How do I perform chebyshev interpolation from a to b with custom angle range?

Typically Chebyshev interpolation from $-1$ to $1$ with angle from $0$ to $\pi$:

• $\xi_j=\cos \left ({\pi j \over N}\right )$
• $x_j=(1+\xi_j) * {L \over 2}$
• $w$:
• $w_0=\pi/(2N)$
• $w_{1,...,N-1}=\pi/(N)$
• $w_N=\pi/(2N)$

I appear to have a need in the same with angle from $0$ to $\pi/2$ only, while solving a collocation grid problem where mesh is very fine inside of the computational domain and gets coarser near computational domain boundary. Literature review does not appear to be fruitful.

• Can you not simply map the input angles to the appropriate range by multiplying by 2? If that's not the solution, you may need to explain more carefully. – Bill Barth Jan 3 '14 at 16:41
• The standard practice is to map whatever computational domain you have to [-1,1]. So if you have $f(t), t \in [0, 1]$, just do $f(g(t)), g(t) = \frac{t+1}{2}$. – Jay Lemmon Jan 4 '14 at 18:04
• This question is poorly written with no prior research. I'm surprised how you people manage to like it. (Mapping is indeed the working solution.) – user5273 Jan 31 '14 at 3:04