SURFACES
The category of 3D surfaces that includes torus, saddle, cone,hyperboloids, paraboloids, ellipsoids, and cones is known as "quadric surfaces".
A quadric surface is a surface that can be defined by a second degree equation in three variables. A quadric surface is an algebric surface.
- Algebraic surfaces: defined by polynomial equations of degree higher than two.
Klein quartic, Barth sextic.
- Parametric surfaces: defined by a set of parameterized equations,
such as a parametric sphere or a parametric surface of revolution.
- Implicit surfaces: defined by an implicit equation of the form F(x,y,z) = 0,
where F is a function of three variables. Boy's surface, Roman surface.
- Fractal surfaces:surfaces that exhibit self-similarity at different scales.
Menger sponge, Sierpinski carpet.
- Non-orientable surfaces: cannot be consistently assigned a normal vector. Möbius strip, the Klein bottle.
These categories are not mutually exclusive