Casey’s Witness Wednesday on Interpolation

He's put up another very informative blog post, leaving the specific topic of grass planting, venturing into more general territory regarding interpolation. And there's a video, from which it is possible to learn a lot of this is a new subject.

Here's the blog post.

Here's the video:

1. Josh Sorengaard

Since I caught up with his postings, I’ve found myself looking forward each Wednesday to the next instalment of Casey’s Witness adventures. While I have no real programming/mathematics background, it’s a testament to Casey’s writing skills that each one still engages and stimulates — on top of the simpler pleasures of watching a job done meticulously well. So consider this a hearty thank you to Casey for taking the time to produce these, and to the team as a whole’s spirit of sharing these little insights.

• Thanks Josh! Glad to hear you are enjoying the series.

– Casey

2. To have all those nice properties I’m assuming that every single W needs to be between 0 and 1 and that something like W0 = 5, W1 = 6 and W2 = -10 doesn’t play as nice.

Having understood all of that I’m at a loss as to how a three point system with 3 Ws would work for interpolation. We are interpolating /what/ exactly? I don’t see how this would work mathematically with 3 points … do we need to redo the tree structure so that instead of starting with 4 points we start with 6? I’m guessing that that’s not the right approach but nothing else comes to mind and I’m probably overcomplicating this stuff :P

3. Are we looking at a release date substantially BEFORE Christmas or around Christmas time?
Thank you!

4. INTPnerd

According to the about section The Witness will be released mid-2014. Technically, this means it will be released June 1, this coming Sunday ;)

• Thank you. Must’ve missed that in the ABOUT section.

5. Martin Sedlak

Very nice!
Casey also showed relation to combinatorics (binomial coefficients) while computing cubic Bezier.
Note that (a+b)^3 is a^3 + 3*a^2*b + 3*a*b^2 + b^3, now replace a with (1-t) and b with t, looks familiar?