  We describe an efficient algorithm to compute a conformally equivalent metric
for a discrete surface, possibly with boundary, exhibiting prescribed Gaussian
curvature at all interior vertices and prescribed geodesic curvature along the
boundary. Our construction is based on the theory developed in [Gu et al. 2018;
Springborn 2020], and in particular relies on results on hyperbolic Delaunay
triangulations. Generality is achieved by considering the surface's intrinsic
triangulation as a degree of freedom, and particular attention is paid to the
proper treatment of surface boundaries. While via a double cover approach the
boundary case can be reduced to the closed case quite naturally, the implied
symmetry of the setting causes additional challenges related to stable
Delaunay-critical configurations that we address explicitly in this work.
