In [1]:

    

import numpy as np
import itertools
from plotly.offline import download_plotlyjs,init_notebook_mode,plot,iplot
import plotly.graph_objs as go
init_notebook_mode(connected=True)


    

In [2]:

    

def p2c(r, theta, phi):
    """Convert polar unit vector to cartesians"""
    return [r * np.sin(theta) * np.cos(phi),
            r * np.sin(theta) * np.sin(phi),
            r * np.cos(theta)]


    

In [3]:

    

class Arrow:
    def __init__(self, theta, phi, out, width=5, color='rgb(0,0,0)'):
        """
        Args:
            theta (float) - radians [0, π]
            phi (float) - radians [0, 2π]
            out (bool) - True if outgoing, False if incoming (to the origin)
            width (int) - line thickness
            color (hex/rgb) - line color
        """
        self.theta = theta
        self.phi = phi
        self.out = out
        self.width = width
        self.color = color
        
        wing_length, wing_angle = self._find_wing_coord()
        
        shaft_xyz = p2c(1., self.theta, self.phi)
        wings_xyz = [p2c(wing_length, self.theta + wing_angle, self.phi),
                     p2c(wing_length, self.theta - wing_angle, self.phi)]
        
        self.shaft = go.Scatter3d(
            x=[0, shaft_xyz[0]],
            y=[0, shaft_xyz[1]],
            z=[0, shaft_xyz[2]],
            showlegend=False, mode='lines', line={'width': self.width, 'color': self.color}
        )
        self.wings = go.Scatter3d(
            x=[wings_xyz[0][0], shaft_xyz[0] / 2., wings_xyz[1][0]],
            y=[wings_xyz[0][1], shaft_xyz[1] / 2., wings_xyz[1][1]],
            z=[wings_xyz[0][2], shaft_xyz[2] / 2., wings_xyz[1][2]],
            showlegend=False, mode='lines', line={'width': self.width, 'color': self.color}
        )
    
        self.data = [self.shaft, self.wings]
    
    
    def _find_wing_coord(self):
        """Finds polar coordinates of arrowhead wing ends"""
        frac = 0.1
        r = 0.5
        sin45 = np.sin(np.pi / 4.)

        if self.out == True:
            d = r - frac * sin45 
        elif self.out == False:
            d = r + frac * sin45    
        else:
            raise TypeError("arg: out must be True or False")

        a = np.sqrt(frac**2 * sin45**2 + d**2)
        alpha = np.arccos(d / a)
        return [a, alpha]


    

In [4]:

    

arr1 = Arrow(theta=0.2*np.pi, phi=0.1*np.pi, out=False, width=2)
arr2 = Arrow(theta=0.7*np.pi, phi=0.9*np.pi, out=True, width=2)

layout = {
    'autosize': True,
    'scene': {
        'aspectmode': 'cube',
        'xaxis': {'range': [-1, 1], 'autorange': False, 'zeroline': True},
        'yaxis': {'range': [-1, 1], 'autorange': False, 'zeroline': True},
        'zaxis': {'range': [-1, 1], 'autorange': False, 'zeroline': True},
        'camera': {
            'up': {'x': 0, 'y': 1, 'z': 0} # DOESN'T WORK -- WHY NOT!?
        }
    }
}

plot_data = arr1.data + arr2.data # joins lists
# plot_data = arr1.data

fig = go.Figure(data=plot_data, layout=layout)
iplot(fig)


    

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