Abstract: Surface parameterization is a significant topic in computer graphics and computer-aided design, with a wide
range of applications. Surface parameterization aims to seek the minimization of some intrinsic geometry distortion
(such as edge length, angle, and area) from 3D surface to a parameterization plane transformation. Angle-preserving
parameterization preserves the local shape of the surface before and after parameterization, also known as conformal
parameterization. This survey introduced the recent progress on triangular mesh surface conformal parameterization
from computer graphics application angle. Based on different parameter domains, it mainly discussed planar
parameterization, spherical parameterization, and hyperbolic parameterization. Finally, this survey presented a list of
open research problems and possible future research directions.

Key words:  triangular meshes, conformal parameterization, conformal transformation, surface topology, discrete Ricci
flow