Armadillo projection with New Zealand, made to illustrate this question by Thomas Ansart.
It's a composed projection, but simpler, since New Zealand is at the margin and outside the main map. Check the variables ended with NZ to see the strange things.
https://d3js.org/d3.v5.min.js
https://d3js.org/d3-geo-projection.v2.min.js
https://d3js.org/topojson.v1.min.js