Hello everyone (and a hapy new year!),

since every student in a MINT-EC-school

^{1} 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-Splines

^{2}, cubic hemite splines

^{3}, NURBS

^{4}) and now want to apply these kinds to the motorsport. Though it might sound confusing in the first moment, in my view, cubic hermite splines

^{3} 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 NURBS

^{4} 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

*m*athematics,

*i*nformatics,

*n*atural sciences and engineering ("

*T*echnik" 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).