Homogeneous coordinates can be used to easily perform a number of transformations, including perspective transformations. Considering a gnomonic projection is a type of perspective projection, I assumed that a transformation of the type could be formulated in a similar way. However, I have not found any literature on the topic. Is it possible, and if so, what would be the transformation matrix?
2026-02-22 21:00:11.1771794011
Can homogeneous coordinates be used to perform a gnomonic projection?
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Sure. W.l.o.g. take the unit sphere at the origin and image plane $z=-1$. The projection matrix is then the standard $\mathtt K [\mathtt I_3 \mid 0]$ from the literature, where $\mathtt K$ is a $3\times3$ matrix that reflects the choice of coordinate system in the image plane. Any other sphere/tangent plane combination can be transformed into this setup via a similarity.