Applying conformal geometry for creating a 3D model spatial-consistent texture map

The aim of this research is to achieve spatial consistency of the UV map. We present an approach to produce a fully spatially consistent UV mapping based on the planar parameterisation of the mesh. We apply our method on a 3D digital replica of an ancient Greek Lekythos vessel. We parameterise the mesh of a 3D model onto a unit square 2D plane using computational conformal geometry techniques. The proposed method is genus independent, due to an iterative 3D mesh cutting procedure. Having now the texture of a 3D model depicted on a spatially continuous two dimensional structure enables us to efficiently apply a vast range of image processing based techniques and algorithms.