Author Topic: A (mathematical) question to the devs  (Read 1052 times)

crashkid3000

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Hello everyone (and a hapy new year!),

since every student in a MINT-EC-school1 during grades 11 and 12 has to write a "Seminararbeit" called term paper in either mathematics, biology, physics or chemistry, I chose mathematics and decided that the topic of my term paper is "splines/spline functions in motorsports". This means, that I firstly presented and explained the (for me) most important kinds of splines (Lagrange-Splines2, cubic hemite splines3, NURBS4) and now want to apply these kinds to the motorsport. Though it might sound confusing in the first moment, in my view, cubic hermite splines3 might have been used already when you tried to get a most possibly "round" connection between two lines/points in a 2D coordinate system (see image), while these NURBS4 should be known already by the guys working with CAD programs.

In general, I just ask you if you are using one of these three examples of splines, how much you use them and where (e.g. in the design/modeling of cars/racetracks, ...).

"happy crashing" wishes you crashkid3000

1: grammar schools which have a focus on mathematics, informatics, natural sciences and engineering ("Technik" in German)
2: kind of splines that simply connect two (or more) points with each other, ignoring "roundness" at interval boundaries and leading often enough to "knees" at these points
3: cubic functions, connecting two points with each other in a certain, adjustable slope
4: non-uniformal rational B-splines

And here's the image:

This "cubic" hermite function interpolates the null of each linear function ((0.25|0) and (1|0), when we write P(x|y)), furthermore having the same slope of each function at these two nulls (2 at the left-hand side null, -2 at the right-hand side null). And just in case if you were asking youself why I wrote cubic in quotes: coincidentally, the cubic part becomes here 0, meaning that this function is actually a square function; nevertheless, the algorithm used wouldn't work always with square funcions, since you define all in all 4 properties (two points with each one slope), but a square function offers just three variables (a*x²+b*x+c).
... enjoys wrecking other cars

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