We introduce TetWeave, a novel isosurface representation for gradient-based mesh optimization that jointly optimizes the placement of a tetrahedral grid used for Marching Tetrahedra and a novel directional signed distance at each point. TetWeave constructs tetrahedral grids on-the-fly via Delaunay triangulation, enabling increased flexibility compared to predefined grids. The extracted meshes are guaranteed to be watertight, two-manifold and intersection-free. The flexibility of TetWeave enables a resampling strategy that places new points where reconstruction error is high and allows to encourage mesh fairness without compromising on reconstruction error. This leads to high-quality, adaptive meshes that require minimal memory usage and few parameters to optimize. Consequently, TetWeave exhibits near-linear memory scaling relative to the vertex count of the output mesh — a substantial improvement over predefined grids. We demonstrate the applicability of TetWeave to a broad range of challenging tasks in computer graphics and vision, such as multi-view 3D reconstruction, mesh compression and geometric texture generation. Our code is available at https://github.com/AlexandreBinninger/TetWeave.

Low-resolution quantized imagery, such as pixel art, is seeing a revival in modern applications ranging from video game graphics to digital design and fabrication, where creativity is often bound by a limited palette of elemental units. Despite their growing popularity, the automated generation of quantized images from raw inputs remains a significant challenge, often necessitating intensive manual input. We introduce SD-$\pi$XL, an approach for producing quantized images that employs score distillation sampling in conjunction with a differentiable image generator. Our method enables users to input a prompt and optionally an image for spatial conditioning, set any desired output size $H \times W$, and choose a palette of $n$ colors or elements. Each color corresponds to a distinct class for our generator, which operates on an $H \times W \times n$ tensor. We adopt a softmax approach, computing a convex sum of elements, thus rendering the process differentiable and amenable to backpropagation. We show that employing Gumbel-softmax reparameterization allows for crisp pixel art effects. Unique to our method is the ability to transform input images into low-resolution, quantized versions while retaining their key semantic features. Our experiments validate SD-$\pi$XL's performance in creating visually pleasing and faithful representations, consistently outperforming the current state-of-the-art. Furthermore, we showcase SD-$\pi$XL's practical utility in fabrication through its applications in interlocking brick mosaic, beading and embroidery design.

Abstract We present SENS, a novel method for generating and editing 3D models from hand‐drawn sketches, including those of abstract nature. Our method allows users to quickly and easily sketch a shape, and then maps the sketch into the latent space of a part‐aware neural implicit shape architecture. SENS analyzes the sketch and encodes its parts into ViT patch encoding, subsequently feeding them into a transformer decoder that converts them to shape embeddings suitable for editing 3D neural implicit shapes. SENS provides intuitive sketch‐based generation and editing, and also succeeds in capturing the intent of the user's sketch to generate a variety of novel and expressive 3D shapes, even from abstract and imprecise sketches. Additionally, SENS supports refinement via part reconstruction, allowing for nuanced adjustments and artifact removal. It also offers part‐based modeling capabilities, enabling the combination of features from multiple sketches to create more complex and customized 3D shapes. We demonstrate the effectiveness of our model compared to the state‐of‐the‐art using objective metric evaluation criteria and a user study, both indicating strong performance on sketches with a medium level of abstraction. Furthermore, we showcase our method's intuitive sketch‐based shape editing capabilities, and validate it through a usability study.

Abstract We propose a method for the construction of a planar curve based on piecewise clothoids and straight lines that intuitively interpolates a given sequence of control points. Our method has several desirable properties that are not simultaneously fulfilled by previous approaches: Our interpolating curves are C2 continuous, their computation does not rely on global optimization and has local support, enabling fast evaluation for interactive modeling. Further, the sign of the curvature at control points is consistent with the control polygon; the curvature attains its extrema at control points and is monotone between consecutive control points of opposite curvature signs. In addition, we can ensure that the curve has self‐intersections only when the control polygon also self‐intersects between the same control points. For more fine‐grained control, the user can specify the desired curvature and tangent values at certain control points, though it is not required by our method. Our local optimization can lead to discontinuity w.r.t. the locations of control points, although the problem is limited by its locality. We demonstrate the utility of our approach in generating various curves and provide a comparison with the state of the art.

Abstract Approximating 3D shapes with piecewise developable surfaces is an active research topic, driven by the benefits of developable geometry in fabrication. Piecewise developable surfaces are characterized by having a Gauss image that is a 1D object – a collection of curves on the Gauss sphere. We present a method for developable approximation that makes use of this classic definition from differential geometry. Our algorithm is an iterative process that alternates between thinning the Gauss image of the surface and deforming the surface itself to make its normals comply with the Gauss image. The simple, local‐global structure of our algorithm makes it easy to implement and optimize. We validate our method on developable shapes with added noise and demonstrate its effectiveness on a variety of non‐developable inputs. Compared to the state of the art, our method is more general, tessellation independent, and preserves the input mesh connectivity.