Phonetics looks at pronunciation from two main perspectives: the articulatory one - what happens in your mouth and body - and the acoustic one - what you hear with your ears. The presentations used by phoneticians reflect this.
In particular, vowels are usually characterised by their acoustic qualities rather than by how they are produced. (Unfortunately, the IPA vowel quadrilateral is extremely misleading in this respect, using labels like High-Low and Front-Back which appear to describe tongue positions but are actually describing acoustic qualities.)
Because the PronSci approach is an articulatory one, we make use of the much less well known vowel models which reflect actual tongue, lip and jaw movements. In particular, those of Sydney Wood and John Esling (e.g. Wood 1993 Phonum - diagrams relating to this reproduced here, especially s.7; and Esling 2005 Can J Ling).