A 2D biquadratic surface can be defined using a polynomial equation that includes terms up to the fourth degree in x and y, such as ax^2 + by^2 + cx^2y + dxy^2 + exy + fx + gy + h + ix^2y^2. Alternatively, it can be represented parametrically with functions x = x(u,v), y = y(u,v), and z = z(u,v) that describe the surface in terms of two parameters. The discussion highlights confusion around the complexity of defining such surfaces and emphasizes the need for clarity in the definition. It also mentions the possibility of defining surfaces through implicit equations, like f(x,y,z)=0. Understanding both parametric and implicit representations is crucial for fitting a biquadratic surface to data.
