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