Analysis of information retrieved from microblogging services such as Twitter can provide valuable insight into public sentiment in a geographic region. This insight can be enriched by visualising information in its geographic context. Two underlying approaches for sentiment analysis are dictionary-based and machine learning. The former is popular for public sentiment analysis, and the latter has found limited use for aggregating public sentiment from Twitter data. The research presented in this paper aims to extend the machine learning approach for aggregating public sentiment. To this end, a framework for analysing and visualising public sentiment from a Twitter corpus is developed. A dictionary-based approach and a machine learning approach are implemented within the framework and compared using one UK case study, namely the royal birth of 2013. The case study validates the feasibility of the framework for analysis and rapid visualisation. One observation is that there is good correlation between the results produced by the popular dictionary-based approach and the machine learning approach when large volumes of tweets are analysed. However, for rapid analysis to be possible faster methods need to be developed using big data techniques and parallel methods.