Cubic Spline Interpolation (Part B) | Lecture 45 | Numerical Methods for Engineers

[@ToothbrushMan]

Small point at 5:37. Alas, this has nothing to do with rope. In shipbuilding, a shipwright would lay out the shape of the hull on the ground using stakes or nails. To interpolate between these nails, they would bend long strips of wood (birch?) around the nails and then draw lines along then strips to get smooth curves. These strips of wood are called "splines" and you can show that they would bend in a very close approximation to cubic polynomials. In fact, putting the second derivative at the end points equal to zero is what the real wooden splines would do. Of course, these strips needed to be as uniform as possible - almost perfect - and a set of splines could be quite expensive. The chief cause of imperfection in splines would be knots in the tree from which they came. Hence the term. They could cause the smooth curve to kink at the knots. Everything is done on computers today of course, but I remember my father having a set of splines when he worked at his draughtsman table.

[@coderide]

Nice, good to know the story behind it.

[@curiash]

One of the best

[@user-xv1gz8bd1d]

Thank you

[@talyaavruch3510]

Thank you for the great video! Is it possible for all the polynomials to be the same even when there are lots of dots to connect and one condition for all of them (say yi=xi^2)? Thanks!

[@eggtimer2]

I wish there was anyone who could explain a spline under tension!

[@اممحمد-ق2ه]

Hello Professor. I have a system of three equations and I want to review the distinguished group, but my calculator is not very efficient. I ask you to help me, please.

[@sorayyakrimi215]

Grazie Professor.

[@justusmzb7441]

Well, My professor is of a different opinion on the last part XD

[@mr.es1857]

Why cubic interpolation?? are there any fourth power or fifth power interpolations out there? Maybe the equations systems gets really tough or maybe it takes a lot of computation time... Help me put with this....

[@martijnb5887]

In a motion system system where a set of positions is prescribed, using cubic splines to determine the entire trajectory ensures that the velocity and acceleration are continuous. Acceleration continuous means continuous forces, which makes the motion smooth and the mechanics happy. Changes in the force are not constant though, which requires instantaneous changes of the currents through the motors, which makes the power amplifiers not happy. Therefore, a fourth order spline can be used to control motion of e.g. a lathe or a mill.

[@KangJangkrik]

Excuse me sir, I would like to ask if you still willing to reply. I have to implement Cubic Spine Interpolation on embedded system for college project and seems like the video didn't mention the "ready-to-use" formula for that problem. There is no matlab function for microcontroller and everything must be written in C, bare hands. Perhaps am I missed something? Thank you

[@coderide]

isn't any library available for that in c?

[@KangJangkrik]

@@coderide which one?

[@user__unknown]

Maitabasa mudzidzisi. 👏

[@NaseerAhmad-dd6pp]

Today's riddle for all let me see who will get correct ans. Q suppose you hve land On ist day you planted one tree On 2nd day you planted 2 trees On 3rd day you plant 4 trees On 5th day you planted 8 trees And ------------------ so on It takes you 100 days to complete the whole land. Now question for all the participants How many days it will take to you to complete the half field of land????

[@МухамедКеримкул]

99

[@isxp]

I think you accidentally left this video as Unlisted. People can find the video using the playlist, but if a person searched the title on youtube, they would not be able to find it.

[@ProfJeffreyChasnov]

Thank you very much! I have now made it public.

[@liberatemi9642]

Try modulating your voice professor - otherwise you sound as if you’re intentionally trying to make a dry subject drier.