The Wikipedia explanation is too much for me to handle, I need a true for this one
In: Mathematics
B-splines, or Basis Splines, combine the ideas of a basis and a spline.
A basis is a concept from linear algebra. Consider for example the set of all three-dimensional vectors, (x,y,z). A *basis* for that set is a collection of vectors that can combine to form any element of the set. The most simple basis here is {(1,0,0), (0,1,0), (0,0,1)}. Want the vector (5,6,7)? That’s just 5*(1,0,0) + 6*(0,1,0) + 7*(0,0,1), etc. By contrast {(1,0,0), (0,1,0), (0,2,0)} would not be a basis.
A spline is a way of approximating a function with a bunch of other, simpler functions joined together at “knots.” The simplest one is a piecewise linear function.
A Basis Spline is therefore a collection of splines that can be used, via linear combination, to build any other spline. If you’re considering a quadratic spline with 3 knots, there’s a set of basis splines (also quadratic with 3 knots) that can be used to construct it.
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