A quad-mesh rigid origami, or flexible quad-mesh, is a polyhedral surface with quadrilateral faces connected in the combinatorics of a rectangular grid, capable of undergoing continuous isometric deformations. Known variations include the Miura-ori (Miura, 1985); V-hedra or eggbox pattern (Voss, 1888; Sauer and Graf, 1931; Montagne et al., 2022); anti V-hedra or flat-foldable pattern (Tachi, 2009); hybrid V-hedra (Tachi, 2010); T-hedra or trapezoidal pattern (Sauer and Graf, 1931; Sharifmoghaddam et al., 2020); and anti-T-hedra (Erofeev and Ivanov, 2020). Izmestiev’s list of flexible Kokotsakis quadrilaterals (2017) paves the way for the generalization of large flexible quad-meshes through providing 3 × 3 ‘building blocks’. We made an initial attempt on constructing large patterns by stitching these blocks in He and Guest (2020). Successful examples include using the proportional couplings and the equimodular couplings. I have developed a keen interest in identifying the convergence of quad-mesh rigid origami to smooth surfaces. The correlation between the isometric deformation of a discrete surface and its smooth counterpart is not only intriguing from a mathematical standpoint but also holds significant practical value in the fields of structural engineering and architectural design. The smooth limit for a V-hedron is known to be a V-surface (Bianchi, 1890; Sauer, 1970), and the smooth limit for a T-hedron is known to be a T-surface (Izmestiev et al, 2024). I will report on our recent progress (arXiv:2412.04298) in identifying the smooth surface limits of new quad-mesh rigid origami constructed using proportional and equimodular couplings.