Techniques and tools for mesh processing are described. For example, a multi-chart geometry image represents arbitrary surfaces on object models. The multi-chart geometry image is created by resampling a surface onto a regular 2D grid, using a flexible atlas construction to map the surface piecewise onto charts of arbitrary shape. This added flexibility reduces parameterization distortion and thus provides greater geometric fidelity, particularly for shapes with long extremities, high genus, or disconnected components. As another example, zippering creates a watertight surface on reconstructed triangle meshes. The zippering unifies discrete paths of samples along chart boundaries to form the watertight mesh.