A while ago I wrote to my mayor to ask for better recycling of electronics and other technological items in my home town. The mayor responded rapidly with good news!
In the last installment of this series, we left off Hermite splines asking how we should choose the derivatives at end points so that patches line up nicely, in a visually (or any other context-specific criterion) pleasing way.
Cardinal splines solve part of this problem quite elegantly. I say part of the problem because they address only the problem of the first derivative, ensuring that the curve resulting from neighboring patches are -continuous, that is, the patches line up at the same point, and are -continuous, that is, the first derivatives line up as well. We can imagine splines what are (up to) -continuous, that is, patches lining up, and up to the -th derivatives lining up as well.
Even when you actually want to recycle computer parts (especially scrap parts that do not quite work anymore) it’s quite hard to do so. One possible solution is to simply chuck everything in the usual recycling bin and hope for the best. Or you can try to find a metal reseller. Or you can use the parts in a creative way. Kind of.
I disassembled the CFM01 and got quite a lot of spare parts from the 1U Pentium III servers. The casings aren’t all that interesting since they’re fairly cheap (compared to, say, a Dell PowerEdge server) and the CPUs are useless. Nobody wants them. Even recycling the all-copper heat sink proved a problem. So I used them differently.
In previous posts, we discussed linear and cubic interpolation. So let us continue where we left the last entry: Cubic interpolation does not guaranty that neighboring patches join with the same derivative and that may introduce unwanted artifacts.
Well, the importance of those artifacts may vary; but we seem to be rather sensitive to curves that change too abruptly, or in unexpected ways. One way to ensure that cubic patches meet gracefully is to add the constraints that the derivative should be equal on both side of a joint. Hermite splines do just that.
There are many reasons why you’d like to know if your user liked something or not. It can be used later for recommendation, for example, or to assess whether or not the users want the new feature you’ve just added. And it seems to me that not only the question but also the choices of answers offered matters a lot.
So, let’s say you add an (optional) survey to your application to collect feedback. You can ask a yes/no question like “do you like the new feature?”. The obvious yes/no answer isn’t so obvious. If the users select yes, it means yes, but what if they click no?