We propose a computational method that repurposes embroidery as a tool for 3D fabrication. Given an input mesh, our method computes a freeform stitching pattern, such that an embroidered flat fabric approximates the target geometry. The stitching is done with polyester threads that permanently shrink when heat is applied, thereby generating curvature. Our approach is based on vector field optimization: we jointly optimize a shrinking field over the mesh surface and a corresponding planar parameterization that also allows for seams to arise in order to achieve higher curvatures than through shrinkage alone. Our energy formulation balances fabrication adherence, field smoothness, stitch consistency and validity of stretch values, and is minimized via an alternating algorithm. We demonstrate our method on a variety of target shapes and validate our results through both a digital preview tool and physical fabrication.

The low-poly style is a popular genre of vector graphics that depicts objects and scenes as flat-shaded meshes of low polygon count, often with a limited palette. In this paper, we propose a method to generate 2D low-poly meshes to abstract images. While it has been possible to achieve this look with general-purpose image generators and vector-based diffusion models, the resulting images are not guaranteed to be valid polygonal meshes. A key problem is that polygons overlap or intersect and, in the case of pixel-based image generators, the shapes are often not polygons. Moreover, the colors are not guaranteed to be constrained to a fixed palette. Aside from aesthetic considerations, this has practical consequences: it complicates editing and fabricating the results. We solve this problem by representing an image as a 2D polygonal mesh and optimizing the topology, geometry and coloring of the mesh using score distillation sampling, while enforcing geometric constraints, such as manifoldness and bijectivity. This presents unique challenges due to the discrete nature of the topology, which we handle using a fine-to-coarse strategy based on mesh simplification. By also constraining the colors to a fixed palette, we are able to produce various fabrications such as mosaics, embroidery, crocheting, patchwork and stencils from the resulting vector images.

We propose a modification of the As-Rigid-As-Possible (ARAP) mesh deformation energy with higher order smoothness, which overcomes a prominent limitation of the original ARAP formulation: spikes and lack of continuity at the manipulation handles. Our method avoids spikes even when using single-point positional constraints. Since no explicit rotations have to be specified, the user interaction can be realized through a simple click-and-drag interface, where points on the mesh can be selected and moved around while the rest of the mesh surface automatically deforms accordingly. Our method preserves the benefits of ARAP deformations: it is easy to implement and thus useful for practical applications, while its efficiency makes it usable in real-time, interactive scenarios on detailed models.

Distortion-minimizing surface parameterization is an essential step for computing 2D pieces necessary to fabricate a target 3D shape from flat material. Garment design and textile fabrication are a prominent application example. Common distortion measures quantify length, angle or area preservation in an isotropic manner, so that when applied to woven textile fabrication, they implicitly assume fabric behaves like paper, which is inextensible in all directions and does not permit shearing. However, woven fabric differs significantly from paper: it exhibits anisotropy along the yarn directions and allows for some degree of shearing. We propose a novel distortion energy based on Chebyshev nets that anisotropically penalizes shearing and stretching. Our energy formulation can be used as an optimization objective for surface parameterization and is simple to minimize via a local-global algorithm. We demonstrate its advantages in modeling nets or woven fabric behavior over the commonly used isotropic distortion energies.