Title : 
How to Solve a Cubic Equation, Part 4: The 111 Case
         
        
        
            Author_Institution : 
Microsoft Research
         
        
        
        
        
        
        
            Abstract : 
It should not be surprising that in solving cubic equations, sooner or later you are going to have to take the cube root of something. But it´s not immediately obvious what cubic equations have to do with arc cosines. Well, in the general case of complex coefficients and roots we would need to take the cube root of a complex number
         
        
            Keywords : 
equations; complex coefficients; complex roots; cube root; cubic equation; Differential algebraic equations; Differential equations; Numerical stability; Blinn; cubic equations; Algorithms; Mathematics; Numerical Analysis, Computer-Assisted;
         
        
        
            Journal_Title : 
Computer Graphics and Applications, IEEE
         
        
        
        
        
            DOI : 
10.1109/MCG.2007.10