Question: Defining big piecewise parametric function

Hello, I have about 80 equations for x and 80 equations for y. They are called Sx_0 .. Sx_80 for x and Sy_0 .. Sy_80. They all depend on parameter m.

I want to define a new piecewise function P such as,

P evaluated at m=i  is equal to [  Sx_floor(i) evaluated at i , Sy_floor(i) evaluated at i ]

For example,

P(20.4) would be equal to [  Sx_20 evaluated at 20.4 , Sy_20 evaluated at 20.4]
P(37.9) would be equal to [  Sx_37 evaluated at 37.9 , Sy_37 evaluated at 37.9]

I need this because I want to compute arclength of the function P, let's say, from m=2 to m=52. The arclength goes through many pieces of the function, so I need a way to take this into account.

Thank you very much


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