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import math
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from collections import OrderedDict
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from time import sleep
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from tkinter import *
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import tkinter.font as tkFont
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from tkinter import messagebox
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from tkinter.ttk import Treeview
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import sympy
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from numpy import arange
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from functionUtil import FunctionUtil
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# 获取文本的宽度和高度
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def get_text_dimensions(canvas, text, font):
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text_id = canvas.create_text(0, 0, text=text, font=font, anchor="center")
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bbox = canvas.bbox(text_id)
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width = bbox[2] - bbox[0]
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height = bbox[3] - bbox[1]
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canvas.delete(text_id)
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return width, height
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# 在画布中央绘制文本
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def center_text(canvas, text, font):
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canvas_width = int(canvas.cget("width"))
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text_width, text_height = get_text_dimensions(canvas, text, font)
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x = canvas_width // 2
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y = 200
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canvas.create_text(x, y, text=text, font=font, anchor="center")
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class Graph(Canvas):
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def __init__(self, master=None, **kwargs):
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super().__init__(master, **kwargs)
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self.width = int(self.cget('width'))
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self.height = int(self.cget('height'))
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self.origin = (self.width / 2, self.height / 2)
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self.bili_x = 20
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self.bili_y = 20
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self.draw_axis()
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self.draw_scale()
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def draw_axis(self):
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"""
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绘制坐标轴
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"""
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self.delete("all")
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self.create_line(0, self.origin[1], self.width, self.origin[1], fill='white', arrow=LAST) # 一象限xy轴
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self.create_line(self.origin[0], 0, self.origin[0], self.height, fill='white', arrow=FIRST)
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def draw_scale(self):
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"""
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绘制刻度值
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"""
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for i in range(-math.ceil((self.origin[0] / self.bili_x)) + 1, math.ceil((self.width - self.origin[0]) / self.bili_x)):
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j = i * self.bili_x
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if (i % 10 == 0):
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self.create_line(j + self.origin[0], self.origin[1], j + self.origin[0], self.origin[1] - 5, fill='black')
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self.create_text(j + self.origin[0], self.origin[1] + 10, text=i)
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for i in range(-math.ceil((self.height - self.origin[1]) / self.bili_y) + 1, math.ceil((self.origin[1] / self.bili_y))):
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j = -(i * self.bili_y)
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if (i == 0):
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continue
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elif (i % 2 == 0):
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self.create_line(self.origin[0], j + self.origin[1], self.origin[0] + 5, j + self.origin[1], fill='black')
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self.create_text(self.origin[0] - 10, j + self.origin[1], text=i)
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def switch_quadrant(self, quadrant):
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"""
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切换象限
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"""
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if quadrant == 1:
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self.origin = (50, self.height - 50)
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else:
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self.origin = (self.width / 2, self.height / 2)
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self.draw_axis()
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self.draw_scale()
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def draw_graph(self, func, draw_precision=0.1, count=1000, bili_x=20, bili_y=40, c='blue'):
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'xmin,xmax 自变量的取值范围； c 图像颜色'
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'x0,y0 原点坐标 w,h 横纵轴半长 draw_precision 步进'
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self.bili_x, self.bili_y = int(bili_x), int(bili_y)
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self.draw_axis()
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self.draw_scale()
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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
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xmin, xmax = -math.ceil((self.origin[0] / self.bili_x)) + 1, math.ceil((self.width - self.origin[0]) / self.bili_x)
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co2 = []
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try:
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for x in arange(xmin, xmax, draw_precision): # draw_precision----画图精度
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y = sympy.sympify(func, convert_xor=True).subs("x", x).evalf()
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coord = self.origin[0] + w1 * x, self.origin[1] - w2 * y, self.origin[0] + w1 * x + 1, self.origin[1] - w2 * y + 1
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if abs(coord[1]) < self.height: # 超过w,h就截断
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co2.append((self.origin[0] + w1 * x, self.origin[1] - w2 * y))
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if count is None:
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length = len(co2)
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else:
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length = len(co2[:int(count)])
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for i in range(length):
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if (draw_precision >= 1):
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self.create_line(co2, fill=c, width=1)
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if (i + 1 == len(co2)):
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break
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if (abs(co2[i][1] - co2[i + 1][1]) > 100):
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continue
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else:
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self.create_line(co2[i], co2[i + 1], fill=c, width=1)
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sleep(0.01)
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self.update()
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except Exception as E:
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messagebox.showerror("错误", message=f"函数有误!\n{E}")
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class ExpressionCanvas(Canvas):
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def __init__(self, master, *args, **kwargs):
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super().__init__(master, *args, **kwargs)
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self.node_width = 60
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self.node_height = 30
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self.x_spacing = 10
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self.y_spacing = 70
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self.level = {}
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def add_node(self, text, x, y, parent=None):
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node_width = len(text) * 5 + 20
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if node_width < 40:
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node_width = 50
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# 创建节点
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coords = [x - node_width / 2, y, x + node_width / 2, y + self.node_height]
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if coords[1] in self.level:
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max_x = max(self.level[coords[1]])
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if coords[0] <= max_x:
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x = max_x + node_width / 2 + self.x_spacing
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node_id = self.create_rectangle(x - node_width / 2, y, x + node_width / 2, y + self.node_height,
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fill="white")
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sleep(0.2)
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self.update()
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elif text == "x":
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x = self.coords(parent)[0] + node_width / 2
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node_id = self.create_rectangle(x - node_width / 2, y, x + node_width / 2, y + self.node_height,
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fill="white")
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sleep(0.2)
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self.update()
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else:
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node_id = self.create_rectangle(x - node_width / 2, y, x + node_width / 2, y + self.node_height, fill="white")
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sleep(0.2)
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self.update()
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coords = [x - node_width / 2, y, x + node_width / 2, y + self.node_height]
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if coords[1] in self.level:
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self.level[coords[1]].append(coords[2])
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else:
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self.level[coords[1]] = [coords[2]]
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text_id = self.create_text(x + 5, y + self.node_height // 2, text=text, anchor="center")
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sleep(0.2)
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self.update()
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# 绘制父节点和当前节点的连线
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if parent:
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parent_coords = self.coords(parent)
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parent_x = parent_coords[0] + (parent_coords[2] - parent_coords[0]) // 2
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parent_y = parent_coords[1] + (parent_coords[3] - parent_coords[1]) // 2
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self.create_line(parent_x, parent_y + self.node_height // 2, x, y, fill="black")
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self.update()
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return node_id
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def draw_expression(self, expression, x, y, parent=None, sibling_width=0):
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# 创建节点并绘制表达式文本
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node = self.add_node(str(expression), x, y, parent=parent)
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if expression.is_Atom:
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return node
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# 处理子表达式
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num_children = len(expression.args)
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total_width = num_children * self.node_width + (num_children - 1) * self.x_spacing
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start_x = x - total_width // 2
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for subexpr in expression.args:
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subnode = self.draw_expression(subexpr, start_x, y + self.y_spacing, parent=node, sibling_width=total_width)
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start_x += self.node_width + self.x_spacing
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return node
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class FunctionDisplay(Frame):
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def __init__(self, master, attr):
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super().__init__(master)
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self.attr = attr
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self.font_style = tkFont.Font(family="Lucida Grande", size=30)
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self.functions = FunctionUtil()
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self.master = master
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self.create_window()
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def clear_text_canvas(self, event):
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def clear_text():
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self.text_canvas.delete("all")
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self.text_canvas.create_text(20 + 180, 20, text='可识别基本函数', fill='red', font=("Purisa", 25, "bold"))
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center_text(self.text_canvas, self.text, ("Lucida Grande", 15))
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self.menu = Menu(self, tearoff=False)
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self.menu.add_command(label="重置", command=clear_text)
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self.menu.post(event.x_root, event.y_root)
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def add_function(self):
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"""
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用户添加函数
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"""
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input_func = self.func_input.get()
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if input_func == "":
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messagebox.showwarning("注意", message="请输入函数！")
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return
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elif input_func.find("=") < 0:
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messagebox.showerror("注意", message="添加函数的格式为：\nSinPlusCos(x)=sin(x)+cos(x)")
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return
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left_var = input_func.split("=")[0]
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right_var = input_func.split("=")[1]
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try:
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function = self.functions.get_function_by_iter(right_var)
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sympy.sympify(function, evaluate=False)
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except Exception as E:
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messagebox.showerror("注意", message="函数解析错误，请仔细检查函数是否正确！")
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self.func_input.delete(0, END)
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return
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if self.functions.check_function_exit(left_var):
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result = messagebox.askokcancel(title='标题~', message=f'函数{left_var}已经存在，是否需要覆盖！')
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if result:
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self.functions.add_function(left_var, right_var)
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messagebox.showinfo(title="提示", message="覆盖成功！")
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self.func_input.delete(0, END)
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return
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self.functions.add_function(left_var, right_var)
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messagebox.showinfo(title="提示", message="添加成功！")
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self.func_input.delete(0, END)
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def update_quadrant(self):
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"""
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更换象限
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"""
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self.axis_canvas.switch_quadrant(self.quadrant.get())
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self.print_function()
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def print_function(self):
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"""
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输出
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"""
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self.text_canvas.delete("all")
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self.text_canvas.level.clear()
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input_func = self.func_input.get()
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if input_func == "":
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messagebox.showwarning("注意", message="请输入函数！")
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return
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step = eval(self.x_step.get()) if not self.x_step.get() == "" else 0.1
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count = self.x_count.get() if not self.x_count.get() == "" else None
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x_scale = self.x_scale.get() if not self.x_scale.get() == "" else 20
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y_scale = self.y_scale.get() if not self.y_scale.get() == "" else 40
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if input_func.find("=") >= 0:
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left_var = input_func.split("=")[0]
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right_var = input_func.split("=")[1]
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if self.functions.check_function_exit(right_var):
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func = self.functions.get_function_by_iter(right_var)
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self.axis_canvas.draw_graph(func, step, count,
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x_scale, y_scale)
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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)
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else:
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self.axis_canvas.draw_graph(right_var, step, count,
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x_scale, y_scale)
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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)
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else:
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if self.functions.check_function_exit(input_func):
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func = self.functions.get_function_by_iter(input_func)
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self.axis_canvas.draw_graph(func, step, count,
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x_scale, y_scale)
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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)
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else:
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self.axis_canvas.draw_graph(input_func, step, count,
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x_scale, y_scale)
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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)
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def create_form(self):
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bottom_frame = Frame(self.master, width=self.attr["width"], height=self.attr["height"] * 0.3)
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self.func_input = Entry(bottom_frame, font=self.font_style, bg="#c0d9d9", width=40)
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self.func_input.grid(row=0, column=0, columnspan=4, padx=30)
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self.add_func_button = Button(bottom_frame, text="用户命名并新增基本函数", command=self.add_function, font=("Lucida Grande", 20))
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self.add_func_button.grid(row=0, column=4, padx=10)
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Label(bottom_frame, text="x步长", font=("Lucida Grande", 20)).grid(row=1, column=0, padx=30)
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self.x_step = Entry(bottom_frame, font=self.font_style, bg="#c0d9d9", width=10)
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self.x_step.grid(row=1, column=1, padx=10, pady=10)
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Label(bottom_frame, text="x个数", font=("Lucida Grande", 20)).grid(row=1, column=2, padx=30)
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self.x_count = Entry(bottom_frame, font=self.font_style, bg="#c0d9d9", width=10)
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self.x_count.grid(row=1, column=3, padx=10, pady=10)
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Label(bottom_frame, text="坐标轴", font=("Lucida Grande", 20)).grid(row=2, column=0, padx=30)
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self.quadrant = IntVar()
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self.quadrant.set(4)
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Radiobutton(bottom_frame, text="四象限", font=("Lucida Grande", 20), indicatoron=False, command=self.update_quadrant, value=4, variable=self.quadrant).grid(row=2, column=1, padx=10, pady=10)
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Radiobutton(bottom_frame, text="一象限", font=("Lucida Grande", 20), indicatoron=False, command=self.update_quadrant, value=1, variable=self.quadrant).grid(row=2, column=2, padx=10, pady=10)
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Label(bottom_frame, text="x放大倍数", font=("Lucida Grande", 20)).grid(row=3, column=0, padx=30)
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self.x_scale = Entry(bottom_frame, font=self.font_style, bg="#c0d9d9", width=10)
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self.x_scale.grid(row=3, column=1, padx=10, pady=10)
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Label(bottom_frame, text="y放大倍数", font=("Lucida Grande", 20)).grid(row=3, column=2, padx=30)
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self.y_scale = Entry(bottom_frame, font=self.font_style, bg="#c0d9d9", width=10)
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self.y_scale.grid(row=3, column=3, padx=10, pady=10)
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Button(bottom_frame, text="输出", font=("Lucida Grande", 20),
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command=self.print_function, height=3, width=5).grid(row=1, rowspan=3, column=4, sticky="w")
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bottom_frame.place(x=0, y=self.attr["height"] * 0.65 + 20)
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def show_user_function(self):
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children_window = Toplevel(root)
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children_window.title("用户自定义函数")
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children_window.geometry('350x260+450+200')
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packet_frame = Frame(children_window)
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packet_frame.grid(row=0, column=0, columnspan=3, padx=10, pady=5)
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function_treeview = Treeview(packet_frame, columns=("function_name", "function"), show="headings")
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function_treeview.heading("function_name", text="函数名称")
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function_treeview.column("function_name", width=100, anchor=CENTER)
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function_treeview.heading("function", text="函数体")
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function_treeview.column("function", width=200, anchor=CENTER)
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function_treeview.pack(side="left", fill="both")
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scrollbar = Scrollbar(packet_frame, orient="vertical", command=function_treeview.yview)
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scrollbar.pack(side="right", fill="y")
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function_treeview.configure(yscrollcommand=scrollbar.set)
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def delete_item():
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selected_item = function_treeview.selection()
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for item in selected_item:
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item_data = function_treeview.item(item)
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function_treeview.delete(item)
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self.functions.data.pop(item_data["values"][0])
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self.functions.save()
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context_menu = Menu(root, tearoff=False)
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context_menu.add_command(label="删除", command=delete_item)
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def popup_menu(event):
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if function_treeview.identify_region(event.x, event.y) == "cell":
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function_treeview.selection_set(function_treeview.identify_row(event.y))
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context_menu.post(event.x_root, event.y_root)
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function_treeview.bind("<Button-3>", popup_menu)
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for function_name, function in self.functions.data.items():
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function_treeview.insert("", "end", values=(function_name, function))
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def create_window(self):
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self.axis_canvas = Graph(self.master, width=self.attr["width"] * 0.65, height=self.attr["height"] * 0.65, bg="#cdcdcd")
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self.axis_canvas.place(x=0, y=0)
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self.text_canvas = ExpressionCanvas(self.master, width=self.attr["width"] * 0.35, height=self.attr["height"] * 0.65, bg="#cdcdcd")
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menubar = Menu(root)
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menubar.add_command(label='查看自定义函数', command=self.show_user_function)
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root.config(menu=menubar)
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# self.text = "可支持下列函数的加减乘除组合运算\n" \
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# "常用运算符：+,-,*,/,**,//,%\n" \
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# "常用函数：\n" \
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# " sqrt(x)：求平方根\n" \
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# "数学常数：\n" \
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# " 虚数单位：I\n" \
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# " 自然对数的底：E\n" \
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# " 无穷大：oo\n" \
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# " 圆周率：pi\n" \
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# "三角函数：sin(x),cos(x),tan(x)\n" \
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# " sec(x),csc(x),cot(x),sinc(x)\n" \
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# " 及其反函数：sinh(),cosh()等\n" \
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# "复杂函数：\n" \
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# " 伽马函数：gamma(x)\n" \
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# " 贝塔函数：beta()\n" \
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# " 误差函数：erf(x)\n" \
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# "指数运算：\n" \
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# " 指数运算：exp()\n" \
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# " 自然对数：log()\n" \
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# " 以十为底的对数：log(var, 10)\n" \
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# " 自然对数：ln()或log()\n"
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self.text = "可支持下列函数的加减乘除组合运算\n" \
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"\ty=sin(x)\n" \
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"\tcos(x)\n" \
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"\ttan(x)\n" \
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"\tcot(x)\n" \
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"\tx^n\n" \
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"\tP1(x)=x^3+x^2+x+5\n" \
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"---将括号内的表达式命名为P1,P1可\n" \
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"出现于用户构造中"
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self.text_canvas.create_text(20 + 180, 20, text='可识别基本函数', fill='red', font=("Purisa", 25, "bold"))
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center_text(self.text_canvas, self.text, ("Lucida Grande", 15))
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self.text_canvas.bind("<ButtonPress-3>", func=self.clear_text_canvas)
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self.text_canvas.place(x=int(self.attr["width"] * 0.65), y=0)
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self.create_form()
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if __name__ == '__main__':
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root = Tk()
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screenwidth = root.winfo_screenwidth()
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screenheight = root.winfo_screenheight()
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root_attr = {
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"width": 1200,
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"height": 800,
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}
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alignstr = '%dx%d+%d+%d' % (root_attr['width'], root_attr['height'], (screenwidth - root_attr['width']) / 2,
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(screenheight - root_attr['height']) / 2)
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root.geometry(alignstr)
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root.resizable(width=False, height=False)
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app = FunctionDisplay(root, root_attr)
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root.mainloop()
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