Field-Aware Parameterization for 3D Painting

We present a two-phase method that generates a near-isometric parameterization using a local chart of the surface while still being aware of the geodesic metric. During the first phase, we utilize a novel method that approximates polar coordinates to obtain a preliminary parameterization as well as the gradient of the geodesic field. For the second phase, we present a new optimization that generates a near isometric parameterization while considering the gradient field, allowing us to generate high quality parameterizations while keeping the geodesic information. This local parameterization is applied in a view-dependent 3D painting system, providing a local adaptive map computed at interactive rates.