Concept

Splines is a piece-wise polynomial

𝑠(𝑥)|Ω𝑗=𝑎𝑗+𝑏𝑗𝑥+𝑐𝑗𝑥2+𝑑𝑗𝑥3+

where Ω𝑗 is 𝑗-th domain, every domain has their own function.