import plotly.offline as py
from plotly.graph_objs import *
import numpy as np
from numpy import pi, cos, sin, exp, log, sqrt
py.init_notebook_mode()

def curve(rfun,tmin=-2,tmax=2,tpts=200,color='black'):
    domain = np.linspace(tmin,tmax,tpts)
    r = [[rfun(t)[i] for t in domain] for i in range(3)]
    trace = Scatter3d(x=r[0],y=r[1],z=r[2],mode='lines',
                      line=Line(color=color,width=3))
    return(trace)

def snake(u,v):
    lu, lv = len(u), len(v)
    path = []

    i, j = 0, 0
    istep, jstep = 1, 1
    while(i < lu):
        while(0 <= j < lv):
            path.append((u[i],v[j]))
            j += jstep
        j -= jstep
        i += istep
        jstep *= -1

    i -= istep
    i -= istep
    istep *= -1
    while(0 <= j < lv):
        while(0 <= i < lu):
            path.append((u[i],v[j]))
            i += istep
        i -= istep
        j += jstep
        istep *= -1
    return path

def surface(rfun,tmin=-2,tmax=2,tpts=20,umin=-2,umax=2,upts=20,color='black'):
    t, u = np.linspace(tmin,tmax,tpts), np.linspace(umin,umax,upts)
    path = snake(t,u)
    r = [[rfun(t,u)[i] for (t,u) in path] for i in range(3)]
    trace = Scatter3d(x=r[0],y=r[1],z=r[2],mode='lines',
                      line=Line(color=color,width=3))
    return(trace)

plane1 = surface(lambda t,u: (t,u,(8-3*t+4*u)/5),color='red') #Cartesian form: 3x-4y+5z=8
line2 = curve(lambda t: (t,-3-4*t,4+3*t),color='blue') #Cartesian form: x+y+z=1 and 4*x+y=-3
py.iplot(Figure(data=Data([plane1,line2])))
#Angle of incidence: 19.4 degrees

plane3 = surface(lambda t,u: (2-3*t+u,1+5*u,7+6*t-u),color='green') 
line4 = curve(lambda t: (4*t-1,t,5-2*t),color='purple',tmin=-5,tmax=5)
py.iplot(Figure(data=Data([plane3,line4])))