Surface relaxation techniques are disclosed for smoothing the shapes of three-dimensional (3D) virtual geometry. In one embodiment, a surface relaxation application determines, for each of a number of vertices of a 3D virtual geometry, span-aware weights for each edge incident to the vertex based on the alignment of other edges incident to the vertex with an orthonormal frame of the edge constructed using a decal map. The surface relaxation application uses such span-aware weights to compute weighted averages that provide surface relaxation offsets. Further, the surface relaxation application may restore relaxation offsets from an original to a deformed geometry by determining relaxation offsets for both geometries and transferring the relaxation offsets from the original to the deformed 3D geometry using a blending of the determined relaxation offsets and a rotation. In another embodiment, volume is preserved by computing relaxation offsets in the plane and lifting relaxed vertices back to 3D.