SmtC: Show me the Code
Ole Peter Smith
Instituto de Matemática e Estatística
Universidade Federal de Goiás
http://www.olesmith.com.br

2nd Order
Quando eu dou de comer aos pobres
Me chamam de santo
Quando eu pergunto por que eles são pobres
Me chamam de comunista
Dom Helder Câmera
< 1st Order | Determinant | Curvature >
  • Determinant:
    [; D(t)= \underline{ \widehat{r} }'(t) \cdot \underline{r}''(t) = y''(t)x'(t)-x''(t)y'(t) ;]
    • [;D(t()>0;]: Goes to the Left
    • [;D(t()<0;]: Goes to the Right
    • [;D(t()=0;]: 2nd Order Effects
Python Listing: Determinant.py. 
    ##!
    ##! Calculate curve Determinant.
    ##!
    
    def Calc_Determinant(self,t):
        if (t.__class__.__name__=="float"):
            return self.dR(t).Hat2()*self.d2R(t)
        else:
            return self.dR[t].Hat2()*self.d2R[t]

    Dets=[]
    
    ##!
    ##! Calculate and store Determinants.
    ##!
    
    def Calc_Determinants(self,ts=[]):
        ts=self.Get_ts(ts)
        self.Dets=[]
        for i in range( len(ts )):
            self.Dets[i].append(  self.Calc_Determinant(i) )
            
        return self.Dets
< 1st Order | Determinant | Curvature >
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