TutteNet: Injective 3D Deformations by Composition of 2D Mesh Deformations

Figure 1 . Elastically deforming a NeRF [55] based on user-designated positioning of the head (turned) tail (bent) and body (lowered), and optimizing the degrees of freedom of TutteNet to minimize the elastic energy of the deformation. TutteNet guarantees an injective (1-to-1) deformation of the ambient 3D space surrounding the T-Rex, ensuring the NeRF is rendered correctly without artifacts by enabling "pulling back" points and view directions from deformed space. Each layer within TutteNet views the T-Rex over a different 2D plane (in this case, alternating between the 3 main axes in a tri-plane manner). In each layer, the T-Rex is enveloped with a regular 2D mesh of the unit square (top row). The 2D mesh is deformed using the layer's optimizeable parameters which define a Tutte's embedding [19, 80] (bottom row). This defines an injective 2D piecewise-linear map, which can be applied to the 3D T-Rex, without modifying the normal direction to the plane, resulting in an injective 3D deformation i . Composition of these layers yields the final expressive 3D injective deformation.