I'm not quite sure I get the difference between these two representations. I had thought that the implicit definition was a function, whereas the explicit representation is just a series of points.
However, here you've defined the points on a sphere as a vector-valued function $f(u, v) = (cos(u)sin(v), sin(u)sin(v), cos(v))$. Wouldn't that be implicit?
cmate
From how I understood, representation is implicit when point values are not explicitly known but we only know the relationship (Slide 20). Here we would know explicitly what x, y, z values would be for a point (u,v), than just an implicit relationship between three values. I think it is confusing since on this slide each x, y, z values are aggregated/summarised by u and v range and sin and cos functions, but still that cos/sin functions are just for explicitly getting each value, not one implicit function for the shape.
ecohen2
^^ I am also a little confused about this since if we know the relationship isn't implicit just all the points that satisfy that relationship?
csciutto
Figured it out!
http://www.hao-li.com/cs599-ss2015/slides/Lecture02.1.pdf
I'm not quite sure I get the difference between these two representations. I had thought that the implicit definition was a function, whereas the explicit representation is just a series of points.
However, here you've defined the points on a sphere as a vector-valued function $f(u, v) = (cos(u)sin(v), sin(u)sin(v), cos(v))$. Wouldn't that be implicit?
From how I understood, representation is implicit when point values are not explicitly known but we only know the relationship (Slide 20). Here we would know explicitly what x, y, z values would be for a point (u,v), than just an implicit relationship between three values. I think it is confusing since on this slide each x, y, z values are aggregated/summarised by u and v range and sin and cos functions, but still that cos/sin functions are just for explicitly getting each value, not one implicit function for the shape.
^^ I am also a little confused about this since if we know the relationship isn't implicit just all the points that satisfy that relationship?
Figured it out! http://www.hao-li.com/cs599-ss2015/slides/Lecture02.1.pdf
In linear algebra terms: