You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
369 lines
17 KiB
369 lines
17 KiB
from time import sleep
|
|
from ttkbootstrap import *
|
|
import tkinter.font as tkFont
|
|
from tkinter import messagebox
|
|
|
|
import numpy as np
|
|
from matplotlib.figure import Figure
|
|
from matplotlib.backends.backend_tkagg import FigureCanvasTkAgg
|
|
|
|
import sympy
|
|
from numpy import arange
|
|
from sympy import symbols, lambdify
|
|
|
|
from functionUtil import FunctionUtil
|
|
|
|
|
|
# 在画布中央绘制文本
|
|
def center_text(canvas, text, font):
|
|
canvas_width = int(canvas.cget("width"))
|
|
x = canvas_width // 2
|
|
y = 200
|
|
canvas.create_text(x, y, text=text, font=font, anchor="center")
|
|
|
|
|
|
class Graph(Canvas):
|
|
"""
|
|
绘制函数图形
|
|
"""
|
|
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()
|
|
self.fig = FigureCanvasTkAgg()
|
|
|
|
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 draw_graph_3d(self, func, draw_precision=0.1, count=1000, bili_x=20, bili_y=40, ):
|
|
self.fig.get_tk_widget().destroy()
|
|
self.delete("all")
|
|
# 创建 sympy 符号
|
|
x, y = symbols('x y')
|
|
self.bili_x, self.bili_y = int(bili_x), int(bili_y)
|
|
# 将表达式转换为可计算的函数
|
|
expr = lambdify((x, y), func, modules=['numpy'])
|
|
xmin, xmax = -math.ceil((self.origin[0] / self.bili_x)) + 1, math.ceil(
|
|
(self.width - self.origin[0]) / self.bili_x)
|
|
# 创建数据网格
|
|
X = np.linspace(xmin, xmax, int(draw_precision * 100))
|
|
Y = np.linspace(xmin, xmax, int(draw_precision * 100))
|
|
X, Y = np.meshgrid(X, Y)
|
|
Z = expr(X, Y)
|
|
# 创建一个 Figure 对象
|
|
fig = Figure(figsize=(5.5, 6), dpi=100)
|
|
# 在 Figure 上创建一个 3D 子图
|
|
ax = fig.add_subplot(111, projection='3d')
|
|
# 绘制三维图形
|
|
ax.plot_surface(X, Y, Z, cmap='viridis')
|
|
self.fig = FigureCanvasTkAgg(fig, master=self)
|
|
self.fig.draw()
|
|
self.fig.get_tk_widget().pack(fill=BOTH, ipadx=0, ipady=0, pady=0, padx=0)
|
|
|
|
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.fig.get_tk_widget().destroy()
|
|
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 = -math.ceil((self.origin[0] / self.bili_x)) + 1, math.ceil(
|
|
(self.width - self.origin[0]) / self.bili_x)
|
|
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:
|
|
try:
|
|
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()
|
|
except Exception as E:
|
|
pass
|
|
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()
|
|
self.load_user_function()
|
|
|
|
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='提示', 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)
|
|
self.load_user_function()
|
|
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)
|
|
self.load_user_function()
|
|
|
|
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:
|
|
input_func = input_func.split("=")[1]
|
|
if self.functions.check_function_exit(input_func):
|
|
func = self.functions.get_function_by_iter(input_func)
|
|
self.axis_canvas.draw_graph_3d(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_3d(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 load_user_function(self):
|
|
self.user_function_canvas.delete(ALL)
|
|
self.user_function_canvas.create_text(20 + 90, 35, text='可识别基本函数', fill='red', font=("Purisa", 20, "bold"))
|
|
num = 2
|
|
self.user_function_canvas.create_text(0, 70, anchor="nw", text="函数", font=("", 15))
|
|
self.user_function_canvas.create_text(100, 70, anchor="nw", text="函数体", font=("", 15))
|
|
for function, function_body in self.functions.data.items():
|
|
self.user_function_canvas.create_text(0, 20 * num + 50, anchor="nw", text=function, font=("", 15))
|
|
self.user_function_canvas.create_text(100, 20 * num + 50, anchor="nw", text=function_body, font=("", 15))
|
|
num += 1
|
|
self.user_function_canvas.update()
|
|
self.user_function_canvas.configure(scrollregion=self.user_function_canvas.bbox("all"))
|
|
|
|
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 create_window(self):
|
|
self.axis_canvas = Graph(self.master, width=self.attr["width"] * 0.45, 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")
|
|
self.text_canvas.place(x=int(self.attr["width"] * 0.45), y=0)
|
|
user_function = Frame(self.master, width=self.attr["width"] * 0.2, height=self.attr["height"] * 0.65)
|
|
user_function.place(x=int(self.attr["width"] * 0.8), y=0)
|
|
self.user_function_canvas = Canvas(user_function, width=self.attr["width"] * 0.18,
|
|
height=self.attr["height"] * 0.63, background="#cdcdcd")
|
|
y_scrollbar = Scrollbar(user_function, orient="vertical", command=self.user_function_canvas.yview)
|
|
x_scrollbar = Scrollbar(user_function, orient="horizontal", command=self.user_function_canvas.xview)
|
|
x_scrollbar.pack(side=BOTTOM, fill=BOTH)
|
|
y_scrollbar.pack(side=RIGHT, fill=BOTH)
|
|
self.user_function_canvas.pack(side=TOP, fill=BOTH)
|
|
self.user_function_canvas.config(yscrollcommand=y_scrollbar.set, xscrollcommand=x_scrollbar.set)
|
|
for i in range(1, 200):
|
|
self.user_function_canvas.create_text(80, i * 20 + 35, text="fdsaf{}".format(i))
|
|
self.user_function_canvas.config(scrollregion=self.user_function_canvas.bbox("all"))
|
|
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()
|