# Version 1

# watch out for the file path setting in the Povray class in the graphics.py
# module, which is pre-coded to point to an existing directory

from math import cos,sin,pi,acos,asin,atan,tan
import graphics
from graphics import Povray

# constant
rad2deg = 180/pi # convert radians to degrees
deg2rad = pi/180 # convert degrees to radians

class Vector(graphics.Vector):
    """
    Inherits from previous version in graphics.py but adds
    new methods based on trig functions
    """

    def angle(self, other):
        """
        angle between this and another vector in degrees (to 4 decimal digits)
        """
        dab = self.dot(other)
        ab  = self.length() * other.length()
        return round ( acos(dab/ab) * rad2deg, 4 )

    def rotx(self, degs):
        """
        rotate self around the x axis by deg degrees, return new vector
        """
        t = degs * deg2rad
        newy = self.y * cos(t) - self.z * sin(t) 
        newz = self.y * sin(t) + self.z * cos(t)
        return Vector(self.x, newy, newz)

    def roty(self, degs):
        """
        rotate self around the y axis by deg degrees, return new vector
        """
        t = degs * deg2rad
        newx = self.x * cos(t) - self.z * sin(t) 
        newz = self.x * sin(t) + self.z * cos(t)
        return Vector(newx, self.y, newz)
    
    def rotz(self, degs):
        """
        rotate self around the z axis by deg degrees, return new vector
        """
        t = degs * deg2rad
        newx = self.x * cos(t) - self.y * sin(t) 
        newy = self.x * sin(t) + self.y * cos(t)
        return Vector(newx, newy, self.z)
    
def test():
    """
    Draw a pentagon by rotating a vector around the
    circle and connecting the tips
    """
    p = Povray("pentagon.pov")
    
    p.sphradius = 0.14  # bigger spheres
    p.sphcolor = 'Blue' # make them blue
    
    v0 = Vector(4,0,0)  # point out to the right
    
    v1 = v0.rotz(72)    # sweep 72 degrees to new vector 
    p.edge(v0,v1)       # ... and connect the two tips
    p.point(v0)
    
    v0, v1 = v1, v1.rotz(72)  # rotate another 72 degrees
    p.edge(v0,v1)             # connect previous to new vector
    p.point(v0)    

    v0, v1 = v1, v1.rotz(72)  # and so on
    p.edge(v0,v1)
    p.point(v0)    

    v0, v1 = v1, v1.rotz(72)
    p.edge(v0,v1)
    p.point(v0)    

    v0, v1 = v1, v1.rotz(72)  # do it 5 times (5 * 72 = 360)
    p.edge(v0,v1)
    p.point(v0)    

    p.close()
    
def ngon(n):
    p = Povray("ngon.pov")
    p.sphradius = 0.14  # bigger spheres
    p.sphcolor = 'Blue' # make them blue

    sweep = 360.0/n
    
    v0 = Vector(4,0,0)  # point out to the right
    v1 = v0.rotz(sweep) # sweep to new vector 
    
    for i in range(n):
        p.edge(v0,v1)       # ... and connect the two tips
        p.point(v0)
        v0, v1 = v1, v1.rotz(sweep)  # and so on