#!/usr/bin
# -*- coding: utf-8 -*-

import numpy as np
import numpy.linalg as npla
import math as m


dicoNoeud={}
dicoElement={}


class Noeud():
    def __init__(self, idt, x, y):
        
        self.idt = idt
        self.x = x
        self.y = y
        dicoNoeud[self.idt]= self

    def __str__(self):
        a = "Noeud " + str(self.idt) + " :\n"
        a += "- coordonnees : " + str(self.x) + " ; " + str(self.y)
        return a

    def dist(self, xext , yext):
        a = m.sqrt((self.x-xext)**2+(self.y-yext)**2)
        return a
        
    def distnoeud(self, noeud_ext):
	a = m.sqrt((self.x-noeud_ext.x)**2+(self.y-noeud_ext.y)**2)
	return a

class Ressort():
       
    def __init__(self,idt,n1,n2):

        self.idt = idt
        self.n1 = n1 
        self.n2 = n2
        dicoElement[self.idt]=self
        
    def setProp(self,k):
        self.k = k
        self.type= "r"   
     
    def matrice(self):
        adj= (self.n2.x - self.n1.x)
        self.L= self.n1.distnoeud(self.n2)
        self.angle = m.acos(adj/self.L)
        c= m.cos(self.angle)
        s= m.sin(self.angle)
        cs= c*s
        c2 = c*c
        s2= s*s
        d=np.array([[ c2, cs,-c2, -cs],\
                    [ cs, s2,-cs, -s2],\
                    [-c2,-cs, c2,  cs],\
                    [-cs,-s2, cs,  s2]])
        d= d*self.k
        return d

class Barre():
           
    def __init__(self,idt,n1,n2):

        self.idt = idt
        self.n1 = n1 
        self.n2 = n2
        dicoElement[self.idt]=self
        
    def setProp(self,E,S):
        self.E = E
	self.S = S    
        self.L= self.n1.distnoeud(self.n2)
        self.type= "b"
                 
    def matrice(self):
        adj= (self.n2.x - self.n1.x)
        self.angle = m.acos(adj/self.L)
        c= round(m.cos(self.angle),2)
        s= round(m.sin(self.angle),2)
        cs= c*s
        c2 = c*c
        s2= s*s
        d=np.array([[ c2, cs,-c2, -cs],\
                    [ cs, s2,-cs, -s2],\
                    [-c2,-cs, c2,  cs],\
                    [-cs,-s2, cs,  s2]])

        k= (self.E*self.S)/self.L
        d= d*k
        return d
        
class Poutre():

    def __init__(self,idt,n1,n2):
        self.idt = idt
        self.n1 = n1 
        self.n2 = n2
        dicoElement[self.idt]=self
    
    def setProp(self,E,I,S):
        self.E = E
	self.I = I    
        self.S = S
        self.L = self.n1.distnoeud(self.n2)
        self.type = "p" 
    
    def matrice(self):
      
        k1= (self.E*self.S/self.L)
        k2= (self.I*self.E)/(self.L**3)
      
        kg=np.array([[  k1              , 0.             , 0.              , -k1            , 0.              , 0.               ],\
                     [ 0.               , 12*k2          , 6*self.L*k2     , 0.             , -12*k2          , 6*self.L*k2      ],\
                     [ 0.               , 6*self.L*k2    , 4*(self.L**2)*k2, 0.             , -6*self.L*k2    , 2*(self.L**2)*k2 ],\
                     [ -k1              , 0.             , 0.              , k1             , 0.              , 0.               ],\
                     [ 0.               , -12*k2         , -6*self.L*k2    , 0.             , 12*k2           , -6*self.L*k2     ],\
                     [ 0.               , 6*self.L*K2    , 2*(self.L**2)*k2, 0.             , -6*self.L*k2    , 4*(self.L**2)*k2 ]])
                    
        adj= (self.n2.x - self.n1.x)
        self.angle = m.acos(adj/self.L)
        c= round(m.cos(self.angle),2)
        s= round(m.sin(self.angle),2)
        self.q  = np.array([[ c                , -s              , 0.              , 0.              ,  0.             , 0.                ],\
                            [ s                ,  c              , 0.              , 0.              ,  0.             , 0.                ],\
                            [ 0.               ,  0.             , 1.              , 0.              ,  0.             , 0.                ],\
                            [ 0.               ,  0.             , 0.              , c               , -s              , 0.                ],\
                            [ 0.               ,  0.             , 0.              , s               ,  c              , 0.                ],\
                            [ 0.               ,  0.             , 0.              , 0.              ,  0.             , 1.                ]])
        transp_q= np.transpose(self.q)
        d= np.dot(transp_q,kg)
        d= np.dot(d,q)
     
     
        return d