Definition of 2D Biquadratic Surface - 65 Characters

[Shaddyab]

What is the definition of 2D biquardatic surface?

is it:
ax^2 + by^2 +cx^2y + dxy^2 +exy +fx +gy +h + ix^2y^2

or is it simpler than this.

 

[mathman]

What you have is part of a definition.

A parametric representation of a biquadratic surface looks like:

x=x(u,v)
y=y(u,v)
z=z(u,v)

Where the three functions of u and v have the form you described.

 

[Shaddyab]

I think I am more confused right now.
I am trying to fit a biquardatic surface to my data and I would like to know what is the definition of such a surface

Thanks

 

[mathman]

I think I am more confused right now.
I am trying to fit a biquardatic surface to my data and I would like to know what is the definition of such a surface

Thanks

Do you know how to define a surface? There is the parametric approach, where (x,y,z) are defined as functions of two parameters. Alternatively on can describe a surface in the form f(x,y,z)=0.

Example - sphere: x² + y² +z² - r² = 0.

or
x=rcosucosv
y=rcosusinv
z=rsinu

where -π/2 ≤ u ≤ π/2 and 0 ≤ v < 2π.

 

[CellCoree]

The definition of a 2D biquadratic surface is a surface that can be represented by a polynomial equation up to the fourth degree in two variables, x and y. This equation typically includes terms such as x^2, y^2, xy, and constants.