Lecture 7: Intro to Geometry, Splines, and Bezier Curves (19)

kkkhanl

What exactly do the dots represent in this diagram?

Staffjamesfobrien

0.25 spacing of u. So evaluating the curve (line) at ... u=-.5, u=-.25, u=0, u=0.25, u=.5 ...

Aseemrd

Will using different representations of the same curve cause significantly different renders or does it not matter too much which representation we end up choosing?

Staffjamesfong1

@Aseemrd For a perfectly-built rendering pipeline, the exact representation should not matter, only the implied surface. Careful though: if we were to compute $\partial x/\partial u$ for the second parameterization, we end up with a singularity near $u=0$. Your renderer might not be happy with that!

What exactly do the dots represent in this diagram?

0.25 spacing of u. So evaluating the curve (line) at ... u=-.5, u=-.25, u=0, u=0.25, u=.5 ...

Will using different representations of the same curve cause significantly different renders or does it not matter too much which representation we end up choosing?

@Aseemrd For a perfectly-built rendering pipeline, the exact representation should not matter, only the implied surface. Careful though: if we were to compute $\partial x/\partial u$ for the second parameterization, we end up with a singularity near $u=0$. Your renderer might not be happy with that!