  We study log Calabi-Yau varieties obtained as a blow-up of a toric variety
along hypersurfaces in its toric boundary. Mirrors to such varieties are
constructed by Gross-Siebert from a canonical scattering diagram built by using
punctured log Gromov-Witten invariants of Abramovich-Chen-Gross-Siebert. We
show that there is a piecewise linear isomorphism between the canonical
scattering diagram and a scattering diagram defined algortihmically, following
a higher dimensional generalisation of the Kontsevich-Soibelman construction.
We deduce that the punctured log Gromov-Witten invariants of the log Calabi-Yau
variety can be captured from this algorithmic construction. As a particular
example, we compute these invariants for a non-toric blow-up of the three
dimensional projective space along two lines. This generalizes previous results
of Gross-Pandharipande-Siebert on "The Tropical Vertex" to higher dimensions.
