#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""


"""
from numpy import dot, cross, array, zeros, random
import volmdlr as vm
import math
from scipy.linalg import norm


def PointProjectionPlane(point, plane_origin, plane_normal):
    """
    Plane is defined by (plane_point,plane_normal)
    :returns : coordinates in global coordinate system
    """
    return vm.Point2D(point-dot(point-plane_origin,plane_normal)*plane_normal)

#def PointLocalProjectionPlane(point, plane_origin, x1, x2):
#    """
#    Plane is defined by (plane_point,x1,x2)
#    :returns : coordinates in local coordinate system
#    """
#    x1 = x1.vector
#    x2 = x2.vector
#    point = point.vector
#    plane_origin = plane_origin.vector
#    plane_normal = cross(x1,x2)
#    xp = point-dot(point-plane_origin,plane_normal)*plane_normal-plane_origin# projeted point
#    return vm.Point2D((dot(xp,x1),dot(xp,x2)))

def Euler2TransferMatrix(psi, theta, phi):
    """
    Give Transition Matrix from euler angles
    Angles in radians
    """

    cpsi=math.cos(psi)
    spsi=math.sin(psi)
    ctheta=math.cos(theta)
    stheta=math.sin(theta)
    cphi=math.cos(phi)
    sphi=math.sin(phi)
    P=array([[cphi*cpsi-sphi*ctheta*spsi,-spsi*cphi-cpsi*ctheta*sphi,stheta*sphi],
             [cpsi*sphi+spsi*ctheta*cphi,-sphi*spsi+cphi*ctheta*cpsi,-stheta*cphi],
             [spsi*stheta,cpsi*stheta,ctheta]])
    return P
    

def TransferMatrix2Euler(R):
    if ((R[2,2]!=1)&(R[2,2]!=-1)):
        theta=math.acos(R[2,2])
        psi=math.atan2(R[2,0]/math.sin(theta),R[2,1]/math.sin(theta))
        phi=math.atan2(R[0,2]/math.sin(theta),-R[1,2]/math.sin(theta))
    else:
        phi=0
        if R[2,2]==1:
            theta=0
            psi=math.atan2(R[1,0],R[0,0])
        else:
            theta=math.pi
            psi=-math.atan2(R[1,0],R[0,0])
    return(array([psi,theta,phi]))

    
def Direction2Euler(u, v=random.random(3)):
#    u=npy.array([ux,uy,uz])
    u = u/norm(u)
    R = zeros((3,3))
    R[:,0] = u
    v = v-dot(u,v)*u
    v = v/norm(v)
    w = cross(u,v)
    R[:,1] = v
    R[:,2] = w
    euler = TransferMatrix2Euler(R)
    return euler


def Huygens2D(I1, area, point1, point2):
    """
    area acts the same way as the mass in 3D
    """
    a, b = point1.vector-point2.vector
    I2 = I1+area*array([[b**2,-a*b],[-a*b,a**2]])
    return I2

