there is a knot in my brain. Assume some Datapoints in $\mathbb{R}^3$. I want to fit a surface through them. I found a lot of surfaces such as multiple quadric surfaces (so dont worry that i haven't googled it). I have the following questions:
- Is it correct to say, that a plane is a surface? equation: $0=ax+by+cz+d$
- Isnt $z=ax^2+by^2$ a surface as well?
- Is each other polynomial e.g. $z=ax+by+cx^2+dy^2+ex^3+fy^3$ as well a surface? In that case a cubic? When I google cubic surfaces, I get some really strange one.
I would appreciate any hints which clear my mind.
Horsti