y, Z] = transform_function(X, Y, Z, a, b, c, d);
    % 计算五角柱与平面相交的曲线
    [x, y, z] = intersect_plane(X, Y, Z, n);
end

function [X, Y, Z] = transform_function(X, Y, Z, a, b, c, d)
    % 将五角柱变换成与平面在同一坐标系下的位置和角度
    % a,b,c,d为平面方程ax+by+cz+d=0中的系数
    X = X - mean(X(:));
    Y = Y - mean(Y(:));
    Z = Z - mean(Z(:));
    % 先绕z轴旋转beta角度，再绕y轴旋转gamma角度，最后绕x轴旋转alpha角度
    beta = atan2(-a, b);
    gamma = atan2(c, sqrt(a^2 + b^2));
    alpha = atan2(-b*sin(beta)+a*cos(beta), c);
    R = [cos(beta)*cos(gamma), -cos(alpha)*sin(gamma)+sin(alpha)*sin(beta)*cos(gamma), sin(alpha)*sin(gamma)+cos(alpha)*sin(beta)*cos(gamma);
         cos(beta)*sin(gamma), cos(alpha)*cos(gamma)+sin(alpha)*sin(beta)*sin(gamma), -sin(alpha)*cos(gamma)+cos(alpha)*sin(beta)*sin(gamma);
         -sin(beta), sin(alpha)*cos(beta), cos(alpha)*cos(beta)];
    P = [X(:) Y(:) Z(:)]';
    P = R*P;
    X = reshape(P(1,:), size(X));
    Y = reshape(P(2,:), size(Y));
    Z = reshape(P(3,:), size(Z));
    % 平移
    t = [0; 0; -d/c];
    X = X + t(1);
    Y = Y + t(2);
    Z = Z + t(3);
end

function [x, y, z] = intersect_plane(X, Y, Z, n)
    % 计算五角柱与平面相交的曲线
    x = [];
    y = [];
    z = [];
    for i = 1:(5*n)
        % 计算平面与当前四边形的交点
        [x1, y1, z1] = intersect_triangle(X(:,i), Y(:,i), Z(:,i));
        [x2, y2, z2] = intersect_triangle(X(:,mod(i,5*n)+1), Y(:,mod(i,5*n)+1), Z(:,mod(i,5*n)+1));
        % 将曲线分段，每段为一个三角形
        if ~isempty(x1) && ~isempty(x2)
            x3 = [x1, x2];
            y3 = [y1, y2];
            z3 = [z1, z2];
            for j = 1:(n-2)
                [x4, y4, z4] = intersect_triangle(X(:,i), Y(:,i), Z(:,i),...
                                                  X(:,i+1+mod(j,n)), Y(:,i+1+mod(j,n)), Z(:,i+1+mod(j,n)),...
                                                  X(:,i+2+mod(j,n)), Y(:,i+2+mod(j,n)), Z(:,i+2+mod(j,n)));
                if ~isempty(x4)
                    x3 = [x3, x4];
                    y3 = [y3, y4];
                    z3 = [z3, z4];
                else
                    break;
                end
            end
            x = [x, x3];
            y = [y, y3];
            z = [z, z3];
        end
    end
end

function [x, y, z] = intersect_triangle(x1, y1, z1, x2, y2, z2, x3, y3, z3)
    % 计算平面与当前三角形的交点
    % 如果交点在三角形内，则返回交点
    % 否则返回空
    if nargin==3
        x2 = x1([2 3 1]);
        y2 = y1([2 3 1]);
        z2 = z1([2 3 1]);
        x3 = x1([3 1 2]);
        y3 = y1([3 1 2]);
        z3 = z1([3 1 2]);
    end
    a = (y2-y1).*(z3-z1) - (z2-z1).*(y3-y1);
    b = (z2-z1).*(x3-x1) - (x2-x1).*(z3-z1);
    c = (x2-x1).*(y3-y1) - (y2-y1).*(x3-x1);
    d = -a*x1 - b*y1 - c*z1;
    if c==0
        x = [];
        y = [];
        z = [];
        return;
    end
    x = (-d - b*y1 - c*z1)/a;
    y = (-d - a*x1 - c*z1)/b;
    z = (-d - a*x1 - b*y1)/c;
    if (0<=x)&&(x<=1)&&(0<=y)&&(y<=1)&&(0<=z)&&(z<=1)&&(x+y+z<=1)
        return;
    else
        x = [];
        y = [];
        z = [];
        return;
    end
end

3、绘制其中5种平面与五角柱面相交的曲线：

% 绘制平面1
[a, b, c, d] = deal(0, 0, 1, 0);
[x, y, z] = plane_function(a, b, c, d, pi/4, pi/3, pi/6, 0, 0, 0, 50);
[x1, y1, z1] = intersect_function(5, 2, 1, a, b, c, d);
figure;
surf(x, y, z, 'FaceColor', 'red', 'FaceAlpha', 0.3, 'EdgeColor', 'none');
hold on;
plot3(x1, y1, z1, 'LineWidth', 3);
axis equal;
xlabel('x');
ylabel('y');
zlabel('z');
title('平面1与五角柱的相交曲线');

% 绘制平面2
[a, b, c, d] = deal(1, 0, 1, 0);
[x, y, z] = plane_function(a, b, c, d, pi/3, pi/4, pi/6, 0, 0, 0, 50);
[x1, y1, z1] = intersect_function(5, 2, 1, a, b, c, d);
figure;
surf(x, y, z, 'FaceColor', 'blue', 'FaceAlpha', 0.3, 'EdgeColor', 'none');
hold on;
plot3(x1, y1, z1, 'LineWidth', 3);
axis equal;
xlabel('x');
ylabel('y');
zlabel('z');
title('平面2与五角柱的相交曲线');

% 绘制平面3
[a, b, c, d] = deal(1, 1, 1, 0);
[x, y, z] = plane_function(a, b, c, d, pi/6, pi/3, pi/4, 0, 0, 0, 50);
[x1, y1, z1] = intersect_function(5, 2, 1, a, b, c, d);
figure;
surf(x, y, z, 'FaceColor', 'green', 'FaceAlpha', 0.3, 'EdgeColor', 'none');
hold on;
plot3(x1, y1, z1, 'LineWidth', 3);
axis equal;
xlabel('x');
ylabel('y');
zlabel('z');
title('平面3与五角柱的相交曲线');

% 绘制平面4
[a, b, c, d] = deal(1, -1, 0, 0);
[x, y, z] = plane_function(a, b, c, d, pi/4, pi/6, pi/3, 0, 0, 0, 50);
[x1, y1, z1] = intersect_function(5, 2, 1, a, b, c, d);
figure;
surf(x, y, z, 'FaceColor', 'yellow', 'FaceAlpha', 0.3, 'EdgeColor', 'none');
hold on;
plot3(x1, y1, z1, 'LineWidth', 3);
axis equal;
xlabel('x');
ylabel('y');
zlabel('z');
title('平面4与五角柱的相交曲线');

% 绘制平面5
[a, b, c, d] = deal(1, -1, -1, 0);
[x, y, z] = plane_function(a, b, c, d, pi/3, pi/6, pi/4, 0, 0, 0, 50);
[x1, y1, z1] = intersect_function(5, 2, 1, a, b, c, d);
figure;
surf(x, y, z, 'FaceColor', 'magenta', 'FaceAlpha', 0.3, 'EdgeColor', 'none');
hold on;
plot3(x1, y1, z1, 'LineWidth', 3);
axis equal;
xlabel('x');
ylabel('y');
zlabel('z');
title('平面5与五角柱的相交曲线');