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.

Line work is a core element for the stylization of computer animations used by recent shows. However, existing stylization techniques are limited to edge treatments based on brush strokes or textures applied solely on top of curves. In this work, we propose new stylization effects by offering artists direct control over the inside and outside of surface contours. To this end, we introduce a method that creates ribbons, geometry strips of possibly varying width, that extrude from each side of the surface contour with temporally coherent orientations. Our contributions include the generation of spatially and temporally consistent normal orientations along visible contours and a trimming routine that converts arrangements of offset curves into ribbons free of intersections. We demonstrate the expressiveness and versatility of stylized ribbons by applying various effects on both character and shadow edges from animation sequences.

Linework on 3D animated characters is an important aspect of stylized looks for films. We present CurveCrafter, a system allowing animators to create new lines on 3D models and to edit the shape and opacity of silhouette curves. Our tools allow users to draw, redraw, erase, edit and retime user created curves. Silhouette curves can have their shape edited or reverted, and their opacity erased or revealed. Our algorithm for propagating edits over tracked silhouette curves ensures temporal consistency even as curves expand and merge. Five professional animators used our system to animate lines on three shots with different characters. Additionally, the effects lead from the short film Pete used our system to more easily recreate edits on a film shot. CurveCrafter was able to successfully enhance the resulting animations with additional linework.

Computer animation relies heavily on rigging setups that articulate character surfaces through a broad range of poses. Although many deformation strategies have been proposed over the years, constructing character rigs is still a cumbersome process that involves repetitive authoring of point weights and corrective sculpts with limited and indirect shaping controls. This paper presents a new approach for character articulation that produces detail-preserving deformations fully controlled by 3D curves that profile the deforming surface. Our method starts with a spline-based rigging system in which artists can draw and articulate sparse curvenets that describe surface profiles. By analyzing the layout of the rigged curvenets, we quantify the deformation along each curve side independent of the mesh connectivity, thus separating the articulation controllers from the underlying surface representation. To propagate the curvenet articulation over the character surface, we formulate a deformation optimization that reconstructs surface details while conforming to the rigged curvenets. In this process, we introduce a cut-cell algorithm that binds the curvenet to the surface mesh by cutting mesh elements into smaller polygons possibly with cracks, and then derive a cut-aware numerical discretization that provides harmonic interpolations with curve discontinuities. We demonstrate the expressiveness and flexibility of our method using a series of animation clips.