Machine knitting is a well-established fabrication technique for complex soft objects, and both companies and researchers have developed tools for generating machine knitting patterns. However, existing representations for machine knitted objects are incomplete (do not cover the complete domain of machine knittable objects) or overly specific (do not account for symmetries and equivalences among knitting instruction sequences). This makes it difficult to define correctness in machine knitting, let alone verify the correctness of a given program or program transformation. The major contribution of this work is a formal semantics for knitout, a low-level Domain Specific Language for knitting machines. We accomplish this by using what we call the fenced tangle , which extends concepts from knot theory to allow for a mathematical definition of knitting program equivalence that matches the intuition behind knit objects. Finally, using this formal representation, we prove the correctness of a sequence of rewrite rules; and demonstrate how these rewrite rules can form the foundation for higher-level tasks such as compiling a program for a specific machine and optimizing for time/reliability, all while provably generating the same knit object under our proposed semantics. By establishing formal definitions of correctness, this work provides a strong foundation for compiling and optimizing knit programs.

Industrial knitting machines are commonly used to manufacture complicated shapes from yarns; however, designing patterns for these machines requires extensive training. We present the first general visual programming interface for creating 3D objects with complex surface finishes on industrial knitting machines. At the core of our interface is a new, augmented, version of the stitch mesh data structure. The augmented stitch mesh stores low-level knitting operations per-face and encodes the dependencies between faces using directed edge labels. Our system can generate knittable augmented stitch meshes from 3D models, allows users to edit these meshes in a way that preserves their knittability, and can schedule the execution order and location of each face for production on a knitting machine. Our system is general, in that its knittability-preserving editing operations are sufficient to transform between any two machine-knittable stitch patterns with the same orientation on the same surface. We demonstrate the power and flexibility of our pipeline by using it to create and knit objects featuring a wide range of patterns and textures, including intarsia and Fair Isle colorwork; knit and purl textures; cable patterns; and laces.

Analyzing depressions plays an important role in meteorology, especially in the study of cyclones. In particular, the study of the temporal evolution of cyclones requires a robust depression tracking framework. To cope with this demand we propose a pipeline for the exploration of cyclones and their temporal evolution. This entails a generic framework for their identification and tracking. The fact that depressions and cyclones are not well-defined objects and their shape and size characteristics change over time makes this task especially challenging. Our method combines the robustness of topological approaches and the detailed tracking information from optical flow analysis. At first cyclones are identified within each time step based on well-established topological concepts. Then candidate tracks are computed from an optical flow field. These tracks are clustered within a moving time window to distill dominant coherent cyclone movements, which are then forwarded to a final tracking step. In contrast to previous methods our method requires only a few intuitive parameters. An integration into an exploratory framework helps in the study of cyclone movement by identifying smooth, representative tracks. Multiple case studies demonstrate the effectiveness of the method in tracking cyclones, both in the northern and southern hemisphere.

We present the first computational approach that can transform three-dimensional (3D) meshes, created by traditional modeling programs, directly into instructions for a computer-controlled knitting machine. Knitting machines are able to robustly and repeatably form knitted 3D surfaces from yarn but have many constraints on what they can fabricate. Given user-defined starting and ending points on an input mesh, our system incrementally builds a helix-free, quad-dominant mesh with uniform edge lengths, runs a tracing procedure over this mesh to generate a knitting path, and schedules the knitting instructions for this path in a way that is compatible with machine constraints. We demonstrate our approach on a wide range of 3D meshes.

Industrial knitting machines can produce finely detailed, seamless, 3D surfaces quickly and without human intervention. However, the tools used to program them require detailed manipulation and understanding of low-level knitting operations. We present a compiler that can automatically turn assemblies of high-level shape primitives (tubes, sheets) into low-level machine instructions. These high-level shape primitives allow knit objects to be scheduled, scaled, and otherwise shaped in ways that require thousands of edits to low-level instructions. At the core of our compiler is a heuristic transfer planning algorithm for knit cycles, which we prove is both sound and complete. This algorithm enables the translation of high-level shaping and scheduling operations into needle-level operations. We show a wide range of examples produced with our compiler and demonstrate a basic visual design interface that uses our compiler as a backend.

Scientific phenomena are often studied through collections of related scalar fields generated from different observations of the same phenomenon. Exploration of such data requires a robust distance measure to compare scalar fields for tasks such as identifying key events and establishing correspondence between features in the data. Towards this goal, we propose a topological data structure called the complete extremum graph and define a distance measure on it for comparing scalar fields in a feature-aware manner. We design an algorithm for computing the distance and show its applications in analysing time varying data.