Convexity describes the degree to which any space can be extended in two dimensions. It means that no tangent drawn on the perimeter passes through the space at any point.
Hillier, B. & Hanson, J. (1984), The Social Logic of Space, Cambridge University Press: Cambridge. pp.91,97;
Hillier, B. , Hanson, J., and Peponis, J. (1987) , Syntactic Analysis of Settlements, Arch. & Comport/Arch. Behav., Vol.3, n.3, 217-231. pp.222.