sprintf(p, "\\x%02x", *q++);解析

最新推荐文章于 2025-01-24 10:11:52 发布
最新推荐文章于 2025-01-24 10:11:52 发布
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本文解析了C语言中使用sprintf函数配合格式化字符串\x%02x进行16进制ASCII码输出的具体含义及应用场景。通过实例说明如何将一个字符的ASCII码值转换为16进制形式，并以两位数输出。

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        今天编程遇到了一句sprintf(p, "\\x%02x", *q++);，甚为不解，经过验证及查找，才明白"\\x%02x"的意思。下面作一解析：

        "\\x%02x"中“\\”输出是“\”，“x”输出是“x”，“%02x”是格式化输出，表示按照右对齐输出两位16进制，不足两位的左边以为补0。所以，"\\x%02x"的最后输出类似于“\x61”或者“\x6f”或者“\x03”。而在C语言中，“\xhh” 表示一个ASCII码用16进制表示，其中hh是1到2个16进制数。

        因此，“\x61”表示的是ASCII字符a。

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sprintf使用例子：1、BCD转换成字符char src = 0x3A;char tmp[6];memset(tmp, 0x00, sizeof(tmp));sprintf(tmp, "%02X", src);说明：1)打印出tmp为3A2)%02X含义：02：0表示长度不足用0填充，2表示格式化后总长度是2X：表示以大写16进制形式输出2、字符串数值相加char * p = "0000000...
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#include #include #define lo(f) ((f)&0xff) #define hi(f) (lo(f>>8)) int main(void) { int key; do {  key=bioskey(0);  printf("0x%02x 0x%02x %c\n",hi(key),lo(key),lo(key));//这条语句中0x%02x是什么意思？？
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1.X代表16进制输出 2.02代表不足两位前面补零，超过2位不影响 例子： sprintf(data,"%02X",123) 输出123 sprintf(data,"%02X",1) 输出01
%% 三关节机械臂正弦轨迹跟踪控制 % 作者：MATLAB助手 % 参考：[^1][^2][^3] clear; clc; close all; %% 机械臂参数设置 l1 = 1.0; % 连杆1长度 (m) l2 = 0.8; % 连杆2长度 (m) l3 = 0.6; % 连杆3长度 (m) dt = 0.01; % 时间步长 (s) T = 10; % 总仿真时间 (s) t = 0:dt:T; % 时间向量 %% 轨迹生成 - 末端正弦运动轨迹 % 参考轨迹: x = A*sin(wt), y = B*sin(wt + phi) + C A = 0.5; B = 0.4; C = 0.8; phi = pi/3; w = 1.0; x_d = A * sin(w*t); % X轴期望轨迹 y_d = B * sin(w*t + phi) + C; % Y轴期望轨迹 z_d = zeros(size(t)); % Z轴固定（平面机械臂） % 计算轨迹导数（用于前馈控制） dx_d = A*w*cos(w*t); dy_d = B*w*cos(w*t + phi); dz_d = zeros(size(t)); %% 初始化变量 q = zeros(3, length(t)); % 关节角度 [q1; q2; q3] dq = zeros(3, length(t)); % 关节角速度 q_ref = zeros(3, length(t));% 参考关节角度 % 初始位置（对应轨迹起点） q0 = ikine_3dof([x_d(1), y_d(1), z_d(1)], l1, l2, l3); q(:,1) = q0; %% 控制器参数 Kp = diag([150, 120, 100]); % 比例增益 Kd = diag([30, 25, 20]); % 微分增益 Ki = diag([5, 4, 3]); % 积分增益（可选） integral_error = zeros(3,1);% 积分误差累积 %% 主控制循环 for i = 1:length(t)-1 % 1. 计算当前末端位置 [x_curr, y_curr, z_curr] = fkine_3dof(q(:,i), l1, l2, l3); % 2. 计算位置误差 e_pos = [x_d(i); y_d(i); z_d(i)] - [x_curr; y_curr; z_curr]; % 3. 逆运动学求解期望关节角度（迭代算法） q_ref(:,i) = ikine_3dof([x_d(i), y_d(i), z_d(i)], l1, l2, l3); % 4. 计算关节误差 e_q = q_ref(:,i) - q(:,i); % 5. 计算关节速度误差（数值差分） if i > 1 dq_ref = (q_ref(:,i) - q_ref(:,i-1)) / dt; else dq_ref = zeros(3,1); end e_dq = dq_ref - dq(:,i); % 6. PID控制律 integral_error = integral_error + e_q * dt; tau = Kp * e_q + Kd * e_dq + Ki * integral_error; % 7. 简单动力学模型更新（二阶系统） I = diag([0.5, 0.3, 0.2]); % 关节转动惯量 ddq = I \ tau; % 加速度 = 扭矩 / 惯量 % 8. 状态更新 dq(:,i+1) = dq(:,i) + ddq * dt; q(:,i+1) = q(:,i) + dq(:,i+1) * dt; end %% 可视化结果 % 轨迹跟踪结果 figure('Name', '轨迹跟踪性能'); subplot(2,1,1); plot(t, x_d, 'r--', 'LineWidth', 2); hold on; plot(t, y_d, 'b--', 'LineWidth', 2); [x_act, y_act, ~] = arrayfun(@(i) fkine_3dof(q(:,i), l1, l2, l3), 1:length(t)); plot(t, x_act, 'r-', t, y_act, 'b-'); legend('X期望', 'Y期望', 'X实际', 'Y实际'); title('末端执行器轨迹跟踪'); xlabel('时间 (s)'); ylabel('位置 (m)'); grid on; subplot(2,1,2); plot(t, vecnorm([x_d - x_act; y_d - y_act], 2, 1), 'LineWidth', 1.5); title('轨迹跟踪误差'); xlabel('时间 (s)'); ylabel('误差范数 (m)'); grid on; % 关节角度跟踪 figure('Name', '关节角度跟踪'); for j = 1:3 subplot(3,1,j); plot(t, q_ref(j,:), '--', 'LineWidth', 2); hold on; plot(t, q(j,:), '-', 'LineWidth', 1.5); title(sprintf('关节%d角度跟踪', j)); xlabel('时间 (s)'); ylabel('角度 (rad)'); legend('参考', '实际'); grid on; end % 机械臂运动动画 animate_robot(q, l1, l2, l3, x_d, y_d, dt); %% ========== 关键函数定义 ========== % 正运动学函数 function [x, y, z] = fkine_3dof(q, l1, l2, l3) q1 = q(1); q2 = q(2); q3 = q(3); x = l1*cos(q1) + l2*cos(q1+q2) + l3*cos(q1+q2+q3); y = l1*sin(q1) + l2*sin(q1+q2) + l3*sin(q1+q2+q3); z = 0; % 平面机械臂 end % 逆运动学函数（迭代算法 - 雅可比转置法） function q = ikine_3dof(target_pos, l1, l2, l3) max_iter = 100; tol = 1e-4; alpha = 0.1; % 步长因子 % 初始猜测（选择合理的初始角度） q = [pi/4; pi/3; -pi/6]; for k = 1:max_iter % 计算当前正运动学 [x, y, ~] = fkine_3dof(q, l1, l2, l3); current_pos = [x; y]; % 计算误差 e = target_pos(1:2)' - current_pos; % 检查收敛 if norm(e) < tol break; end % 计算雅可比矩阵（数值方法） J = jacobian_3dof(q, l1, l2, l3); % 雅可比转置法更新 dq = alpha * J' * e; q = q + dq; % 关节限位 q = wrapToPi(q); % 角度保持在[-pi, pi] end end % 雅可比矩阵计算（解析法） function J = jacobian_3dof(q, l1, l2, l3) q1 = q(1); q2 = q(2); q3 = q(3); % 平面机械臂的2×3雅可比矩阵 J = [-l1*sin(q1)-l2*sin(q1+q2)-l3*sin(q1+q2+q3), -l2*sin(q1+q2)-l3*sin(q1+q2+q3), -l3*sin(q1+q2+q3); l1*cos(q1)+l2*cos(q1+q2)+l3*cos(q1+q2+q3), l2*cos(q1+q2)+l3*cos(q1+q2+q3), l3*cos(q1+q2+q3)]; end % 机械臂动画函数 %% 修改后的机械臂动画函数 - 添加dt作为输入参数 function animate_robot(q, l1, l2, l3, x_d, y_d, dt) % 添加dt参数 figure('Name', '机械臂运动动画'); % 绘制期望轨迹 plot(x_d, y_d, 'b--', 'LineWidth', 1.5); hold on; axis equal; grid on; xlabel('X (m)'); ylabel('Y (m)'); title('三关节机械臂轨迹跟踪动画'); % 设置坐标轴范围 x_range = [min(x_d)-0.5, max(x_d)+0.5]; y_range = [min(y_d)-0.5, max(y_d)+0.5]; axis([x_range, y_range]); % 动画循环 for i = 1:10:size(q,2) % 跳帧显示 % 计算各关节位置 q1 = q(1,i); q2 = q(2,i); q3 = q(3,i); % 关节0位置（基座） p0 = [0; 0]; % 关节1位置 p1 = [l1*cos(q1); l1*sin(q1)]; % 关节2位置 p2 = p1 + [l2*cos(q1+q2); l2*sin(q1+q2)]; % 末端位置 p3 = p2 + [l3*cos(q1+q2+q3); l3*sin(q1+q2+q3)]; % 绘制机械臂 cla; plot(x_d, y_d, 'b--', 'LineWidth', 1.5); hold on; plot(p3(1), p3(2), 'ro', 'MarkerSize', 8, 'MarkerFaceColor', 'r'); % 绘制连杆 plot([p0(1), p1(1)], [p0(2), p1(2)], 'k-o', 'LineWidth', 2, 'MarkerSize', 6); plot([p1(1), p2(1)], [p1(2), p2(2)], 'k-o', 'LineWidth', 2, 'MarkerSize', 6); plot([p2(1), p3(1)], [p2(2), p3(2)], 'k-o', 'LineWidth', 2, 'MarkerSize', 6); % 添加当前时间信息 text(x_range(1)+0.1, y_range(2)-0.1, sprintf('时间: %.2f s', (i-1)*dt)); drawnow; end end 将上面的轨迹改为三次多项式轨迹，其他要求不变
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对于点到点的运动，假设起始时刻$t_0=0$，终止时刻$t_f$，给定：起始位置：$q(0)=q_0$，起始速度：$\dot{q}(0)=v_0$终止位置：$q(t_f)=q_f$，终止速度：$\dot{q}(t_f)=v_f$则可以得到方程组：$$q_0=a_0$$$$v_0=a_1$$...
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Will need to set environment variables as * appropriate. * Parameters: client socket descriptor * path to the CGI script */ /**********************************************************************/ void execute_cgi(int client, const char *path, const char *method, const char *query_string) { // 缓冲区 char buf[1024]; int cgi_output[2]; int cgi_input[2]; pid_t pid; int status; int i = 0; char c; int numchars = 1; int content_length = -1; // 默认字符 buf[0] = 'A'; buf[1] = '\0'; // 忽略大小写比较字符串 if (strcasecmp(method, "GET") == 0) while ((numchars > 0) && strcmp("\n", buf)) /* read & discard headers */ numchars = get_line(client, buf, sizeof(buf)); else /* POST */ { numchars = get_line(client, buf, sizeof(buf)); while ((numchars > 0) && strcmp("\n", buf)) { // 如果是POST请求，就需要得到Content-Length，Content-Length：这个字符串一共长为15位，所以 // 取出头部一句后，将第16位设置结束符，进行比较 // 第16位置为结束 buf[15] = '\0'; if (strcasecmp(buf, "Content-Length:") == 0) // 内存从第17位开始就是长度，将17位开始的所有字符串转成整数就是content_length content_length = atoi(&(buf[16])); numchars = get_line(client, buf, sizeof(buf)); } if (content_length == -1) { bad_request(client); return; } } sprintf(buf, "HTTP/1.0 200 OK\r\n"); send(client, buf, strlen(buf), 0); // 建立output管道 if (pipe(cgi_output) < 0) { cannot_execute(client); return; } // 建立input管道 if (pipe(cgi_input) < 0) { cannot_execute(client); return; } if ((pid = fork()) < 0) { cannot_execute(client); return; } if (pid == 0) /* child: CGI script */ { char meth_env[255]; char query_env[255]; char length_env[255]; // 子进程输出重定向到output管道的1端 dup2(cgi_output[1], 1); // 子进程输入重定向到input管道的0端 dup2(cgi_input[0], 0); // 关闭无用管道口 close(cgi_output[0]); close(cgi_input[1]); // CGI环境变量 sprintf(meth_env, "REQUEST_METHOD=%s", method); putenv(meth_env); if (strcasecmp(method, "GET") == 0) { sprintf(query_env, "QUERY_STRING=%s", query_string); putenv(query_env); } else { /* POST */ sprintf(length_env, "CONTENT_LENGTH=%d", content_length); putenv(length_env); } // 替换执行path execl(path, path, NULL); // int m = execl(path, path, NULL); // 如果path有问题，例如将html网页改成可执行的，但是执行后m为-1 // 退出子进程，管道被破坏，但是父进程还在往里面写东西，触发Program received signal SIGPIPE, Broken pipe. exit(0); } else { /* parent */ close(cgi_output[1]); close(cgi_input[0]); if (strcasecmp(method, "POST") == 0) for (i = 0; i < content_length; i++) { recv(client, &c, 1, 0); ssize_t bytes_written = write(cgi_input[1], &c, 1); if (bytes_written <= 0) { // 错误处理 perror("Failed to write to CGI"); close(cgi_input[1]); close(cgi_input[0]); break; } } // 从output管道读到子进程处理后的信息，然后send出去 while (read(cgi_output[0], &c, 1) > 0) send(client, &c, 1, 0); // 完成操作后关闭管道 close(cgi_output[0]); close(cgi_input[1]); // 等待子进程返回 waitpid(pid, &status, 0); } } /**********************************************************************/ /* Get a line from a socket, whether the line ends in a newline, * carriage return, or a CRLF combination. Terminates the string read * with a null character. If no newline indicator is found before the * end of the buffer, the string is terminated with a null. If any of * the above three line terminators is read, the last character of the * string will be a linefeed and the string will be terminated with a * null character. * Parameters: the socket descriptor * the buffer to save the data in * the size of the buffer * Returns: the number of bytes stored (excluding null) */ /**********************************************************************/ // 得到一行数据,只要发现c为\n,就认为是一行结束，如果读到\r,再用MSG_PEEK的方式读入一个字符，如果是\n，从socket用读出 // 如果是下个字符则不处理，将c置为\n，结束。如果读到的数据为0中断，或者小于0，也视为结束，c置为\n int get_line(int sock, char *buf, int size) { int i = 0; char c = '\0'; int n; while ((i < size - 1) && (c != '\n')) { n = recv(sock, &c, 1, 0); /* DEBUG printf("%02X\n", c); */ if (n > 0) { if (c == '\r') { // 偷窥一个字节，如果是\n就读走 n = recv(sock, &c, 1, MSG_PEEK); /* DEBUG printf("%02X\n", c); */ if ((n > 0) && (c == '\n')) recv(sock, &c, 1, 0); else // 不是\n（读到下一行的字符）或者没读到，置c为\n 跳出循环,完成一行读取 c = '\n'; } buf[i] = c; i++; } else c = '\n'; } buf[i] = '\0'; return (i); } /**********************************************************************/ /* Return the informational HTTP headers about a file. */ /* Parameters: the socket to print the headers on * the name of the file */ /**********************************************************************/ // 加入http的headers const char *get_content_type(const char *path) { const char *ext = strrchr(path, '.'); if (ext) { if (strcasecmp(ext, ".css") == 0) return "text/css"; if (strcasecmp(ext, ".js") == 0) return "application/javascript"; if (strcasecmp(ext, ".png") == 0) return "image/png"; if (strcasecmp(ext, ".jpg") == 0 || strcasecmp(ext, ".jpeg") == 0) return "image/jpeg"; if (strcasecmp(ext, ".gif") == 0) return "image/gif"; if (strcasecmp(ext, ".ico") == 0) return "image/x-icon"; if (strcasecmp(ext, ".svg") == 0) return "image/svg+xml"; if (strcasecmp(ext, ".woff") == 0) return "font/woff"; if (strcasecmp(ext, ".woff2") == 0) return "font/woff2"; } return "text/html"; } /*! * @brief * * @param[in] client Comment * @param[in] filename Comment */ void headers(int client, const char *filename) { char buf[1024]; const char *content_type = get_content_type(filename); sprintf(buf, "HTTP/1.0 200 OK\r\n"); send(client, buf, strlen(buf), 0); sprintf(buf, SERVER_STRING); send(client, buf, strlen(buf), 0); sprintf(buf, "Content-Type: %s\r\n", content_type); send(client, buf, strlen(buf), 0); sprintf(buf, "\r\n"); send(client, buf, strlen(buf), 0); } /*! * @brief * * @param[in] client Comment */ void not_found(int client) { char buf[1024]; sprintf(buf, "HTTP/1.0 404 NOT FOUND\r\n"); send(client, buf, strlen(buf), 0); sprintf(buf, SERVER_STRING); send(client, buf, strlen(buf), 0); sprintf(buf, "Content-Type: text/html\r\n"); send(client, buf, strlen(buf), 0); sprintf(buf, "\r\n"); send(client, buf, strlen(buf), 0); sprintf(buf, "<HTML><TITLE>Not Found</TITLE>\r\n"); send(client, buf, strlen(buf), 0); sprintf(buf, "<BODY><P>The server could not fulfill\r\n"); send(client, buf, strlen(buf), 0); sprintf(buf, "your request because the resource specified\r\n"); send(client, buf, strlen(buf), 0); sprintf(buf, "is unavailable or nonexistent.\r\n"); send(client, buf, strlen(buf), 0); sprintf(buf, "</BODY></HTML>\r\n"); send(client, buf, strlen(buf), 0); } /**********************************************************************/ /* Send a regular file to the client. Use headers, and report * errors to client if they occur. * Parameters: a pointer to a file structure produced from the socket * file descriptor * the name of the file to serve */ /**********************************************************************/ /*! * @brief 如果不是CGI文件，直接读取文件返回给请求的http客户端 * * @param[in] client Comment * @param[in] filename Comment */ void serve_file(int client, const char *filename) { FILE *resource = NULL; int numchars = 1; char buf[1024]; // 默认字符 buf[0] = 'A'; buf[1] = '\0'; while ((numchars > 0) && strcmp("\n", buf)) /* read & discard headers */ { numchars = get_line(client, buf, sizeof(buf)); } resource = fopen(filename, "rb"); printf("Serving file: %s\n", filename); if (resource == NULL) { not_found(client); } else { headers(client, filename); cat(client, resource); } fclose(resource); } /**********************************************************************/ /* This function starts the process of listening for web connections * on a specified port. If the port is 0, then dynamically allocate a * port and modify the original port variable to reflect the actual * port. * Parameters: pointer to variable containing the port to connect on * Returns: the socket */ /**********************************************************************/ int startup(u_short *port) { int httpd = 0; struct sockaddr_in name; httpd = socket(PF_INET, SOCK_STREAM, 0); if (httpd == -1) { error_die("socket"); } memset(&name, 0, sizeof(name)); name.sin_family = AF_INET; name.sin_port = htons(*port); name.sin_addr.s_addr = htonl(INADDR_ANY); // 绑定socket if (bind(httpd, (struct sockaddr *)&name, sizeof(name)) < 0) { error_die("bind"); } // 如果端口没有设置，提供个随机端口 if (*port == 0) /* if dynamically allocating a port */ { socklen_t namelen = sizeof(name); if (getsockname(httpd, (struct sockaddr *)&name, &namelen) == -1) { error_die("getsockname"); } *port = ntohs(name.sin_port); } // 监听 if (listen(httpd, 5) < 0) error_die("listen"); return (httpd); } /**********************************************************************/ /* Inform the client that the requested web method has not been * implemented. * Parameter: the client socket */ /**********************************************************************/ // 如果方法没有实现，就返回此信息 void unimplemented(int client) { char buf[1024]; sprintf(buf, "HTTP/1.0 501 Method Not Implemented\r\n"); send(client, buf, strlen(buf), 0); sprintf(buf, SERVER_STRING); send(client, buf, strlen(buf), 0); sprintf(buf, "Content-Type: text/html\r\n"); send(client, buf, strlen(buf), 0); sprintf(buf, "\r\n"); send(client, buf, strlen(buf), 0); sprintf(buf, "<HTML><HEAD><TITLE>Method Not Implemented\r\n"); send(client, buf, strlen(buf), 0); sprintf(buf, "</TITLE></HEAD>\r\n"); send(client, buf, strlen(buf), 0); sprintf(buf, "<BODY><P>HTTP request method not supported.\r\n"); send(client, buf, strlen(buf), 0); sprintf(buf, "</BODY></HTML>\r\n"); send(client, buf, strlen(buf), 0); } /**********************************************************************/ int main(void) { int server_sock = -1; u_short port = 80; int client_sock = -1; struct sockaddr_in client_name; // 这边要为socklen_t类型 socklen_t client_name_len = sizeof(client_name); pthread_t newthread; server_sock = startup(&port); printf("httpd running on port %d\n", port); while (1) { client_sock = accept(server_sock, (struct sockaddr *)&client_name, &client_name_len); if (client_sock == -1) { error_die("accept"); } // 每次收到请求，创建一个线程来处理接受到的请求 // 把client_sock转成地址作为参数传入pthread_create if (pthread_create(&newthread, NULL, (void *)accept_request, (void *)(intptr_t)client_sock) != 0) { perror("pthread_create"); } } close(server_sock); return (0); } 修改代码实现以多线程方式实现web server功能(必修)
最新发布
08-08
*q++ = *p++; } } *q = '\0'; } // 忽略SIGPIPE信号处理 void handle_sigpipe(int sig) { // 忽略SIGPIPE信号，防止写操作导致进程终止 } // 创建线程池 ThreadPool* create_thread_pool(int size) { ...
% meshfree_vibration_analysis.m % Free vibration analysis of laminated closed conical/cylindrical shells and annular plates % using TRPIM meshfree strong-form method (FSDT) in MATLAB % pinv clear; clc; close all; %% 1. Parameters % Geometry R1 = 1.0; % base radius L = 4.0; % axial length h = 0.1; % thickness phiSpan = 3/2*pi; % circumferential span (full shell) % Material (orthotropic laminate) E1 = 150e9; E2 = 10e9; mu12 = 0.25; rho = 1500; G12 = 5e9; G13 = 5e9; G23 = 6e9; ks = 5/6; layup = [0,90,0]; % fiber angles [deg] Nk = numel(layup); % Discretization nx = 16; ntheta = 16; % nodes in x and theta directions dist_func = @(a,b,n) 0.5*( (b-a)*(1 - cos(pi*(0:n-1)/(n-1))) ) + a; % 'gauss_lobatto' % dist_func = @(a,b,n) (0:n-1).^2 / (n-1)^2 * (b - a) + a; % 平方渐变示例 X=linspace(0,L,nx); T=linspace(0,phiSpan,ntheta); % T=linspace(0,phiSpan,ntheta+1); T(end)=[]; [xg, tg] = meshgrid(X,T); yg = R1 * cos(tg); zg = R1 * sin(tg); nnodes = [xg(:), yg(:), zg(:), tg(:)]; nodes = [xg(:), tg(:)]; N = size(nodes,1); % TRIPM settings rbf_type = 'MQ'; % 'MQ','EXP','TPS' dc = 2*(L/(nx-1)+phiSpan/(ntheta-1))/2; % characteristic length q = 1.03; % MQ exponent\meta = 2; % TPS exponent mp=0; mq=0; m = mp*mq; % Tchebychev polynomial total order bc_type='C'; % Support domain: K-nearest neighbors ns = 25; % support size idxNN = knnsearch(nnodes(:,1:3),nnodes(:,1:3),'K',ns); % in=nnodes(idxNN(1,:),:); % f1=draw_shell(in); f=draw_shell(nnodes); hold on surf(xg,yg,zg, 'FaceAlpha',0.3, 'EdgeColor','none'); % 标记目标点（红色） target_idx = 1; scatter3(nnodes(target_idx,1), nnodes(target_idx,2), nnodes(target_idx,3), ... 100, [0 0 0], 'filled', 'MarkerFaceAlpha',0.8) % 绘制欧氏距离邻居（蓝色线段） for i = 1:ns scatter3(nnodes(idxNN(target_idx,i),1), nnodes(idxNN(target_idx,i),2), nnodes(idxNN(target_idx,i),3), ... 100, [1 0.3 0.3], 'filled', 'MarkerFaceAlpha',0.8) plot3([nnodes(target_idx,1) nnodes(idxNN(target_idx,i),1)], ... [nnodes(target_idx,2) nnodes(idxNN(target_idx,i),2)], ... [nnodes(target_idx,3) nnodes(idxNN(target_idx,i),3)], ... 'b-', 'LineWidth',0.8, 'Color',[1 0.6 0]) end %% 2. Precompute basis matrices (G matrix inverse) for each node Ginv = cell(N,1); supp = cell(N,1); for i = 1:N Xi = nodes(i,1); Ti = nodes(i,2); nbr = idxNN(i,:); supp{i} = nbr; % build R0 and Tm at support nodes Xs = nodes(nbr,1); Ts = nodes(nbr,2); % compute pairwise radial basis R0 = zeros(ns); for a=1:ns for b=1:ns % Tab(a,b)=Ts(a)-Ts(b); % Tan1=wrapToPi(Tab); % rab = sqrt((Xs(a)-Xs(b))^2 - R1^2*(2*cos(Ts(a) - Ts(b))-2)); rab = sqrt((Xs(a)-Xs(b))^2 + (R1*wrapToPi(Ts(a)-Ts(b)))^2); R0(a,b) = radialRB(rab, rbf_type, dc, q); end end % Tchebychev basis at support nodes xp = 2*(Xs - 0)/L - 1; tp = 2*(Ts - 0)/phiSpan - 1; Tm = tchebyBasis(xp,tp,mp,mq); % assemble G G = [R0, Tm; Tm', zeros(size(Tm,2))]; % fprintf('cond(G) = %g\n', cond(G)); % %给 G 矩阵加正则化,加一点微小阻尼 % epsReg = 1e-8 * max(abs(diag(G))); % G = G + eye(size(G)) * epsReg; Ginv{i} = inv(G); % [U,S,V] = svd(G); % s = diag(S); % tol = max(size(G)) * eps(max(s)); % s_inv = s; % s_inv(s > tol) = 1./s(s > tol); % Ginv{i} = V * diag(s_inv) * U'; end %% 3. Collocation: assemble global K and M ndof = 5; totalDOF = ndof*N; K = sparse(totalDOF,totalDOF); M = sparse(totalDOF,totalDOF); % material stiffness matrices A,B,D and transverse shear [A,B,D_mat,As,I] = laminateABD(layup,E1,E2,mu12,G12,G13,G23,h,rho,ks); Dstruct = [A,B,zeros(3,2);B,D_mat,zeros(3,2);zeros(2,6),As]; Phi=cell(N,1); for i = 1:N % evaluation at node i Xi = nodes(i,1); Ti = nodes(i,2); nbr = supp{i}; nn = numel(nbr); % compute shape function and derivatives at eval point Phi{i} = computeShape(nodes(nbr,:), [Xi,Ti], Ginv{i}, rbf_type, dc, q, mp,mq, L, phiSpan, R1); % local stiffness and mass kernels [Ki_cell, Mi_cell] = localKM(Phi{i}, A, B, D_mat, As, R1, I(1), I(2), I(3)); % assemble rows = (i-1)*ndof + (1:ndof); for k = 1:nn col = (nbr(k)-1)*ndof + (1:ndof); K(rows,col) = K(rows,col) + Ki_cell(:,:,k); M(rows,col) = M(rows,col) + Mi_cell(:,:,k); end end figure; subplot(1,2,1); spy(K); subplot(1,2,2); spy(M); %可视化稀疏结构，排查是否有整行全为0 %% 4. Apply boundary springs (clamped, simply supported, free as in Table 1) [K,M]=springBC(A,B,D_mat,As,R1,K, M, nodes, ndof,bc_type,Phi,supp); %% 5. Solve eigenproblem eigMode = 20; % opts.issym = 1; opts.isreal=1; [V,D] = eigs(K,M,eigMode,'SM'); freq = sqrt(diag(D))/(2*pi); [~, idx] = sort(freq); freq = freq(idx); V = V(:, idx); % % 过滤非物理解 % valid_idx = imag(freq) == 0 & freq > 0 & freq < 1e10; % freq = freq(valid_idx); % V = V(:, valid_idx); disp('Natural frequencies (Hz):'); disp(freq); %% --- Functions --- function Rb = radialRB(r, type, dc, q) switch type case 'MQ', Rb = (r^2 + dc^2)^q; end end function Tm = tchebyBasis(xp,tp,mp,mq) m=mp*mq; if m==0 Tm=[]; else Tm = zeros(length(xp),m); for i=1:length(xp) x=xp(i); t=tp(i); Te = zeros(1,m); % 计算二维切比雪夫基 for P=0:mp-1 for Q=0:mq-1 PQ=P*mq+Q+1; Te(PQ)=cos(Q*acos(t))*cos(P*acos(x)); end end Tm(i,:)=Te; end end end function Phi = computeShape(suppCoord, evalCoord, Ginv, rbf_type, dc, q, mp,mq, L, phiSpan, R) nn = size(suppCoord,1); % distances & derivatives at eval Re = zeros(1,nn); dRe_x=zeros(1,nn); dRe_t=zeros(1,nn); dRe_xx=zeros(1,nn); dRe_xt=zeros(1,nn); dRe_tt=zeros(1,nn); for i=1:nn dx = evalCoord(1)-suppCoord(i,1); % dt = evalCoord(2)-suppCoord(i,2); % r = sqrt(dx^2 - R^2*(2*cos(dt)-2)); dt = wrapToPi((evalCoord(2)-suppCoord(i,2))); r = sqrt(dx^2 + dt^2*R^2); switch rbf_type case 'MQ' % Re(i) = (r^2 + dc^2)^q; % dRe_x(i) = 2*q*(r^2 + dc^2)^(q-1)*dx; % dRe_t(i) = 2*q*(r^2 + dc^2)^(q-1)*R^2*sin(dt); % dRe_xx(i) = 2*q*(r^2 + dc^2)^(q-1) + 4*(q-1)*q*dx^2*(r^2 + dc^2)^(q-2); % dRe_xt(i) = 4*(q-1)*q*dx*R^2*sin(dt)*(r^2 + dc^2)^(q-2); % dRe_tt(i) = 2*q*(r^2 + dc^2)^(q-1)*R^2*cos(dt)+ 4*q*(q-1)*R^4*(sin(dt))^2*(r^2 + dc^2)^(q-2); Re(i) = (r^2 + dc^2)^q; dRe_x(i) = 2*q*(r^2 + dc^2)^(q-1)*dx; dRe_t(i) = 2*q*(r^2 + dc^2)^(q-1)*R^2*dt; dRe_xx(i) = 2*q*(r^2 + dc^2)^(q-1) + 4*(q-1)*q*dx^2*(r^2 + dc^2)^(q-2); dRe_xt(i) = 4*(q-1)*q*dx*R^2*dt*(r^2 + dc^2)^(q-2); dRe_tt(i) = 2*q*(r^2 + dc^2)^(q-1)*R^2+ 4*q*(q-1)*R^4*dt^2*(r^2 + dc^2)^(q-2); end end % Tcheby at eval x = 2*(evalCoord(1)-0)/L -1; t = 2*(evalCoord(2)-0)/phiSpan -1; m=mp*mq; Te = zeros(1,m); dTe_x=zeros(1,m); dTe_t=zeros(1,m); dTe_xx=zeros(1,m); dTe_xt=zeros(1,m); dTe_tt=zeros(1,m); % 计算切比雪夫多项式 [Tx, dTx_norm, d2Tx_norm] = chebyshevT_derivatives(0:mp-1, x); [Ty, dTy_norm, d2Ty_norm] = chebyshevT_derivatives(0:mq-1, t); % 应用坐标变换的导数修正 dTx = dTx_norm * 2/L; d2Tx = d2Tx_norm * (2/L)^2; dTy = dTy_norm * 2/phiSpan; d2Ty = d2Ty_norm * (2/phiSpan)^2; % 计算二维切比雪夫基 idx=1; for P=1:mp for Q=1:mq Te(idx)= Tx(P)*Ty(Q); dTe_x(idx)= dTx(P)*Ty(Q); dTe_t(idx)= Tx(P)*dTy(Q); dTe_xx(idx)= d2Tx(P)*Ty(Q); dTe_xt(idx)= dTx(P)*dTy(Q); dTe_tt(idx)= Tx(P)*d2Ty(Q); idx = idx + 1; end end % assemble Phi at eval % Phi_bar(1,:) = round([Re,Te]*Ginv,5); Phi_bar(1,:) = [Re,Te]*Ginv; Phi_bar(2,:) = [dRe_x,dTe_x]*Ginv; Phi_bar(3,:) = [dRe_t,dTe_t]*Ginv; Phi_bar(4,:) = [dRe_xx,dTe_xx]*Ginv; Phi_bar(5,:) = [dRe_xt,dTe_xt]*Ginv; Phi_bar(6,:) = [dRe_tt,dTe_tt]*Ginv; Phi=Phi_bar(:,1:nn); end function [T, dT, d2T] = chebyshevT_derivatives(n, x) % 计算切比雪夫多项式 T_n(x) 及其一阶、二阶导数 x = x(:); % 转换为列向量 T = zeros(length(x), length(n)); dT = zeros(length(x), length(n)); d2T = zeros(length(x), length(n)); for i = 1:length(n) order = n(i); if order == 0 T(:,i) = ones(size(x)); dT(:,i) = zeros(size(x)); d2T(:,i) = zeros(size(x)); elseif order == 1 T(:,i) = x; dT(:,i) = ones(size(x)); d2T(:,i) = zeros(size(x)); else % 初始化递推 T0 = ones(size(x)); T1 = x; dT0 = zeros(size(x)); dT1 = ones(size(x)); d2T0 = zeros(size(x)); d2T1 = zeros(size(x)); % 递推计算 for k = 2:order T2 = 2*x.*T1 - T0; dT2 = 2*T1 + 2*x.*dT1 - dT0; d2T2 = 4*dT1 + 2*x.*d2T1 - d2T0; % 更新 T0 = T1; T1 = T2; dT0 = dT1; dT1 = dT2; d2T0 = d2T1; d2T1 = d2T2; end T(:,i) = T1; dT(:,i) = dT1; d2T(:,i) = d2T1; end end end function [Ki,Mi] = localKM(Phi, A, B, D, As, R, I0, I1, I2) ndof=5; nn=size(Phi,2); Ki = zeros(ndof,ndof,nn); Mi = zeros(ndof,ndof,nn); for j=1:nn phi=Phi(1,j); dphidx=Phi(2,j); dphidt=Phi(3,j); dphidxx=Phi(4,j); dphidxt=Phi(5,j); dphidtt=Phi(6,j); % K Tn11 = A(1,1) * dphidxx + (A(3,3)/R^2) * dphidtt + (2*A(1,3)/R) * dphidxt; Tn12 = A(1,3) * dphidxx + (A(1,2)/R) * dphidxt + (A(3,3)/R) * dphidxt + (A(2,3)/R^2) * dphidtt; Tn13 = (A(1,2)/R) * dphidx + (A(2,3)/R^2) * dphidt; Tn14 = B(1,1) * dphidxx + (2*B(1,3)/R) * dphidxt + (B(3,3)/R^2) * dphidtt; Tn15 = B(1,3) * dphidxx + (B(1,2)/R) * dphidxt + (B(3,3)/R) * dphidxt + (B(2,3)/R^2) * dphidtt; Tn21 = Tn12; Tn22 = A(3,3) * dphidxx + (A(2,2)/R^2) * dphidtt + (2*A(2,3)/R) * dphidxt - (As(1,1)/R^2) * phi; Tn23 = (A(2,3)/R) * dphidx + (A(2,2)/R^2) * dphidt + (As(1,2)/R) * dphidx + (As(1,1)/R^2) * dphidt; Tn24 = B(1,3) * dphidxx + (B(1,2)/R) * dphidxt + (B(3,3)/R) * dphidxt + (B(2,3)/R^2) * dphidtt + (As(1,2)/R) * phi; Tn25 = B(3,3) * dphidxx + (2*B(2,3)/R) * dphidxt + (B(2,2)/R^2) * dphidtt + (As(1,1)/R) * phi; Tn31 = -Tn13; Tn32 = -Tn23; Tn33 = As(2,2) * dphidxx - (A(2,2)/R^2) * phi + (As(1,1)/R^2) * dphidtt + (2*As(1,2)/R) * dphidxt; Tn34 = As(2,2) * dphidx - (B(1,2)/R) * dphidx - (B(2,3)/R^2) * dphidt + (As(1,2)/R) * dphidt; Tn35 = As(1,2) * dphidx - (B(2,3)/R) * dphidx - (B(2,2)/R^2) * dphidt + (As(1,1)/R) * dphidt; Tn41 = Tn14; Tn42 = Tn24; Tn43 = -Tn34; Tn44 = D(1,1) * dphidxx - As(2,2) * phi + (D(3,3)/R^2) * dphidtt + (2*D(1,3)/R) * dphidxt; Tn45 = D(1,3) * dphidxx + (D(1,2)/R) * dphidxt + (D(3,3)/R) * dphidxt + (D(2,3)/R^2) * dphidtt - As(1,2) * phi; Tn51 = Tn15; Tn52 = Tn25; Tn53 = -Tn35; Tn54 = Tn45; Tn55 = D(3,3) * dphidxx - As(1,1) * phi + (D(2,2)/R^2) * dphidtt + (2*D(2,3)/R) * dphidxt; Kij= [Tn11, Tn12, Tn13, Tn14, Tn15; Tn21, Tn22, Tn23, Tn24, Tn25; Tn31, Tn32, Tn33, Tn34, Tn35; Tn41, Tn42, Tn43, Tn44, Tn45; Tn51, Tn52, Tn53, Tn54, Tn55]; Ki(:,:,j)=Kij; % M Mij= -[I0*phi,0,0,I1*phi,0; 0,I0*phi,0,0,I1*phi; 0,0,I0*phi,0,0; I1*phi,0,0,I2*phi,0; 0,I1*phi,0,0,I2*phi]; Mi(:,:,j)=Mij; end end function [K,M]=springBC(A,B,D,As,R,K,M,nodes,ndof,bc_type,allPhi,supp) % Example: clamp x=0 and x=L, free elsewhere switch bc_type case 'F' %自由 ku=0;kv=0;kw=0;kx=0;kt=0; case 'S' %简支 ku=10^14;kv=10^14;kw=10^14;kx=0;kt=10^14; case 'SD' %弹性简支 ku=0;kv=10^14;kw=10^14;kx=0;kt=0; case 'C' %固支 ku=10^14;kv=10^14;kw=10^14;kx=10^14;kt=10^14; case 'E' %任意弹性 ku=10^7;kv=10^14;kw=10^14;kx=10^14;kt=10^14; end tol = 1e-8; N = size(nodes,1); for i=1:N Phi=allPhi{i}; phi=Phi(1,:); dphidx=Phi(2,:); dphidt=Phi(3,:); x = nodes(i,1); t = nodes(i,2); indices=supp{i}; nn=length(indices); if abs(x)<tol for j=1:nn Cxn=calculate_Cxn(A,B,D,As,R,phi(j),dphidx(j),dphidt(j)); k_spring=blkdiag(ku,kv,kw,kx,kt)* phi(j); dofl = (indices(j)-1)*ndof+1:indices(j)*ndof; dofh = (i-1)*ndof+1:i*ndof; K(dofh,dofl)=0; M(dofh,dofl)=0; K(dofh,dofl)=Cxn-k_spring; end elseif abs(x- max(nodes(:,1)))<tol for j=1:nn Cxn=calculate_Cxn(A,B,D,As,R,phi(j),dphidx(j),dphidt(j)); k_spring=blkdiag(ku,kv,kw,kx,kt)* phi(j); dofl = (indices(j)-1)*ndof+1:indices(j)*ndof; dofh = (i-1)*ndof+1:i*ndof; K(dofh,dofl)=0; M(dofh,dofl)=0; K(dofh,dofl)=Cxn+k_spring; end elseif abs(t)<tol for j=1:nn Ctn=calculate_Ctn(A,B,D,As,R,phi(j),dphidx(j),dphidt(j)); k_spring=blkdiag(ku,kv,kw,kx,kt)* phi(j); dofl = (indices(j)-1)*ndof+1:indices(j)*ndof; dofh = (i-1)*ndof+1:i*ndof; K(dofh,dofl)=0; M(dofh,dofl)=0; K(dofh,dofl)=Ctn-k_spring; end elseif abs(t- max(nodes(:,2)))<tol for j=1:nn Ctn=calculate_Ctn(A,B,D,As,R,phi(j),dphidx(j),dphidt(j)); k_spring=blkdiag(ku,kv,kw,kx,kt)* phi(j); dofl = (indices(j)-1)*ndof+1:indices(j)*ndof; dofh = (i-1)*ndof+1:i*ndof; K(dofh,dofl)=0; M(dofh,dofl)=0; K(dofh,dofl)=Ctn+k_spring; end end end end function Cxn=calculate_Cxn(A,B,D,As,R,phi,dphidx,dphidt) Cxn11 = A(1,1) * dphidx + A(1,3)/R * dphidt; Cxn12 = A(1,3) * dphidx + A(1,2)/R * dphidt; Cxn13 = A(1,2)/R * phi; Cxn14 = B(1,1) * dphidx + B(1,3)/R * dphidt; Cxn15 = B(1,3) * dphidx + B(1,2)/R * dphidt; Cxn21 = A(1,3) * dphidx + A(3,3)/R * dphidt; Cxn22 = A(3,3) * dphidx + A(2,3)/R * dphidt; Cxn23 = A(2,3)/R * phi; Cxn24 = B(1,3) * dphidx + B(3,3)/R * dphidt; Cxn25 = B(3,3) * dphidx + B(2,3)/R * dphidt; Cxn31 = 0; Cxn32 = -As(1,2)/R * phi; Cxn33 = As(2,2) * dphidx + As(1,2)/R * dphidt; Cxn34 = As(2,2) * phi; Cxn35 = As(1,2) * phi; Cxn41 = Cxn14; Cxn42 = Cxn15; Cxn43 = B(1,2)/R * phi; Cxn44 = D(1,1) * dphidx + D(1,3)/R * dphidt; Cxn45 = D(1,3) * dphidx + D(1,2)/R * dphidt; Cxn51 = Cxn24; Cxn52 = Cxn25; Cxn53 = B(2,3)/R * phi; Cxn54 = D(1,3) * dphidx + D(3,3)/R * dphidt; Cxn55 = D(3,3) * dphidx + D(2,3)/R * dphidt; Cxn= [Cxn11, Cxn12, Cxn13, Cxn14, Cxn15; Cxn21, Cxn22, Cxn23, Cxn24, Cxn25; Cxn31, Cxn32, Cxn33, Cxn34, Cxn35; Cxn41, Cxn42, Cxn43, Cxn44, Cxn45; Cxn51, Cxn52, Cxn53, Cxn54, Cxn55]; end function Ctn=calculate_Ctn(A,B,D,As,R,phi,dphidx,dphidt) Ctn11 = A(1,3) * dphidx + A(3,3)/R * dphidt; Ctn12 = A(3,3) * dphidx + A(2,3)/R * dphidt; Ctn13 = A(2,3)/R * phi; Ctn14 = B(1,3) * dphidx + B(3,3)/R * dphidt; Ctn15 = B(3,3) * dphidx + B(2,3)/R * dphidt; Ctn21 = A(1,2) * dphidx + A(2,3)/R * dphidt; Ctn22 = A(2,3) * dphidx + A(2,2)/R * dphidt; Ctn23 = A(2,2)/R * phi; Ctn24 = B(1,2) * dphidx + B(2,3)/R * dphidt; Ctn25 = B(2,3) * dphidx + B(2,2)/R * dphidt; Ctn31 = 0; Ctn32 = -As(1,1)/R * phi; Ctn33 = As(1,2) * dphidx + As(1,1)/R * dphidt; Ctn34 = As(1,2) * phi; Ctn35 = As(1,1) * phi; Ctn41 = Ctn14; Ctn42 = Ctn15; Ctn43 = B(2,3)/R * phi; Ctn44 = D(1,3) * dphidx + D(3,3)/R * dphidt; Ctn45 = D(3,3) * dphidx + D(2,3)/R * dphidt; Ctn51 = Ctn24; Ctn52 = Ctn25; Ctn53 = B(2,2)/R * phi; Ctn54 = D(1,2) * dphidx + D(2,3)/R * dphidt; Ctn55 = D(2,3) * dphidx + D(2,2)/R * dphidt; Ctn= [Ctn11, Ctn12, Ctn13, Ctn14, Ctn15; Ctn21, Ctn22, Ctn23, Ctn24, Ctn25; Ctn31, Ctn32, Ctn33, Ctn34, Ctn35; Ctn41, Ctn42, Ctn43, Ctn44, Ctn45; Ctn51, Ctn52, Ctn53, Ctn54, Ctn55]; end function [A,B,D,As,I] = laminateABD(layup,E1,E2,mu12,G12,G13,G23,h,rho,ks) Nk = numel(layup); z = linspace(-h/2,h/2,Nk+1); A=zeros(3); B=zeros(3); D=zeros(3); As = zeros(2); I = [0, 0, 0]; for k=1:Nk th=layup(k)*pi/180; c=cos(th); s=sin(th); [Q,As0] = orthotropicQ(E1,E2,mu12,G12,G13,G23,ks); T = [c^2, s^2, -2*c*s; s^2, c^2, 2*c*s; c*s, -c*s, c^2-s^2]; Qbar = T*Q*T'; % transform Ts = [c, s; -s, c]; Asbar = Ts * As0 * Ts'; A = A + Qbar*(z(k+1)-z(k)); B = B + Qbar*(z(k+1)^2-z(k)^2)/2; D = D + Qbar*(z(k+1)^3-z(k)^3)/3; As = As + Asbar * (z(k+1) - z(k)); I = I + rho * [(z(k+1) - z(k)), (z(k+1)^2 - z(k)^2)/2, (z(k+1)^3 - z(k)^3)/3]; % A=round(A,5); % B=round(B,5); % D=round(D,5); % As=round(As,5); end end function [Q,As] = orthotropicQ(E1,E2,mu12,G12,G13,G23,ks) mu21 = E2*mu12/E1; Q = [E1/(1-mu12*mu21), mu12*E2/(1-mu12*mu21), 0; mu12*E2/(1-mu12*mu21), E2/(1-mu12*mu21), 0; 0,0,G12]; As = [ks*G23, 0; 0, ks*G13]; end function f=draw_shell(nodes) f=figure; % 生成示例数据 x = nodes(:,1); y = nodes(:,2); z = nodes(:,3); % 绘制三维点 scatter3(x, y, z, 'filled'); hold on; % 添加标题和坐标轴标签 title('三维点图'); xlabel('X轴'); ylabel('Y轴'); zlabel('Z轴'); % 设置坐标轴比例一致 axis equal; end 这是我的代码，你帮我分析分析
06-23
例如，对x的导数：`dRe_x(i)=2*q*(r^2+dc^2)^(q-1)*dx;`这是正确的（因为r关于x的导数是dx/r，再乘以rbf关于r的导数）。但是，注意在圆柱壳上，度量不是欧氏的，所以导数计算应考虑曲面度量。然而，代码中直接使用了...
function chladni_gui % 创建主窗口 fig = figure('Name', 'Chladni Lab：克拉尼图形仿真与波动可视化', 'NumberTitle', 'off', ... 'Position', [100, 100, 1200, 800], 'Color', [0.1, 0.1, 0.15]); % 预先计算贝塞尔函数零点表（用于圆形板） zeros_table = compute_bessel_zeros(0:20, 1:20); setappdata(fig, 'bessel_zeros', zeros_table); % 创建标签 uicontrol('Style', 'text', 'String', 'Chladni Lab', ... 'Position', [50, 750, 300, 40], 'FontSize', 24, ... 'ForegroundColor', [0.96, 0.4, 0.62], 'BackgroundColor', [0.1, 0.1, 0.15]); uicontrol('Style', 'text', 'String', '基于MATLAB的克拉尼图形仿真与波动可视化平台', ... 'Position', [350, 760, 500, 20], 'FontSize', 12, ... 'ForegroundColor', [0.7, 0.7, 0.9], 'BackgroundColor', [0.1, 0.1, 0.15]); % 创建图形显示区域 ax1 = axes('Parent', fig, 'Position', [0.05, 0.35, 0.45, 0.55], ... 'Color', [0.18, 0.18, 0.23]); title(ax1, '克拉尼图形仿真', 'Color', 'w', 'FontSize', 14); axis(ax1, 'equal'); grid(ax1, 'on'); set(ax1, 'XColor', [0.8, 0.8, 0.8], 'YColor', [0.8, 0.8, 0.8], ... 'GridColor', [0.4, 0.4, 0.4]); % 创建波动可视化区域 ax2 = axes('Parent', fig, 'Position', [0.55, 0.35, 0.45, 0.55], ... 'Color', [0.18, 0.18, 0.23]); title(ax2, '沙粒波动可视化', 'Color', 'w', 'FontSize', 14); axis(ax2, 'equal'); grid(ax2, 'on'); set(ax2, 'XColor', [0.8, 0.8, 0.8], 'YColor', [0.8, 0.8, 0.8], ... 'GridColor', [0.4, 0.4, 0.4]); % 创建控制面板 control_panel = uipanel('Title', '参数控制', 'FontSize', 11, 'ForegroundColor', 'w', ... 'BackgroundColor', [0.2, 0.2, 0.25], ... 'Position', [0.05, 0.05, 0.9, 0.25]); % 创建形状选择控件 uicontrol('Parent', control_panel, 'Style', 'text', 'String', '振动板形状:', ... 'Position', [20, 170, 100, 20], ... 'ForegroundColor', 'w', 'BackgroundColor', [0.2, 0.2, 0.25]); shape_popup = uicontrol('Parent', control_panel, 'Style', 'popupmenu', ... 'String', {'方形板', '圆形板', '三角形板'}, ... 'Position', [20, 150, 120, 20], ... 'Callback', @updatePlot); % 创建p滑块 uicontrol('Parent', control_panel, 'Style', 'text', 'String', 'p 值 (模态参数):', ... 'Position', [20, 120, 120, 20], ... 'ForegroundColor', 'w', 'BackgroundColor', [0.2, 0.2, 0.25]); p_slider = uicontrol('Parent', control_panel, 'Style', 'slider', 'Min', 0, 'Max', 20, 'Value', 3, ... 'Position', [20, 100, 120, 20], ... 'Callback', @updatePlot); p_text = uicontrol('Parent', control_panel, 'Style', 'text', 'String', '3', ... 'Position', [150, 100, 30, 20], ... 'ForegroundColor', 'w', 'BackgroundColor', [0.2, 0.2, 0.25]); % 创建q滑块 uicontrol('Parent', control_panel, 'Style', 'text', 'String', 'q 值 (模态参数):', ... 'Position', [20, 70, 120, 20], ... 'ForegroundColor', 'w', 'BackgroundColor', [0.2, 0.2, 0.25]); q_slider = uicontrol('Parent', control_panel, 'Style', 'slider', 'Min', 0, 'Max', 20, 'Value', 2, ... 'Position', [20, 50, 120, 20], ... 'Callback', @updatePlot); q_text = uicontrol('Parent', control_panel, 'Style', 'text', 'String', '2', ... 'Position', [150, 50, 30, 20], ... 'ForegroundColor', 'w', 'BackgroundColor', [0.2, 0.2, 0.25]); % 创建模式选择 uicontrol('Parent', control_panel, 'Style', 'text', 'String', '振动模式:', ... 'Position', [200, 170, 100, 20], ... 'ForegroundColor', 'w', 'BackgroundColor', [0.2, 0.2, 0.25]); mode_popup = uicontrol('Parent', control_panel, 'Style', 'popupmenu', ... 'String', {'对称模式', '反对称模式'}, ... 'Position', [200, 150, 120, 20], ... 'Callback', @updatePlot); % 创建网格分辨率控制 uicontrol('Parent', control_panel, 'Style', 'text', 'String', '网格分辨率:', ... 'Position', [200, 120, 120, 20], ... 'ForegroundColor', 'w', 'BackgroundColor', [0.2, 0.2, 0.25]); res_popup = uicontrol('Parent', control_panel, 'Style', 'popupmenu', ... 'String', {'低 (100x100)', '中 (200x200)', '高 (300x300)'}, ... 'Value', 2, ... 'Position', [200, 100, 120, 20], ... 'Callback', @updatePlot); % 创建频率显示 freq_text = uicontrol('Parent', control_panel, 'Style', 'text', 'String', '频率: 440 Hz', ... 'Position', [200, 50, 150, 30], ... 'FontSize', 12, 'ForegroundColor', [0.96, 0.4, 0.62], ... 'BackgroundColor', [0.2, 0.2, 0.25]); % 创建波动控制按钮 uicontrol('Parent', control_panel, 'Style', 'pushbutton', 'String', '开始波动仿真', ... 'Position', [350, 150, 120, 30], 'FontSize', 10, ... 'ForegroundColor', 'w', 'BackgroundColor', [0.2, 0.4, 0.6], ... 'Callback', @startWaveSimulation); uicontrol('Parent', control_panel, 'Style', 'pushbutton', 'String', '暂停/继续', ... 'Position', [350, 110, 120, 30], 'FontSize', 10, ... 'ForegroundColor', 'w', 'BackgroundColor', [0.4, 0.4, 0.6], ... 'Callback', @togglePause); uicontrol('Parent', control_panel, 'Style', 'pushbutton', 'String', '重置沙粒', ... 'Position', [350, 70, 120, 30], 'FontSize', 10, ... 'ForegroundColor', 'w', 'BackgroundColor', [0.6, 0.4, 0.4], ... 'Callback', @resetSandParticles); % 沙粒数量控制 uicontrol('Parent', control_panel, 'Style', 'text', 'String', '沙粒数量:', ... 'Position', [500, 170, 100, 20], ... 'ForegroundColor', 'w', 'BackgroundColor', [0.2, 0.2, 0.25]); sand_slider = uicontrol('Parent', control_panel, 'Style', 'slider', 'Min', 100, 'Max', 2000, ... 'Value', 800, 'Position', [500, 150, 150, 20]); sand_text = uicontrol('Parent', control_panel, 'Style', 'text', 'String', '800', ... 'Position', [660, 150, 50, 20], ... 'ForegroundColor', 'w', 'BackgroundColor', [0.2, 0.2, 0.25]); % 波动速度控制 uicontrol('Parent', control_panel, 'Style', 'text', 'String', '波动速度:', ... 'Position', [500, 120, 100, 20], ... 'ForegroundColor', 'w', 'BackgroundColor', [0.2, 0.2, 0.25]); speed_slider = uicontrol('Parent', control_panel, 'Style', 'slider', 'Min', 0.1, 'Max', 5, ... 'Value', 1.5, 'Position', [500, 100, 150, 20]); speed_text = uicontrol('Parent', control_panel, 'Style', 'text', 'String', '1.5', ... 'Position', [660, 100, 50, 20], ... 'ForegroundColor', 'w', 'BackgroundColor', [0.2, 0.2, 0.25]); % 阻尼系数控制 uicontrol('Parent', control_panel, 'Style', 'text', 'String', '阻尼系数:', ... 'Position', [500, 70, 100, 20], ... 'ForegroundColor', 'w', 'BackgroundColor', [0.2, 0.2, 0.25]); damping_slider = uicontrol('Parent', control_panel, 'Style', 'slider', 'Min', 0.01, 'Max', 0.2, ... 'Value', 0.08, 'Position', [500, 50, 150, 20]); damping_text = uicontrol('Parent', control_panel, 'Style', 'text', 'String', '0.08', ... 'Position', [660, 50, 50, 20], ... 'ForegroundColor', 'w', 'BackgroundColor', [0.2, 0.2, 0.25]); % 创建信息面板 info_panel = uipanel('Title', '物理信息', 'FontSize', 11, 'ForegroundColor', 'w', ... 'BackgroundColor', [0.2, 0.2, 0.25], ... 'Position', [0.05, 0.01, 0.9, 0.03]); info_text = uicontrol('Parent', info_panel, 'Style', 'text', ... 'String', 'Chladni图案展示振动板在不同频率下的驻波节点分布。波动可视化模拟沙粒在振动板上的运动过程。', ... 'Position', [10, 5, 1080, 20], ... 'HorizontalAlignment', 'left', ... 'ForegroundColor', [0.8, 0.8, 0.9], ... 'BackgroundColor', [0.2, 0.2, 0.25], ... 'FontSize', 10); % 存储GUI句柄 handles = struct('ax1', ax1, 'ax2', ax2, 'p_slider', p_slider, 'q_slider', q_slider, ... 'p_text', p_text, 'q_text', q_text, ... 'mode_popup', mode_popup, 'res_popup', res_popup, ... 'freq_text', freq_text, 'info_text', info_text, ... 'shape_popup', shape_popup, 'sand_slider', sand_slider, ... 'sand_text', sand_text, 'speed_slider', speed_slider, ... 'speed_text', speed_text, 'damping_slider', damping_slider, ... 'damping_text', damping_text); % 初始化沙粒数据 sand_data = struct('particles', [], 'velocities', [], 'isSimulating', false, ... 'isPaused', false, 't', 0, 'Z', []); guidata(fig, handles); setappdata(fig, 'sand_data', sand_data); % 初始绘图 updatePlot(); % 更新滑块文本的回调 set(p_slider, 'Callback', @(src,~) set(p_text, 'String', num2str(round(get(src, 'Value')))); set(q_slider, 'Callback', @(src,~) set(q_text, 'String', num2str(round(get(src, 'Value')))); set(sand_slider, 'Callback', @(src,~) set(sand_text, 'String', num2str(round(get(src, 'Value')))); set(speed_slider, 'Callback', @(src,~) set(speed_text, 'String', num2str(get(src, 'Value'), '%.2f')); set(damping_slider, 'Callback', @(src,~) set(damping_text, 'String', num2str(get(src, 'Value'), '%.2f')); % 更新绘图函数 function updatePlot(~, ~) handles = guidata(gcf); zeros_table = getappdata(gcf, 'bessel_zeros'); % 获取参数值 p = round(get(handles.p_slider, 'Value')); q = round(get(handles.q_slider, 'Value')); mode_idx = get(handles.mode_popup, 'Value'); res_idx = get(handles.res_popup, 'Value'); shape_idx = get(handles.shape_popup, 'Value'); % 设置网格分辨率 resolutions = [100, 200, 300]; N = resolutions(res_idx); % 创建网格 x = linspace(-0.5, 0.5, N); y = linspace(-0.5, 0.5, N); [X, Y] = meshgrid(x, y); % 根据形状计算图案 if shape_idx == 1 % 方形板 % 计算频率 freq = 100 * (p + q); % 更新信息文本 mode_str = {'对称模式', '反对称模式'}; info = sprintf('方形振动板\n振动模式: %s\n模态参数: m = %d, n = %d\n物理原理: z(x,y) = cos(mπx)cos(nπy) %s cos(nπx)cos(mπy)', ... mode_str{mode_idx}, p, q, char(177)); % 计算波函数 psi1 = cos(p*pi*X) .* cos(q*pi*Y); psi2 = cos(q*pi*X) .* cos(p*pi*Y); % 根据模式组合 if mode_idx == 1 % 对称模式 Z = psi1 + psi2; else % 反对称模式 Z = psi1 - psi2; end elseif shape_idx == 2 % 圆形板 % 确保q至少为1 q = max(1, q); % 获取贝塞尔函数零点 if p+1 <= size(zeros_table, 1) && q <= size(zeros_table, 2) k = zeros_table(p+1, q); else k = 1; % 默认值 end % 修正频率计算 freq = 50 * k; % 更新信息文本 mode_str = {'对称模式 (cos)', '反对称模式 (sin)'}; info = sprintf('圆形振动板\n振动模式: %s\n模态参数: n = %d (角向), m = %d (径向)\n物理原理: z(r,θ) = J_%d(k_{%d,%d}·r)·trig(%dθ)\n频率比例因子: 50', ... mode_str{mode_idx}, p, q, p, p, q, p); % 转换为极坐标 R = sqrt(X.^2 + Y.^2); Theta = atan2(Y, X); % 计算贝塞尔函数部分 J_part = besselj(p, k*R); % 根据模式选择三角函数 if mode_idx == 1 % 对称模式 trig_part = cos(p*Theta); else % 反对称模式 trig_part = sin(p*Theta); end % 组合得到振幅 Z = J_part .* trig_part; % 将圆形外的区域设为NaN（不显示） Z(R > 0.5) = NaN; else % 三角形板 (shape_idx == 3) % 计算频率 freq = 80 * (p + q); % 更新信息文本 mode_str = {'对称模式', '反对称模式'}; info = sprintf('等边三角形振动板\n振动模式: %s\n模态参数: m = %d, n = %d\n物理原理: 基于重心坐标的特征函数', ... mode_str{mode_idx}, p, q); % 计算三角形特征函数 Z = triangular_plate_mode(X, Y, p, q, mode_idx); % 标记三角形外的点 mask = triangular_mask(X, Y); Z(~mask) = NaN; end % 更新频率显示 set(handles.freq_text, 'String', sprintf('频率: %.0f Hz', freq)); % 绘制克拉尼图形 axes(handles.ax1); cla; % 绘制等高线（节点线） contour(X, Y, Z, [0, 0], 'LineWidth', 2, 'Color', [0.96, 0.4, 0.62]); hold on; % 添加中心点 plot(0, 0, 'ro', 'MarkerSize', 8, 'MarkerFaceColor', 'r'); % 绘制边界 if shape_idx == 2 % 圆形板 theta = linspace(0, 2*pi, 100); plot(0.5*cos(theta), 0.5*sin(theta), 'w-', 'LineWidth', 1.5); elseif shape_idx == 3 % 三角形板 [vx, vy] = equilateral_triangle_vertices(); plot([vx, vx(1)], [vy, vy(1)], 'w-', 'LineWidth', 1.5); end % 设置图形属性 shape_names = {'方形板', '圆形板', '三角形板'}; title(sprintf('克拉尼图案 (%s)', shape_names{shape_idx}), 'Color', 'w'); xlabel('x'); ylabel('y'); axis equal tight; % 根据形状调整坐标轴范围 if shape_idx == 3 xlim([-0.6, 0.6]); ylim([-0.6, 0.6]); else xlim([-0.55, 0.55]); ylim([-0.55, 0.55]); end grid on; box on; set(gca, 'Color', [0.18, 0.18, 0.23], ... 'XColor', [0.8, 0.8, 0.8], 'YColor', [0.8, 0.8, 0.8]); % 添加图例 if shape_idx == 1 legend('波节线', '固定点', 'Location', 'northeast', ... 'TextColor', 'w', 'Color', [0.25, 0.25, 0.3]); else legend('波节线', '中心点', '边界', 'Location', 'northeast', ... 'TextColor', 'w', 'Color', [0.25, 0.25, 0.3]); end % 存储Z值用于波动仿真 sand_data = getappdata(gcf, 'sand_data'); sand_data.Z = Z; setappdata(gcf, 'sand_data', sand_data); end % 开始波动仿真 function startWaveSimulation(~, ~) handles = guidata(gcf); sand_data = getappdata(gcf, 'sand_data'); % 如果已经在仿真中，则停止之前的仿真 if sand_data.isSimulating sand_data.isSimulating = false; setappdata(gcf, 'sand_data', sand_data); pause(0.1); end % 初始化沙粒数据 sand_data.isSimulating = true; sand_data.isPaused = false; sand_data.t = 0; % 获取参数 num_particles = round(get(handles.sand_slider, 'Value')); speed_factor = get(handles.speed_slider, 'Value'); damping = get(handles.damping_slider, 'Value'); % 获取当前形状 shape_idx = get(handles.shape_popup, 'Value'); % 根据形状初始化沙粒位置 particles = zeros(num_particles, 2); velocities = zeros(num_particles, 2); for i = 1:num_particles if shape_idx == 1 % 方形板 particles(i,:) = [rand() - 0.5, rand() - 0.5]; elseif shape_idx == 2 % 圆形板 r = 0.45 * sqrt(rand()); theta = 2 * pi * rand(); particles(i,:) = [r*cos(theta), r*sin(theta)]; else % 三角形板 [vx, vy] = equilateral_triangle_vertices(); while true x = 0.8 * (rand() - 0.5); y = 0.8 * (rand() - 0.5); if inpolygon(x, y, vx, vy) particles(i,:) = [x, y]; break; end end end end sand_data.particles = particles; sand_data.velocities = velocities; setappdata(gcf, 'sand_data', sand_data); % 启动仿真循环 while sand_data.isSimulating if ~sand_data.isPaused % 更新沙粒位置 sand_data = updateSandParticles(sand_data, speed_factor, damping); % 绘制沙粒 axes(handles.ax2); cla; % 绘制边界 shape_idx = get(handles.shape_popup, 'Value'); if shape_idx == 1 % 方形板 rectangle('Position', [-0.5, -0.5, 1, 1], 'EdgeColor', 'w', 'LineWidth', 1.5); elseif shape_idx == 2 % 圆形板 theta = linspace(0, 2*pi, 100); plot(0.5*cos(theta), 0.5*sin(theta), 'w-', 'LineWidth', 1.5); else % 三角形板 [vx, vy] = equilateral_triangle_vertices(); plot([vx, vx(1)], [vy, vy(1)], 'w-', 'LineWidth', 1.5); end hold on; % 绘制沙粒 scatter(sand_data.particles(:,1), sand_data.particles(:,2), 15, ... 'MarkerFaceColor', [0.96, 0.7, 0.3], 'MarkerEdgeColor', 'none'); % 添加中心点 plot(0, 0, 'ro', 'MarkerSize', 8, 'MarkerFaceColor', 'r'); % 设置图形属性 title('沙粒波动可视化', 'Color', 'w'); xlabel('x'); ylabel('y'); if shape_idx == 3 xlim([-0.6, 0.6]); ylim([-0.6, 0.6]); else xlim([-0.55, 0.55]); ylim([-0.55, 0.55]); end axis equal; grid on; box on; set(gca, 'Color', [0.18, 0.18, 0.23], ... 'XColor', [0.8, 0.8, 0.8], 'YColor', [0.8, 0.8, 0.8]); drawnow; end % 短暂暂停以控制速度 pause(0.02); sand_data = getappdata(gcf, 'sand_data'); end end % 更新沙粒位置 function sand_data = updateSandParticles(sand_data, speed_factor, damping) % 获取当前参数 p = round(get(handles.p_slider, 'Value')); q = round(get(handles.q_slider, 'Value')); mode_idx = get(handles.mode_popup, 'Value'); shape_idx = get(handles.shape_popup, 'Value'); % 时间步长 dt = 0.02 * speed_factor; sand_data.t = sand_data.t + dt; particles = sand_data.particles; velocities = sand_data.velocities; Z = sand_data.Z; % 获取网格信息 [N, ~] = size(Z); x = linspace(-0.5, 0.5, N); y = linspace(-0.5, 0.5, N); % 计算波函数的梯度 [dZdx, dZdy] = gradient(Z, x(2)-x(1), y(2)-y(1)); for i = 1:size(particles, 1) px = particles(i, 1); py = particles(i, 2); % 检查粒子是否在边界内 if shape_idx == 1 % 方形板 in_bounds = (px >= -0.5) && (px <= 0.5) && (py >= -0.5) && (py <= 0.5); elseif shape_idx == 2 % 圆形板 in_bounds = (sqrt(px^2 + py^2) <= 0.5); else % 三角形板 [vx, vy] = equilateral_triangle_vertices(); in_bounds = inpolygon(px, py, vx, vy); end if in_bounds % 找到最近的网格点 [~, idx_x] = min(abs(x - px)); [~, idx_y] = min(abs(y - py)); % 获取该点的梯度 gx = dZdx(idx_y, idx_x); gy = dZdy(idx_y, idx_y); % 计算力（指向波节线） force_scale = 0.5; force_x = -gx * force_scale; force_y = -gy * force_scale; % 添加一些随机扰动 rand_scale = 0.05; force_x = force_x + rand_scale * (rand() - 0.5); force_y = force_y + rand_scale * (rand() - 0.5); % 更新速度 velocities(i, 1) = velocities(i, 1) * (1 - damping) + force_x * dt; velocities(i, 2) = velocities(i, 2) * (1 - damping) + force_y * dt; % 更新位置 particles(i, 1) = px + velocities(i, 1) * dt; particles(i, 2) = py + velocities(i, 2) * dt; else % 如果粒子在边界外，将其重置到中心附近 particles(i, :) = [0.05*(rand()-0.5), 0.05*(rand()-0.5)]; velocities(i, :) = [0, 0]; end end sand_data.particles = particles; sand_data.velocities = velocities; setappdata(gcf, 'sand_data', sand_data); end % 暂停/继续波动仿真 function togglePause(~, ~) sand_data = getappdata(gcf, 'sand_data'); if sand_data.isSimulating sand_data.isPaused = ~sand_data.isPaused; setappdata(gcf, 'sand_data', sand_data); end end % 重置沙粒 function resetSandParticles(~, ~) sand_data = getappdata(gcf, 'sand_data'); sand_data.isSimulating = false; sand_data.isPaused = false; % 清除波动可视化区域 axes(handles.ax2); cla; title('沙粒波动可视化', 'Color', 'w'); axis equal; grid on; set(gca, 'Color', [0.18, 0.18, 0.23], ... 'XColor', [0.8, 0.8, 0.8], 'YColor', [0.8, 0.8, 0.8]); if get(handles.shape_popup, 'Value') == 3 xlim([-0.6, 0.6]); ylim([-0.6, 0.6]); else xlim([-0.55, 0.55]); ylim([-0.55, 0.55]); end setappdata(gcf, 'sand_data', sand_data); end end % 计算贝塞尔函数零点的辅助函数 function zeros_table = compute_bessel_zeros(n_vals, m_vals) max_n = max(n_vals); max_m = max(m_vals); zeros_table = zeros(max_n+1, max_m); for n = n_vals for m = m_vals % 使用数值方法求解贝塞尔函数零点 fun = @(x) besselj(n, x); guess = (m + 0.5*n - 0.25)*pi; % 初始猜测值 % 使用fzero查找零点 try zero = fzero(fun, guess); zeros_table(n+1, m) = zero; catch % 如果失败，使用更鲁棒的搜索方法 x = linspace(0, 100, 10000); % 限制搜索范围 y = fun(x); inds = find(diff(sign(y)) ~= 0); if length(inds) >= m zero = x(inds(m)); zeros_table(n+1, m) = zero; else zeros_table(n+1, m) = 0; end end end end end % 生成等边三角形的顶点坐标 function [vx, vy] = equilateral_triangle_vertices() % 等边三角形顶点 (中心在原点) height = 0.9; side = height / (sqrt(3)/2); % 边长 vx = [0, -side/2, side/2]; vy = [height/2, -height/2, -height/2]; end % 创建三角形板的掩码 function mask = triangular_mask(X, Y) % 获取三角形顶点 [vx, vy] = equilateral_triangle_vertices(); % 创建多边形掩码 mask = inpolygon(X, Y, vx, vy); end % 三角形板的振动模式函数 function Z = triangular_plate_mode(X, Y, m, n, mode_idx) % 获取三角形顶点 [vx, vy] = equilateral_triangle_vertices(); A = [vx(1), vy(1)]; B = [vx(2), vy(2)]; C = [vx(3), vy(3)]; % 计算面积 (用于重心坐标) total_area = abs((B(1)-A(1))*(C(2)-A(2)) - (C(1)-A(1))*(B(2)-A(2)))/2; % 初始化Z矩阵 Z = zeros(size(X)); % 计算每个点的重心坐标 for i = 1:size(X,1) for j = 1:size(X,2) P = [X(i,j), Y(i,j)]; % 计算子三角形面积 area_A = abs((B(1)-P(1))*(C(2)-P(2)) - (C(1)-P(1))*(B(2)-P(2)))/2; area_B = abs((A(1)-P(1))*(C(2)-P(2)) - (C(1)-P(1))*(A(2)-P(2)))/2; area_C = abs((A(1)-P(1))*(B(2)-P(2)) - (B(1)-P(1))*(A(2)-P(2)))/2; % 计算重心坐标 lambda1 = area_A / total_area; lambda2 = area_B / total_area; lambda3 = area_C / total_area; % 确保重心坐标和为1 if abs(lambda1 + lambda2 + lambda3 - 1) > 1e-6 lambda3 = 1 - lambda1 - lambda2; end % 计算特征函数 if mode_idx == 1 % 对称模式 Z(i,j) = sin(2*pi*(2*m+n)*lambda1) + ... sin(2*pi*(2*n+m)*lambda2) + ... sin(2*pi*(m+n)*lambda3); else % 反对称模式 Z(i,j) = cos(2*pi*(2*m+n)*lambda1) + ... cos(2*pi*(2*n+m)*lambda2) + ... cos(2*pi*(m+n)*lambda3); end end end end 上面这个代码中，文件: chladni_gui84.m 行: 177 列: 96 无效表达式。调用函数或对变量进行索引时，请使用圆括号。否则，请检查不匹配的分隔符。 Caught "std::exception" Exception message is: Invalid character code sequence detected.请你帮我修改并给出正确的完整代码
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arg(value, 2, 16, QChar('0')) 将 value 格式化为十六进制数，宽度为2，不足部分用 0 填充。静态成员函数的调用方式：静态成员函数可以通过类名直接调用，也可以通过类的实例调用，但推荐通过类名调用以明确其静态特性。静态成员函数不能访问非静态成员：静态成员函数不能访问非静态成员变量或非静态成员函数，因为它们需要类的实例来访问。不能访问非静态成员：静态成员函数不能访问非静态成员变量或非静态成员函数，因为它们需要类的实例来访问。// 也可以通过对象调用静态成员函数。
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