If you instead had a function f : R^3 -> R^3, would you get "filled-in" 3D geometry instead of just a surface? Is this ever desirable, or is the surface of our shapes generally all we need for graphics purposes?

daria

If we pick a point (u,v) outside the surface would f(u,v) be 0?

jonasjiang

Does the surface in u-v plane serve as the domain for the function?

kurt

Why do we introduce (u, v) here? Do they have some geometrical meanings?

ShallowDream

Why do we map R^2 to R^3 here?

spidey

^^ Usually, aren't we going from R^3 to R^2? Why and how in this situation do we start of with this 2D model and produce a 3D model from it?

MrRockefeller

can we conclude that explicit->parametric form, implicit->function form?

Concurrensee

Is there exist any good coordinates that accelerates the computation of this form?

If you instead had a function f : R^3 -> R^3, would you get "filled-in" 3D geometry instead of just a surface? Is this ever desirable, or is the surface of our shapes generally all we need for graphics purposes?

If we pick a point (u,v) outside the surface would f(u,v) be 0?

Does the surface in u-v plane serve as the domain for the function?

Why do we introduce (u, v) here? Do they have some geometrical meanings?

Why do we map R^2 to R^3 here?

^^ Usually, aren't we going from R^3 to R^2? Why and how in this situation do we start of with this 2D model and produce a 3D model from it?

can we conclude that explicit->parametric form, implicit->function form?

Is there exist any good coordinates that accelerates the computation of this form?