Interpolation is one form of resampling. One suitable interpolation to avoid aliasing artifacts in the frequency domain is to do Sync interpolation, usually with a windowed Sinc kernel, where the width of the window, and thus the interpolation kernel, depends on the desired signal-to-noise ratio.
The polyphase resampling method, or interpolated polyphase method, is one implementation of this method that uses a precalculated table of the interpolation kernel by phase. But if you don't care about real-time performance, for simpler window functions you can calculate the windowed Sinc interpolation kernal "on the fly" for each interpolated point, thus allowing any interpolation rate, and even time variable interpolation rates.
I have pseudo-code (actually BASIC code) for this here.