Implicit UVs: Real-time semi-global parameterization of implicit surfaces

Implicit representations of shapes are broadly used in computer graphics since they offer many valuable properties in design, modeling, and animation. However, their implicit and volumetric nature makes applying 2D textures fundamentally challenging. We propose a method to compute point-wise and parallelizable semi-global parameterizations of implicit surfaces for texturing, rendering, and modeling purposes. Our method not only defines local patches of parameterization, but also enables the merging of multiple adjacent patches into large and spatially coherent ones that conform to the geometry. Implemented in shaders into a sphere-tracing pipeline, our method allows users to edit the uv-fields with real-time visualization. We demonstrate how to add rendering details (texture, normal, displacement, etc.) using our parameterization, as well extending modeling tools with implicit shell maps. Furthermore, the textured objects remain implicit and can still be used in a modeling pipeline.