Let's say I have a piecewise function that's continuous in an interval [1,7]:
$f(x) = \left\{ \begin{array}{lr} -5x + 6 & : x \in [1,2)\\ -4x + 14 & : x \in [2,3)\\ -0.25x + 2.75 & : x \in [3,7] \end{array} \right.$
How would I get a discretization of that function that consists of 10 equidistant points? [I'm interested in method(s), not calculations for that example.]
More generally, how would I discretize functions with any number of parameters to get n equidistant points (e.g., to represent the surface of a sphere with 100 equidistant points)?