Hitchin grafting representations I: Geometry

We give a geometric interpretation of Fock–Goncharov positivity and show that bending deformations of Fuchsian representations stabilize a uniform Finsler quasi-convex disk in the symmetric space ${\mathrm{P}\mathrm{S}\mathrm{L}}_d(\mathbb{R})\mathrm{/}\mathrm{P}\mathrm{S}\mathrm{O}(d)$.