Regarding the first example, interpolation looks to be far superior, recreating the original pure sine wave. Resampling looks to creating local variations rather than responding to them.

Regarding the second example, I suspect the resampled signal contains data above the Nyquist frequency of the original sampled data at the peak and therefore violates Shannon’s sampling/reconstruction theory. Assuming the data is sampled correctly the interpolated ‘signal’ (I know it’s still sampled) is the only one that could result in the sampled data. [others would not be sampled correctly at the same rate bacause of their higher frequency content].
Also the interpolated data does not appear to coincide with the original data points

Interpolation could help if you have enough samples.
“Linear interpolation” from figures above is the simplest but with sin(x) and cos(x) is better.

May be the following papers will help to understand better the topic:

1. “ET 4 CO 198.pmd”, http://www.ieindia.org/pdf/88/88ET104.pdf

2. “9 CP PE 8.pmd”, http://www.ieindia.org/pdf/89/89CP109.pdf

3. “Revaluation and replacement of basic terms in the sampling theory”,
http://www.pueron.org/pueron/nauchnakritika/Th_Re.pdf

4. http://www.knowledgerush.com/kr/jsp/db/board.jsp?id=54913
A note about the definitions of “sine/cosine wave”, “sinusoidal/co-sinusoidal signal” and the “simplest band limited signals”.

Best regards
Petre Petrov