We present a 3D stylization algortihm that can turn an input shape into the style of a cube while maintaining the content of the original shape. Cubic sculptures can be captured by the as-rigid-as-possible (ARAP) energy with an L1 regularization on rotated usrface bornals. Minimizing this energy naturally leads to a detail-preserving, cubic geometry. This energy can be minimized efficiently using the local-global approach with alternating direction method of multipliers (ADMM).
Our system takes a 3D shape as input and outputs a deformed shape that has the same style as cubic sculptures. Our method can apply constraints, non-uniform cubeness, different global/local cube orientations, and requires no remeshing and generalizes to polyhedral stylization.
- Discriminative geometric styles: one of the main challenges is to define a similarity metric aligned with human perception. Comparison of projected feature curves, sub-components of a shape, or learned features.
- Generative geometric styles: many geometric flows and filters can be used for creating stylized geometry, such as creating edge-preserving smoothing geometry, piece-wise planar or developable shapes and stylized shapes prescribed by image filters.
- Shape deformation: given modeling constraints, how to deform shapes? One of the most popular choices is the ARAP energy, which measures local rigidity of the surface and leads to detail-preserving deformations. But having nearly interactive performance on highly detailed meshes still remains a major challenge. An alternative is to use the deformation optimizing ARAP on a low resolution model and then recover the original details.
- Axis-alignment in polycube maps: this concept is one of the main instruments in the construction of polycube maps, including defining polycube segmentations and the cost function for polycube deformations.
One tempting direction of creating cubic geometry is to use voxelization, but this fails to capture the details depicted by the artists and can't capture the wide spectrum of cubeness across cubic sculptures.
Another tempting direction is to recover geometric features from the polycube results, which leads to a multi-step algorithm and suffers from limitations of particular detail encoding schemes. Our energy is similar to the polycube energy of Huang et al. 2014 in that we also minimize the ARAP energy with a L1 regularization, but the key difference is that we define the l1-norm on the rotated normals of the original mesh instead. This allows us to optimize energy much faster using the local-global approach with ADMM in only a few seconds.
Input to our method is a manifold triangle mesh with/without boundaries. Our method outputs a cubified shape where each subcomponent has the style of an axis-aligned cube. Meanwhile, our stylization maintains the geometric details of the original mesh. We minimize the ARAP and the cubeness.
By changing the lambda and l1-norm, we can obtain different shapes.