[投稿] 函数绘制器 — by Nemo

script_library/index.json

@@ -1,7 +1,7 @@
 {
   "format_version": 1,
-  "data_version": 41,
-  "updated": "2026-03-29T13:08:52.907Z",
+  "data_version": 42,
+  "updated": "2026-03-30T15:16:31.856Z",
   "announcement": null,
   "categories": [
     {
@@ -1005,6 +1005,29 @@
       "updated": null,
       "status": "active",
       "lines": 130
+    },
+    {
+      "id": "script_mndbzbxy",
+      "name": "函数绘制器",
+      "name_en": "函数绘制器",
+      "desc": "输入函数解析式可以直接生成函数图象",
+      "desc_en": "输入函数解析式可以直接生成函数图象",
+      "category": "basic",
+      "file": "scripts/basic/script_mndbzbxy.py",
+      "thumbnail": null,
+      "version": 1,
+      "file_type": "py",
+      "author": "Nemo",
+      "author_en": "Nemo",
+      "tags": [
+        "community"
+      ],
+      "requires": [],
+      "min_app_version": "1.5.0",
+      "added": "2026-03-30",
+      "updated": null,
+      "status": "active",
+      "lines": 290
     }
   ]
 }

script_library/scripts/basic/script_mndbzbxy.py

@@ -0,0 +1,290 @@
+import tkinter as tk
+from tkinter import messagebox
+import numpy as np
+import matplotlib.pyplot as plt
+from matplotlib.backends.backend_tkagg import FigureCanvasTkAgg
+from matplotlib.figure import Figure
+from matplotlib.ticker import MultipleLocator, AutoLocator
+import math
+import re
+
+# ---------------------------- 表达式预处理（支持省略乘号） ----------------------------
+def preprocess_expr(expr: str) -> str:
+    """将数学表达式转换为Python可eval的形式，自动插入*号"""
+    expr = expr.replace('π', 'math.pi').replace('e', 'math.e')
+    expr = expr.replace('^', '**')
+    # 插入隐式乘号：数字与字母/括号之间、字母与字母/括号之间、括号与数字/字母之间
+    pattern = r'(?<=[0-9])(?=[a-zA-Z(])|(?<=[a-zA-Z)])(?=[0-9a-zA-Z(])'
+    expr = re.sub(pattern, '*', expr)
+    return expr
+
+# ---------------------------- 主应用类 ----------------------------
+class FunctionPlotter:
+    def __init__(self, master):
+        self.master = master
+        master.title("函数图像绘制器")
+        master.geometry("500x700")
+        master.configure(bg="#f0f0f0")
+        master.minsize(450, 600)
+
+        self.mode = 'linear'          # 'linear' 或 'quadratic'
+        self.animation = None
+        self.current_line = None
+        self.fig = None
+        self.ax = None
+        self.canvas = None
+
+        self.create_widgets()
+        self.init_plot()
+
+    def create_widgets(self):
+        # ---------- 顶部模式切换按钮 ----------
+        top_frame = tk.Frame(self.master, bg="#f0f0f0", pady=10)
+        top_frame.pack(fill=tk.X)
+
+        self.btn_linear = tk.Button(
+            top_frame, text="📈 一次函数", font=("微软雅黑", 12, "bold"),
+            bg="#e0e0e0", fg="#333", padx=20, pady=5, relief=tk.RAISED,
+            command=lambda: self.switch_mode('linear')
+        )
+        self.btn_linear.pack(side=tk.LEFT, expand=True, fill=tk.X, padx=10)
+
+        self.btn_quadratic = tk.Button(
+            top_frame, text="📉 二次函数", font=("微软雅黑", 12, "bold"),
+            bg="#e0e0e0", fg="#333", padx=20, pady=5, relief=tk.RAISED,
+            command=lambda: self.switch_mode('quadratic')
+        )
+        self.btn_quadratic.pack(side=tk.RIGHT, expand=True, fill=tk.X, padx=10)
+
+        self.update_button_style()
+
+        # ---------- 输入区域 ----------
+        input_frame = tk.Frame(self.master, bg="#f0f0f0", pady=10)
+        input_frame.pack(fill=tk.X, padx=15)
+
+        tk.Label(input_frame, text="函数表达式：y=", font=("微软雅黑", 10), bg="#f0f0f0").pack(anchor=tk.W)
+        self.entry = tk.Entry(input_frame, font=("Consolas", 12), bg="white")
+        self.entry.pack(fill=tk.X, pady=(5,10))
+        self.entry.insert(0, "x+1")
+
+        self.plot_btn = tk.Button(
+            input_frame, text="🎨 绘制图像", font=("微软雅黑", 10, "bold"),
+            bg="#4caf50", fg="white", padx=10, pady=5,
+            command=self.start_plot_animation
+        )
+        self.plot_btn.pack()
+
+        # ---------- 数学符号面板 ----------
+        symbol_frame = tk.LabelFrame(self.master, text="数学符号库", font=("微软雅黑", 9), bg="#f0f0f0", padx=5, pady=5)
+        symbol_frame.pack(fill=tk.X, padx=15, pady=5)
+
+        symbols = ['x', 'x^2', 'x^3', '+', '-', '*', '/', '(', ')', 'π', 'e',
+                   'sin', 'cos', 'tan', 'sqrt', '^', '**']
+        row, col = 0, 0
+        for sym in symbols:
+            btn = tk.Button(
+                symbol_frame, text=sym, font=("Consolas", 9), width=5, relief=tk.GROOVE,
+                command=lambda s=sym: self.insert_symbol(s)
+            )
+            btn.grid(row=row, column=col, padx=2, pady=2, sticky="ew")
+            col += 1
+            if col >= 6:
+                col = 0
+                row += 1
+        for i in range(6):
+            symbol_frame.columnconfigure(i, weight=1)
+
+        # ---------- 状态栏 ----------
+        self.status = tk.Label(self.master, text="就绪", bd=1, relief=tk.SUNKEN, anchor=tk.W, bg="#e0e0e0")
+        self.status.pack(side=tk.BOTTOM, fill=tk.X)
+
+    def init_plot(self):
+        """初始化 matplotlib 图形，设置坐标轴样式和固定刻度间隔为1"""
+        self.fig = Figure(figsize=(6, 4), dpi=100, facecolor='white')
+        self.ax = self.fig.add_subplot(111)
+        self.canvas = FigureCanvasTkAgg(self.fig, master=self.master)
+        self.canvas.get_tk_widget().pack(fill=tk.BOTH, expand=True, padx=15, pady=10)
+
+        self.ax.grid(True, linestyle='--', alpha=0.7)
+        self.ax.axhline(0, color='k', linewidth=0.8)
+        self.ax.axvline(0, color='k', linewidth=0.8)
+        self.ax.set_xlabel('x', fontsize=10)
+        self.ax.set_ylabel('y', fontsize=10)
+        self.ax.set_title('函数图像', fontsize=12)
+
+        # x轴固定刻度间隔1，范围-10~10
+        self.ax.set_xlim(-10, 10)
+        self.ax.xaxis.set_major_locator(MultipleLocator(1))
+        self.ax.xaxis.set_minor_locator(MultipleLocator(0.5))
+
+        # y轴暂用自动，绘图时会根据数据重新调整
+        self.ax.yaxis.set_major_locator(AutoLocator())
+        self.fig.tight_layout()
+        self.canvas.draw()
+
+    def update_button_style(self):
+        if self.mode == 'linear':
+            self.btn_linear.config(bg="#4caf50", fg="white", relief=tk.SUNKEN)
+            self.btn_quadratic.config(bg="#e0e0e0", fg="#333", relief=tk.RAISED)
+        else:
+            self.btn_quadratic.config(bg="#4caf50", fg="white", relief=tk.SUNKEN)
+            self.btn_linear.config(bg="#e0e0e0", fg="#333", relief=tk.RAISED)
+
+    def switch_mode(self, mode):
+        if self.mode == mode:
+            return
+        self.mode = mode
+        self.update_button_style()
+        if mode == 'linear':
+            default_expr = "2x+3"
+        else:
+            default_expr = "x^2+2x+1"
+        self.entry.delete(0, tk.END)
+        self.entry.insert(0, default_expr)
+        self.status.config(text=f"已切换到{'一次' if mode=='linear' else '二次'}函数模式")
+        self.entry.config(bg="#ffffcc")
+        self.master.after(200, lambda: self.entry.config(bg="white"))
+
+    def insert_symbol(self, symbol):
+        pos = self.entry.index(tk.INSERT)
+        text = self.entry.get()
+        new_text = text[:pos] + symbol + text[pos:]
+        self.entry.delete(0, tk.END)
+        self.entry.insert(0, new_text)
+        self.entry.icursor(pos + len(symbol))
+        self.entry.focus_set()
+
+    def evaluate_expression(self, expr_str, x_vals):
+        """计算表达式值，返回y数组，若全部无效则返回None"""
+        try:
+            processed = preprocess_expr(expr_str)
+            namespace = {
+                'math': math,
+                'np': np,
+                'sqrt': math.sqrt,
+                'sin': math.sin,
+                'cos': math.cos,
+                'tan': math.tan,
+                'pi': math.pi,
+                'e': math.e
+            }
+            code = compile(f'lambda x: {processed}', '<string>', 'eval')
+            f = eval(code, namespace)
+            y_vals = []
+            for x in x_vals:
+                try:
+                    y = f(x)
+                    if isinstance(y, complex) or not np.isfinite(y):
+                        y = np.nan
+                    y_vals.append(y)
+                except:
+                    y_vals.append(np.nan)
+            y_arr = np.array(y_vals)
+            if np.all(np.isnan(y_arr)):
+                messagebox.showerror("无效表达式", "表达式在所有x上均无有效值，请检查输入。")
+                return None
+            return y_arr
+        except Exception as e:
+            messagebox.showerror("表达式错误", f"解析表达式出错：\n{str(e)}")
+            return None
+
+    def start_plot_animation(self):
+        """启动绘图动画，确保曲线正常显示"""
+        # 停止旧动画
+        if self.animation is not None:
+            try:
+                self.animation.event_source.stop()
+            except:
+                pass
+            self.animation = None
+
+        expr = self.entry.get().strip()
+        if not expr:
+            messagebox.showwarning("空表达式", "请输入函数表达式")
+            return
+
+        # 生成x点并计算y值
+        x_vals = np.linspace(-10, 10, 200)
+        y_vals = self.evaluate_expression(expr, x_vals)
+        if y_vals is None:
+            return
+
+        # 清除旧曲线
+        if self.current_line is not None:
+            self.current_line.remove()
+            self.current_line = None
+
+        # 动态调整y轴范围（过滤无效点）
+        valid_mask = ~np.isnan(y_vals)
+        if np.any(valid_mask):
+            y_min = np.nanmin(y_vals[valid_mask])
+            y_max = np.nanmax(y_vals[valid_mask])
+            y_range = y_max - y_min
+            if y_range < 1e-6:
+                y_min -= 1
+                y_max += 1
+            else:
+                y_min -= 0.1 * y_range
+                y_max += 0.1 * y_range
+            self.ax.set_ylim(y_min, y_max)
+            # 设置y轴刻度间隔为1（如果范围太大则自动调整）
+            if y_max - y_min <= 20:
+                self.ax.yaxis.set_major_locator(MultipleLocator(1))
+            else:
+                self.ax.yaxis.set_major_locator(MultipleLocator(5))
+            self.ax.yaxis.set_minor_locator(MultipleLocator(1))
+        else:
+            self.ax.set_ylim(-5, 5)
+
+        # 创建空曲线（占位）
+        self.current_line, = self.ax.plot([], [], 'b-', linewidth=2, label=f'y = {expr}')
+        self.ax.legend(loc='upper right')
+        self.canvas.draw()
+
+        # 动画参数
+        self.total_points = len(x_vals)
+        self.x_data = x_vals
+        self.y_data = y_vals
+        self.step = 0
+
+        # 动画更新函数
+        def animate(i):
+            self.step = min(self.total_points, self.step + 5)
+            if self.step >= 1:
+                self.current_line.set_data(self.x_data[:self.step], self.y_data[:self.step])
+                # 强制刷新画布
+                self.canvas.draw_idle()
+                self.canvas.flush_events()
+            if self.step >= self.total_points:
+                self.animation.event_source.stop()
+                self.status.config(text="绘图完成")
+            return self.current_line,
+
+        from matplotlib.animation import FuncAnimation
+        # 帧数 = 总点数/5 + 1
+        frames = self.total_points // 5 + 1
+        self.animation = FuncAnimation(
+            self.fig, animate, frames=frames,
+            interval=30, repeat=False, blit=False
+        )
+        self.status.config(text="正在绘制动画...")
+
+        # 备用机制：如果动画因故未显示，强制重绘一次（极少情况）
+        def fallback_draw():
+            if self.current_line is not None and len(self.current_line.get_xdata()) == 0:
+                self.current_line.set_data(self.x_data, self.y_data)
+                self.canvas.draw()
+                self.status.config(text="已绘制完整曲线")
+        self.master.after(500, fallback_draw)  # 0.5秒后若仍无数据则直接画全
+
+        # 动画结束后启用按钮（粗略延时）
+        def enable_btn():
+            self.plot_btn.config(state=tk.NORMAL)
+        self.plot_btn.config(state=tk.DISABLED)
+        self.master.after(2000, enable_btn)
+
+# ---------------------------- 主程序 ----------------------------
+if __name__ == "__main__":
+    root = tk.Tk()
+    app = FunctionPlotter(root)
+    root.mainloop()