Traditional integral wood joints, despite their strength, durability, and elegance, remain rare in modern workflows due to the cost and difficulty of manual fabrication. CNC milling offers a scalable alternative, but directly milling traditional joints often fails to produce functional results because milling induces geometric deviations—such as rounded inner corners—that alter the target geometries of the parts. Since joints rely on tightly fitting surfaces, such deviations introduce gaps or overlaps that undermine fit or block assembly. We propose to overcome this problem by (1) designing a language that represent millable geometry, and (2) co-optimizing part geometries to restore coupling. We introduce Millable Extrusion Geometry (MXG), a language for representing geometry as the outcome of milling operations performed with flat-end drill bits. MXG represents each operation as a subtractive extrusion volume defined by a tool direction and drill radius. This parameterization enables the modeling of artifact-free geometry under an idealized zero-radius drill bit, matching traditional joint designs. Increasing the radius then reveals milling-induced deviations, which compromise the integrity of the joint. To restore coupling, we formalize tight coupling in terms of both surface proximity and proximity constraints on the mill-bit paths associated with mating surfaces. We then derive two tractable, differentiable losses that enable efficient optimization of joint geometry. We evaluate our method on 30 traditional joint designs, demonstrating that it produces CNC-compatible, tightly fitting joints that approximates the original geometry. By reinterpreting traditional joints for CNC workflows, we continue the evolution of this heritage craft and help ensure its relevance in future making practices.

We present the Mokume dataset for solid wood texturing consisting of 190 cube-shaped samples of various hard and softwood species documented by high-resolution exterior photographs, annual ring annotations, and volumetric computed tomography (CT) scans. A subset of samples further includes photographs along slanted cuts through the cube for validation purposes. Using this dataset, we propose a three-stage inverse modeling pipeline to infer solid wood textures using only exterior photographs. Our method begins by evaluating a neural model to localize year rings on the cube face photographs. We then extend these exterior 2D observations into a globally consistent 3D representation by optimizing a procedural growth field using a novel iso-contour loss. Finally, we synthesize a detailed volumetric color texture from the growth field. For this last step, we propose two methods with different efficiency and quality characteristics: a fast inverse procedural texture method, and a neural cellular automaton (NCA). We demonstrate the synergy between the Mokume dataset and the proposed algorithms through comprehensive comparisons with unseen captured data. We also present experiments demonstrating the efficiency of our pipeline's components against ablations and baselines. Our code, the dataset, and reconstructions are available via https://mokumeproject.github.io/.

Abstract We propose a method for inferring the internal anisotropic volumetric texture of a given wood block from annotated photographs of its external surfaces. The global structure of the annual ring pattern is represented using a continuous spatial scalar field referred to as the growth time field (GTF). First, we train a generic neural model that can represent various GTFs using procedurally generated training data. Next, we fit the generic model to the GTF of a given wood block based on surface annotations. Finally, we convert the GTF to an annual ring field (ARF) revealing the layered pattern and apply neural style transfer to render orientation‐dependent small‐scale features and colors on a cut surface. We show rendered results of various physically cut real wood samples. Our method has physical and virtual applications such as cut‐preview before subtractive fabricating solid wood artifacts and simulating object breaking.

We present a procedural framework for modeling the annual ring pattern of solid wood with knots. Although wood texturing is a well-studied topic, there have been few previous attempts at modeling knots inside the wood texture. Our method takes the skeletal structure of a tree log as input and produces a three-dimensional scalar field representing the time of added growth, which defines the volumetric annual ring pattern. First, separate fields are computed around each strand of the skeleton, i.e., the stem and each knot. The strands are then merged into a single field using smooth minimums. We further suggest techniques for controlling the smooth minimum to adjust the balance of smoothness and reproduce the distortion effects observed around dead knots. Our method is implemented as a shader program running on a GPU with computation times of approximately 0.5 s per image and an input data size of 600 KB. We present rendered images of solid wood from pine and spruce as well as plywood and cross-laminated timber (CLT). Our results were evaluated by wood experts, who confirmed the plausibility of the rendered annual ring patterns. Link to code: https://github.com/marialarsson/procedural_knots.

We present Tsugite - an interactive system for designing and fabricating wood joints for frame structures. To design and manually craft such joints is difficult and time consuming. Our system facilitates the creation of custom joints by a modeling interface combined with computer numerical control (CNC) fabrication. The design space is a 3D grid of voxels that enables efficient geometrical analysis and combinatorial search. The interface has two modes: manual editing and gallery. In the manual editing mode, the user edits a joint while receiving real-time graphical feedback and suggestions provided based on performance metrics including slidability, fabricability, and durability with regard to the direction of fiber. In the gallery mode, the user views and selects feasible joints that have been pre-calculated. When a joint design is finalized, it can be manufactured with a 3-axis CNC milling machine using a specialized path planning algorithm that ensures joint assemblability by corner rounding. This system was evaluated via a user study and by designing and fabricating joint samples and functional furniture.

While tree trunks are standardized as lumber, branches are typically chipped or burned. This paper proposes a workflow to upcycle such mundane and diverse natural material to architectural elements. Introducing an online design interface, we let users participate in the design and fabrication workflow from collecting branches to CNC milling. The branches are first scanned, and then key geometrical features are extracted and uploaded to the online game "BranchConnect". This application lets multiple non-expert users create 2D-layouts. At the point of intersection between two branches, the geometry of a lap joint and its cutting path are calculated on-the-fly. A CNC router mills out the joints accordingly, and the branches are assembled manually. Through this workflow, users go back-and-forth between physical and digital representations of tree branches. The process was validated with two case studies.