Is there ever a purpose of going to a higher degree polynomial or possibly a polynomial in mupltiple variables that could be used for higher degree surfaces?
keenan
@nrauen I haven't seen much (if any) work on using very high degree polynomials to represent surfaces, but that doesn't mean there's not a good use of them somewhere by someone. Another big challenge with higher-degree polynomial interpolation (and which is well-known by anyone who has studied numerical analysis) is Runge's phenomenon. Also, keeping track of things like tangent or curvature continuity across surface patches starts to become a bit of a nightmare.
Is there ever a purpose of going to a higher degree polynomial or possibly a polynomial in mupltiple variables that could be used for higher degree surfaces?
@nrauen I haven't seen much (if any) work on using very high degree polynomials to represent surfaces, but that doesn't mean there's not a good use of them somewhere by someone. Another big challenge with higher-degree polynomial interpolation (and which is well-known by anyone who has studied numerical analysis) is Runge's phenomenon. Also, keeping track of things like tangent or curvature continuity across surface patches starts to become a bit of a nightmare.