Computational Design of Knit Templates

We present an interactive design system for knitting that allows users to create template patterns that can be fabricated using an industrial knitting machine. Our interactive design tool is novel in that it allows direct control of key knitting design axes we have identified in our formative study and does so consistently across the variations of an input parametric template geometry. This is achieved with two key technical advances. First, we present an interactive meshing tool that lets users build a coarse quadrilateral mesh that adheres to their knit design guidelines. This solution ensures consistency across the parameter space for further customization over shape variations and avoids helices, promoting knittability. Second, we lift and formalize low-level machine knitting constraints to the level of this coarse quad mesh. This enables us to not only guarantee hand- and machine-knittability, but also provides automatic design assistance through auto-completion and suggestions. We show the capabilities through a set of fabricated examples that illustrate the effectiveness of our approach in creating a wide variety of objects and interactively exploring the space of design variations.

Vertex arboricity of graphs embedded in a surface of non-negative Euler characteristic

The vertex arboricity [Formula: see text] of a graph [Formula: see text] is the minimum number of colors the vertices of the graph [Formula: see text] can be colored so that every color class induces an acyclic subgraph of [Formula: see text]. There are many results on the vertex arboricity of planar graphs. In this paper, we replace planar graphs with graphs which can be embedded in a surface [Formula: see text] of Euler characteristic [Formula: see text]. We prove that for the graph [Formula: see text] which can be embedded in a surface [Formula: see text] of Euler characteristic [Formula: see text] if no [Formula: see text]-cycle intersects a [Formula: see text]-cycle, or no [Formula: see text]-cycle intersects a [Formula: see text]-cycle, then [Formula: see text] in addition to the [Formula: see text]-regular quadrilateral mesh.