Dirichlet boundary conditions surrounding four walls 
 Domain dimensions: WxH, with 2 triangles per square  
 Based on FEM2DL_Box Matlab program in Polycarpou, Intro to the Finite 
 Element Method in Electromagnetics, Morgan & Claypool (2006) """


# Lagrange.py: Langrange interpolation tabulated data; 2, 4, 8 degree poly

from visual import*
from visual.graph import*
from visual.controls import *

sceneK = display(x=0,y=0,width=500,height=500,
title='Lagrange Interpolation with Toggle Switch')
graph=curve(color= color.yellow,x=range(0,201),radius=3)
xin = array([0, 25, 50, 75, 100, 125, 150, 175, 200])
yin = array([10.6, 6, 45, 83.5, 52.8, 19.9, 10.8, 8.25, 4.7])
expts=[]                          # Poits to fit
yy=zeros((204),float)
w=150
c = controls(x=300, y=50, width=w, height=w, range=60)
t1 = toggle(pos=(0,0), width=30, height=30, text0='1 polynom deg 8', 
      text1='4 polynms deg. 2', action=lambda:  selectpoly())

def selectpoly():
    global polinom                         # Change previous value
    if t1.value:
        polinom = 3        
    else:
        polinom = 9    

def axis():
    xmin=-200
    xmax=200
    xincr=100
    yincr=400.0/6.0
    ymin=-200
    ymax=200 
    curve(color=color.white,pos=[(-200,-200),(200,-200)])       
    curve(color=color.white,pos=[(-200,-200),(-200,200)])       
    for i in range(0,5):                             # x tics & labels
        curve(pos=[(xmin+xincr*i,ymin),(xmin+xincr*i,ymin-10)],
				         color=color.white)
        xnum=i*50
        xtext= str(xnum)                                                        
        label(pos=(xmin+xincr*i,ymin-30),color=color.white,box=0,text=xtext)
    for i in range(0,7):                             # y tics & labels
        ynum=i*15
        ytext= str(ynum)
        curve(pos=[(xmin-10,ymin+yincr*i),(xmin,ymin+yincr*i)],color=color.white)
        label(pos=(xmin-30,ymin +yincr*i),color=color.white,box=0,text=ytext)

def points():                                        # Data
    for i in range (0,9):
        xc=2*xin[i]-200          #x linear trsn. from 0->100 to -200->200
        yc=40*yin[i]/9.0-200     #y linear trsn. from 0->90  to -200->200
        expts.append(sphere(pos=(xc,yc), radius=8,color=color.red))

def legendrepol (x,beg,finish):          #poly interpolation beg:begining
    y = 0.0;
    for  i in range(beg,finish+1): 
       lambd = 1.0;
       for j in range(beg,finish+1):
           if i != j:                       #Lagrange polynom formed here
              lambd *= ((x - xin[j-1])/(xin[i-1] - xin[j-1]))
       y += (yin[i-1] * lambd)
    return y
 
def plotpoly():
    axis()
    points()                                        # 8th degree poly
    if polinom == 9:                           
       xx=0.0
       for  k in range (0,201):                 
           yy[k]=legendrepol(xx,1,9)
           xc=2*xx-200            
           yc=40*yy[k]/9.0-200    
           graph.x[k]=xc
           graph.y[k]=yc
           xx+=1.0
    graph.pos  
    if polinom==3:                                   # 2nd degree poly's
       xx=0.0
       startat=0
       for mm in range(1,8,2):
           for k in range(startat,startat+50 +1):        
              xx=1.0*k
              yy[k]=legendrepol(xx,mm,mm+2)
              xc=2*xx-200       
              yc=40*yy[k]/9.0-200  
              graph.x[k]=xc
              graph.y[k]=yc
           graph.pos
           startat=startat+50

polinom=9
while 1:
    c.interact()                      # Checks toggle switch
    plotpoly()