# Tk_torus.py

# Tk_torus.py

from tkinter import *
from math import sqrt,sin, cos,pi

def torus(x,y,z,angle):
    angle=float(angle)*pi/180
    x1=cos(angle)*x-sin(angle)*y
    y1=sin(angle)*x+cos(angle)*y
    z1=z
    return x1,y1,z1

def project(x,y,z):
    X=xA+(y-x)*sqrt(3)/2
    Y=yA-z+(x+y)/2
    return X,Y

def mix (a,d,g,b,e,h,c,f,i):
    return a*e*i+b*f*g+c*d*h-c*e*g-f*h*a-i*b*d

def normal(a,b,c):
    return sqrt(a*a+b*b+c*c)

def circle(slices):
    delta= 360/slices
    for j in range(0,slices):
        for i in range(0,slices):
            angle=float(i*delta)*pi/180
            x=200+50*cos(angle)
            y=0
            z=0+50*sin(angle)
            x,y,z=torus(x,y,z,delta*j)
            X,Y=project(x,y,z)

            x2,y2,z2=torus(x,y,z,delta)
            X2,Y2=project(x2,y2,z2)

            angle=float((i+1)*delta)*pi/180
            x1=200+50*cos(angle)
            y1=0
            z1=0+50*sin(angle)
            x1,y1,z1=torus(x1,y1,z1,delta*j)
            X1,Y1=project(x1,y1,z1)

            x3,y3,z3=torus(x1,y1,z1,delta)
            X3,Y3=project(x3,y3,z3)

            u,v,w=0,1,1

            level=mix(u,x2-x,x1-x,v,y2-y,y1-y,w,z2-z,z1-z)/(normal(u,v,w)*normal(x2-x,y2-y,z2-z)*normal(x1-x,y1-y,z1-z))*255
            if level<0:
                color="#000000"
            else:
                level=int(level)
                if level<16:
                    color="#00000"+hex(level)[-1:]
                else:
                    color="#0000"+hex(level)[-2:]

            level1=mix(u,x1-x3,x2-x3,v,y1-y3,y2-y3,w,z1-z3,z2-z3)/(normal(u,v,w)*normal(x2-x3,y2-y3,z2-z3)*normal(x1-x3,y1-y3,z1-z3))*255
            if level1<0:
                color1="#000000"
            else:
                level1=int(level1)
                if level1<16:
                    color1="#00000"+hex(level1)[-1:]
                else:
                    color1="#0000"+hex(level1)[-2:]

            if mix(1,x2-x,x1-x,1,y2-y,y1-y,1,z2-z,z1-z)>=0:
                #canvas.create_line(X,Y,X1,Y1,width=2, fill="darkgrey")
                #canvas.create_line(X,Y,X2,Y2,width=2, fill="red")
                canvas.create_polygon(X,Y,X2,Y2,X1,Y1,fill=color)
                canvas.create_polygon(X2,Y2,X3,Y3,X1,Y1,fill=color1)

def axis():
    X,Y=project(0,0,0)
    X1,Y1=project(size*1.5,0,0)
    canvas.create_line(X,Y,X1,Y1,width=2, fill="blue")
    canvas.create_text(X1,Y1-15,text='X',fill='white',font='Arial 15')
    X1,Y1=project(0,size*1.5,0)
    canvas.create_line(X,Y,X1,Y1,width=2, fill="blue")
    canvas.create_text(X1,Y1-15,text='Y',fill='white',font='Arial 15')
    X1,Y1=project(0,0,size*1.5)
    canvas.create_line(X,Y,X1,Y1,width=2, fill="blue")
    canvas.create_text(X1+15,Y1,text='Z',fill='white',font='Arial 15')


xA,yA=450,350
size=200

root= Tk()
root.title("TORUS" )
canvas=Canvas(root, bg="grey", width=900, height=700)
canvas.grid(row=1,column=1)
canvas.create_text(200,100,text='TORUS',fill='white',font='Arial 60 bold')
btn = Button(root,text='Quitt', width =8, command=root.destroy).grid(row=2,column=1)
axis()
circle(180)
X,Y=project(0,0,0)
X1,Y1=project(0,0,size*1.5)
canvas.create_line(X,Y,X1,Y1,width=2, fill="red")
root.mainloop()