Mean value coordinates for quad cages in 3D

SessionNets, Cages and Meshes

Event Type

Technical Papers

TimeWednesday, 5 December 20183:18pm - 3:39pm

LocationHall B5(1) (5F, B Block)

DescriptionSpace coordinates offer an elegant, scalable and versatile framework to propagate (multi-)scalar functions from the boundary vertices of a 3-manifold, often called a cage, within its volume. These generalizations of the barycentric coordinate system have progressively expanded the range of eligible cages to triangle surface meshes with arbitrary topology, concave regions

and a spatially-varying sampling ratio, while preserving a smooth diffusion of the prescribed on-surface functions. In spite of their potential for major computer graphics applications such as freeform deformation or volume texturing, current space coordinate systems have only found a moderate impact in applications. This follows from the constraint on having only triangles in the cage, while many application scenarios favor quad meshes for their ability to align the surface structure with features and to naturally cope with anisotropic sampling. In order to use space coordinates with quad cages, one must triangulate them, which results in large propagation distorsion. Instead, we propose a generalization of a popular coordinate system – Mean Value Coordinates – to quad and tri-quad cages, bridging the gap between high-quality coarse meshing and volume diffusion through space coordinates. Our method can process non-planar quads, comes with a closed-form solution free from global optimization and reproduces the expected behavior of Mean Value Coordinates, namely smoothness within the cage volume and continuity everywhere. As a result, we show how these coordinates compare favorably to classical space coordinates on triangulated quad cages, in particular for freeform deformation and volumetric texturing.

and a spatially-varying sampling ratio, while preserving a smooth diffusion of the prescribed on-surface functions. In spite of their potential for major computer graphics applications such as freeform deformation or volume texturing, current space coordinate systems have only found a moderate impact in applications. This follows from the constraint on having only triangles in the cage, while many application scenarios favor quad meshes for their ability to align the surface structure with features and to naturally cope with anisotropic sampling. In order to use space coordinates with quad cages, one must triangulate them, which results in large propagation distorsion. Instead, we propose a generalization of a popular coordinate system – Mean Value Coordinates – to quad and tri-quad cages, bridging the gap between high-quality coarse meshing and volume diffusion through space coordinates. Our method can process non-planar quads, comes with a closed-form solution free from global optimization and reproduces the expected behavior of Mean Value Coordinates, namely smoothness within the cage volume and continuity everywhere. As a result, we show how these coordinates compare favorably to classical space coordinates on triangulated quad cages, in particular for freeform deformation and volumetric texturing.