Lecture 7: Intro to Geometry, Splines, and Bezier Curves (33)
CharlesLiu02
Do we use u_0 = 0 and u_1 = 1 because it allows us to calculate our matrix coefficients the easiest?
Zc0in
I think we choose these two points for that it is easy to calculate. Actually, you can choose whatever you want.
Staffjamesfobrien
The parameterization is mostly arbitrary, so we might as well pick something that makes things easier.
jonathanlu31
Is u just an arbitrary variable that represents where along the curve the function is at? So for 2D, there'd be x(u) and y(u) and for a 3d surface, you'd have z(u) as well?
Staffjamesfobrien
@ jonathanlu31 , exactly! (Except I think you meant for a 3D curve, not surface. If there is only one parametric variable then the result will be one-dimensional. If you had x(u,v), y(u,v), and z(u,v) then that would give you a 2D surface in 3D.)
Do we use u_0 = 0 and u_1 = 1 because it allows us to calculate our matrix coefficients the easiest?
I think we choose these two points for that it is easy to calculate. Actually, you can choose whatever you want.
The parameterization is mostly arbitrary, so we might as well pick something that makes things easier.
Is u just an arbitrary variable that represents where along the curve the function is at? So for 2D, there'd be x(u) and y(u) and for a 3d surface, you'd have z(u) as well?
@ jonathanlu31 , exactly! (Except I think you meant for a 3D curve, not surface. If there is only one parametric variable then the result will be one-dimensional. If you had x(u,v), y(u,v), and z(u,v) then that would give you a 2D surface in 3D.)