NumericalCalculation/x4/FunctionDisplay_X4.py

import math
from collections import OrderedDict
from time import sleep
from ttkbootstrap import *
import tkinter.font as tkFont
from tkinter import messagebox
from tkinter.ttk import Treeview

import sympy
from numpy import arange
from functionUtil import FunctionUtil


# 获取文本的宽度和高度
def get_text_dimensions(canvas, text, font):
    text_id = canvas.create_text(0, 0, text=text, font=font, anchor="center")
    bbox = canvas.bbox(text_id)
    width = bbox[2] - bbox[0]
    height = bbox[3] - bbox[1]
    canvas.delete(text_id)
    return width, height


# 在画布中央绘制文本
def center_text(canvas, text, font):
    canvas_width = int(canvas.cget("width"))
    text_width, text_height = get_text_dimensions(canvas, text, font)
    x = canvas_width // 2
    y = 200
    canvas.create_text(x, y, text=text, font=font, anchor="center")


class Graph(Canvas):
    def __init__(self, master=None, **kwargs):
        super().__init__(master, **kwargs)
        self.width = int(self.cget('width'))
        self.height = int(self.cget('height'))
        self.origin = (self.width / 2, self.height / 2)
        self.bili_x = 20
        self.bili_y = 20
        self.draw_axis()
        self.draw_scale()

    def draw_axis(self):
        """
        绘制坐标轴
        """
        self.delete("all")
        self.create_line(0, self.origin[1], self.width, self.origin[1], fill='black', arrow=LAST)  # 一象限xy轴
        self.create_line(self.origin[0], 0, self.origin[0], self.height, fill='black', arrow=FIRST)

    def draw_scale(self):
        """
        绘制刻度值
        """
        for i in range(-math.ceil((self.origin[0] / self.bili_x)) + 1, math.ceil((self.width - self.origin[0]) / self.bili_x)):
            j = i * self.bili_x
            if (i % 10 == 0):
                self.create_line(j + self.origin[0], self.origin[1], j + self.origin[0], self.origin[1] - 5, fill='black')
                self.create_text(j + self.origin[0], self.origin[1] + 10, text=i)
        for i in range(-math.ceil((self.height - self.origin[1]) / self.bili_y) + 1, math.ceil((self.origin[1] / self.bili_y))):
            j = -(i * self.bili_y)
            if (i == 0):
                continue
            elif (i % 2 == 0):
                self.create_line(self.origin[0], j + self.origin[1], self.origin[0] + 5, j + self.origin[1], fill='black')
                self.create_text(self.origin[0] - 10, j + self.origin[1], text=i)

    def switch_quadrant(self, quadrant):
        """
        切换象限
        """
        if quadrant == 1:
            self.origin = (50, self.height - 50)
        else:
            self.origin = (self.width / 2, self.height / 2)
        self.draw_axis()
        self.draw_scale()

    def get_xy(self):
        return -math.ceil((self.origin[0] / self.bili_x)) + 1, math.ceil((self.width - self.origin[0]) / self.bili_x)
        
    def draw_graph(self, func, draw_precision=0.1, count=1000,  bili_x=20, bili_y=40, c='blue'):
        'xmin,xmax 自变量的取值范围； c 图像颜色'
        'x0,y0 原点坐标  w,h 横纵轴半长 draw_precision 步进'
        self.bili_x, self.bili_y = int(bili_x), int(bili_y)
        self.draw_axis()
        self.draw_scale()
        w1, w2 = self.bili_x, self.bili_y  # w1,w2为自变量和函数值在横纵轴上的放大倍数
        xmin, xmax = self.get_xy()
        co2 = []
        try:
            for x in arange(xmin, xmax, draw_precision):  # draw_precision----画图精度
                y = sympy.sympify(func, convert_xor=True).subs("x", x).evalf()
                coord = self.origin[0] + w1 * x, self.origin[1] - w2 * y, self.origin[0] + w1 * x + 1, self.origin[1] - w2 * y + 1
                if abs(coord[1]) < self.height:  # 超过w,h就截断
                    co2.append((self.origin[0] + w1 * x, self.origin[1] - w2 * y))
            if count is None:
                length = len(co2)
            else:
                length = len(co2[:int(count)])
            for i in range(length):
                if (draw_precision >= 1):
                    self.create_line(co2, fill=c, width=1)
                if (i + 1 == len(co2)):
                    break
                if (abs(co2[i][1] - co2[i + 1][1]) > 100):
                    continue
                else:
                    self.create_line(co2[i], co2[i + 1], fill=c, width=1)
                sleep(0.01)
                self.update()
        except Exception as E:
            messagebox.showerror("错误", message=f"函数有误!\n{E}")


class ExpressionCanvas(Canvas):
    def __init__(self, master, *args, **kwargs):
        super().__init__(master, *args, **kwargs)
        self.node_width = 60
        self.node_height = 30
        self.x_spacing = 10
        self.y_spacing = 70
        self.level = {}

    def add_node(self, text, x, y, parent=None):
        node_width = len(text) * 5 + 20
        if node_width < 40:
            node_width = 50
        # 创建节点
        coords = [x - node_width / 2, y, x + node_width / 2, y + self.node_height]
        if coords[1] in self.level:
            max_x = max(self.level[coords[1]])
            if coords[0] <= max_x:
                x = max_x + node_width / 2 + self.x_spacing
            node_id = self.create_rectangle(x - node_width / 2, y, x + node_width / 2, y + self.node_height,
                                            fill="white")
            sleep(0.2)
            self.update()
        elif text == "x":
            x = self.coords(parent)[0] + node_width / 2
            node_id = self.create_rectangle(x - node_width / 2, y, x + node_width / 2, y + self.node_height,
                                            fill="white")
            sleep(0.2)
            self.update()
        else:
            node_id = self.create_rectangle(x - node_width / 2, y, x + node_width / 2, y + self.node_height, fill="white")
            sleep(0.2)
            self.update()
        coords = [x - node_width / 2, y, x + node_width / 2, y + self.node_height]
        if coords[1] in self.level:
            self.level[coords[1]].append(coords[2])
        else:
            self.level[coords[1]] = [coords[2]]
        text_id = self.create_text(x + 5, y + self.node_height // 2, text=text, anchor="center")
        sleep(0.2)
        self.update()
        # 绘制父节点和当前节点的连线
        if parent:
            parent_coords = self.coords(parent)
            parent_x = parent_coords[0] + (parent_coords[2] - parent_coords[0]) // 2
            parent_y = parent_coords[1] + (parent_coords[3] - parent_coords[1]) // 2
            self.create_line(parent_x, parent_y + self.node_height // 2, x, y, fill="black")
            self.update()
        return node_id

    def draw_expression(self, expression, x, y, parent=None, sibling_width=0):
        # 创建节点并绘制表达式文本
        node = self.add_node(str(expression), x, y, parent=parent)
        if expression.is_Atom:
            return node
        # 处理子表达式
        num_children = len(expression.args)
        total_width = num_children * self.node_width + (num_children - 1) * self.x_spacing
        start_x = x - total_width // 2
        for subexpr in expression.args:
            subnode = self.draw_expression(subexpr, start_x, y + self.y_spacing, parent=node, sibling_width=total_width)
            start_x += self.node_width + self.x_spacing
        return node


class FunctionDisplay(Frame):
    def __init__(self, master, attr):
        super().__init__(master)
        self.attr = attr
        self.font_style = tkFont.Font(family="Lucida Grande", size=30)
        self.functions = FunctionUtil()
        self.master = master
        self.create_window()

    def clear_text_canvas(self, event):
        def clear_text():
            self.text_canvas.delete("all")
            self.text_canvas.create_text(20 + 180, 20, text='可识别基本函数', fill='red', font=("Purisa", 25, "bold"))
            center_text(self.text_canvas, self.text, ("Lucida Grande", 15))
        self.menu = Menu(self, tearoff=False)
        self.menu.add_command(label="重置", command=clear_text)
        self.menu.post(event.x_root, event.y_root)

    def add_function(self):
        """
        用户添加函数
        """
        input_func = self.func_input.get()
        if input_func == "":
            messagebox.showwarning("注意", message="请输入函数！")
            return
        elif input_func.find("=") < 0:
            messagebox.showerror("注意", message="添加函数的格式为：\nSinPlusCos(x)=sin(x)+cos(x)")
            return
        left_var = input_func.split("=")[0]
        right_var = input_func.split("=")[1]
        try:
            function = self.functions.get_function_by_iter(right_var)
            sympy.sympify(function, evaluate=False)
        except Exception as E:
            messagebox.showerror("注意", message="函数解析错误，请仔细检查函数是否正确！")
            self.func_input.delete(0, END)
            return
        if self.functions.check_function_exit(left_var):
            result = messagebox.askokcancel(title='标题~', message=f'函数{left_var}已经存在，是否需要覆盖！')
            if result:
                self.functions.add_function(left_var, right_var)
                messagebox.showinfo(title="提示", message="覆盖成功！")
                self.func_input.delete(0, END)
            return
        self.functions.add_function(left_var, right_var)
        messagebox.showinfo(title="提示", message="添加成功！")
        self.func_input.delete(0, END)

    def update_quadrant(self):
        """
        更换象限
        """
        self.axis_canvas.switch_quadrant(self.quadrant.get())
        self.print_function()

    def print_function(self):
        """
        输出
        """
        self.text_canvas.delete("all")
        self.text_canvas.level.clear()
        input_func = self.func_input.get()
        if input_func == "":
            messagebox.showwarning("注意", message="请输入函数！")
            return
        step = eval(self.x_step.get()) if not self.x_step.get() == "" else 0.1
        count = self.x_count.get() if not self.x_count.get() == "" else None
        x_scale = self.x_scale.get() if not self.x_scale.get() == "" else 20
        y_scale = self.y_scale.get() if not self.y_scale.get() == "" else 40
        if input_func.find("=") >= 0:
            left_var = input_func.split("=")[0]
            right_var = input_func.split("=")[1]
            if self.functions.check_function_exit(right_var):
                func = self.functions.get_function_by_iter(right_var)
                self.axis_canvas.draw_graph(func, step, count,
                                            x_scale, y_scale)
                self.text_canvas.draw_expression(sympy.sympify(func, evaluate=False, convert_xor=True), int(self.text_canvas.cget("width")) // 2, self.text_canvas.y_spacing)
            else:
                self.axis_canvas.draw_graph(right_var, step, count,
                                            x_scale, y_scale)
                self.text_canvas.draw_expression(sympy.sympify(right_var, evaluate=False, convert_xor=True), int(self.text_canvas.cget("width")) // 2, self.text_canvas.y_spacing)
        else:
            if self.functions.check_function_exit(input_func):
                func = self.functions.get_function_by_iter(input_func)
                self.axis_canvas.draw_graph(func, step, count,
                                            x_scale, y_scale)
                self.text_canvas.draw_expression(sympy.sympify(func, evaluate=False, convert_xor=True), int(self.text_canvas.cget("width")) // 2, self.text_canvas.y_spacing)
            else:
                self.axis_canvas.draw_graph(input_func, step, count,
                                        x_scale, y_scale)
                self.text_canvas.draw_expression(sympy.sympify(input_func, evaluate=False, convert_xor=True), int(self.text_canvas.cget("width")) // 2, self.text_canvas.y_spacing)

    def create_form(self):
        bottom_frame = Frame(self.master, width=self.attr["width"], height=self.attr["height"] * 0.3)
        self.func_input = Entry(bottom_frame, font=self.font_style, width=40)
        self.func_input.grid(row=0, column=0, columnspan=4, padx=30)
        self.add_func_button = Button(bottom_frame, text="用户命名并新增基本函数", command=self.add_function)
        self.add_func_button.grid(row=0, column=4, padx=10)
        Label(bottom_frame, text="x步长", font=("Lucida Grande", 20)).grid(row=1, column=0, padx=30)
        self.x_step = Entry(bottom_frame, font=self.font_style, width=10)
        self.x_step.grid(row=1, column=1, padx=10, pady=10)
        Label(bottom_frame, text="x个数", font=("Lucida Grande", 20)).grid(row=1, column=2, padx=30)
        self.x_count = Entry(bottom_frame, font=self.font_style, width=10)
        self.x_count.grid(row=1, column=3, padx=10, pady=10)

        Label(bottom_frame, text="坐标轴", font=("Lucida Grande", 20)).grid(row=2, column=0, padx=30)
        self.quadrant = IntVar()
        self.quadrant.set(4)
        Radiobutton(bottom_frame, text="四象限", command=self.update_quadrant, value=4, variable=self.quadrant).grid(row=2, column=1, padx=10, pady=10)
        Radiobutton(bottom_frame, text="一象限", command=self.update_quadrant, value=1, variable=self.quadrant).grid(row=2, column=2, padx=10, pady=10)

        Label(bottom_frame, text="x放大倍数", font=("Lucida Grande", 20)).grid(row=3, column=0, padx=30)
        self.x_scale = Entry(bottom_frame, font=self.font_style, width=10)
        self.x_scale.grid(row=3, column=1, padx=10, pady=10)
        Label(bottom_frame, text="y放大倍数", font=("Lucida Grande", 20)).grid(row=3, column=2, padx=30)
        self.y_scale = Entry(bottom_frame, font=self.font_style, width=10)
        self.y_scale.grid(row=3, column=3, padx=10, pady=10)

        Button(bottom_frame, text="输出",
               command=self.print_function, width=5).grid(row=1, rowspan=3, column=4, sticky="w")
        bottom_frame.place(x=0, y=self.attr["height"] * 0.65 + 20)

    def show_user_function(self):
        children_window = Toplevel(root)
        children_window.title("用户自定义函数")
        children_window.geometry('350x260+450+200')
        packet_frame = Frame(children_window)
        packet_frame.grid(row=0, column=0, columnspan=3, padx=10, pady=5)
        function_treeview = Treeview(packet_frame, columns=("function_name", "function"), show="headings")
        function_treeview.heading("function_name", text="函数名称")
        function_treeview.column("function_name", width=100, anchor=CENTER)
        function_treeview.heading("function", text="函数体")
        function_treeview.column("function", width=200, anchor=CENTER)
        function_treeview.pack(side="left", fill="both")
        scrollbar = Scrollbar(packet_frame, orient="vertical", command=function_treeview.yview)
        scrollbar.pack(side="right", fill="y")
        function_treeview.configure(yscrollcommand=scrollbar.set)

        def delete_item():
            selected_item = function_treeview.selection()
            for item in selected_item:
                item_data = function_treeview.item(item)
                function_treeview.delete(item)
                self.functions.data.pop(item_data["values"][0])
                self.functions.save()

        context_menu = Menu(root, tearoff=False)
        context_menu.add_command(label="删除", command=delete_item)

        def popup_menu(event):
            if function_treeview.identify_region(event.x, event.y) == "cell":
                function_treeview.selection_set(function_treeview.identify_row(event.y))
                context_menu.post(event.x_root, event.y_root)

        function_treeview.bind("<Button-3>", popup_menu)
        for function_name, function in self.functions.data.items():
            function_treeview.insert("", "end", values=(function_name, function))

    def create_window(self):
        self.axis_canvas = Graph(self.master, width=self.attr["width"] * 0.65, height=self.attr["height"] * 0.65, bg="#cdcdcd")
        self.axis_canvas.place(x=0, y=0)
        self.text_canvas = ExpressionCanvas(self.master, width=self.attr["width"] * 0.35, height=self.attr["height"] * 0.65, bg="#cdcdcd")
        menubar = Menu(root)
        menubar.add_command(label='查看自定义函数', command=self.show_user_function)
        root.config(menu=menubar)
        # self.text = "可支持下列函数的加减乘除组合运算\n" \
        #             "常用运算符：+,-,*,/,**,//,%\n" \
        #             "常用函数：\n" \
        #             "  sqrt(x)：求平方根\n" \
        #             "数学常数：\n" \
        #             "  虚数单位：I\n" \
        #             "  自然对数的底：E\n" \
        #             "  无穷大：oo\n" \
        #             "  圆周率：pi\n" \
        #             "三角函数：sin(x),cos(x),tan(x)\n" \
        #             "  sec(x),csc(x),cot(x),sinc(x)\n" \
        #             "  及其反函数：sinh(),cosh()等\n" \
        #             "复杂函数：\n" \
        #             "  伽马函数：gamma(x)\n" \
        #             "  贝塔函数：beta()\n" \
        #             "  误差函数：erf(x)\n" \
        #             "指数运算：\n" \
        #             "  指数运算：exp()\n" \
        #             "  自然对数：log()\n" \
        #             "  以十为底的对数：log(var, 10)\n" \
        #             "  自然对数：ln()或log()\n"
        self.text = "可支持下列函数的加减乘除组合运算\n" \
               "\ty=sin(x)\n" \
               "\tcos(x)\n" \
               "\ttan(x)\n" \
               "\tcot(x)\n" \
               "\tx^n\n" \
               "\tP1(x)=x^3+x^2+x+5\n" \
               "---将括号内的表达式命名为P1,P1可\n" \
               "出现于用户构造中"
        self.text_canvas.create_text(20 + 180, 20, text='可识别基本函数', fill='red', font=("Purisa", 25, "bold"))
        center_text(self.text_canvas, self.text, ("Lucida Grande", 15))
        self.text_canvas.bind("<ButtonPress-3>", func=self.clear_text_canvas)
        self.text_canvas.place(x=int(self.attr["width"] * 0.65), y=0)
        self.create_form()


if __name__ == '__main__':
    root = Window()
    screenwidth = root.winfo_screenwidth()
    screenheight = root.winfo_screenheight()
    root_attr = {
        "width": 1200,
        "height": 800,
    }
    alignstr = '%dx%d+%d+%d' % (root_attr['width'], root_attr['height'], (screenwidth - root_attr['width']) / 2,
                                (screenheight - root_attr['height']) / 2)
    root.geometry(alignstr)
    root.resizable(width=False, height=False)
    app = FunctionDisplay(root, root_attr)
    ttk.Style().configure("TButton", font="-size 18")
    ttk.Style().configure("TRadiobutton", font="-size 18")
    root.mainloop()