Toward a Notation for Drawing and Flow

Certain domains of visual expression lend themselves more naturally to the two-dimensional media of paper, canvas, computer, and smartphone than to sculpture or other 3D forms. For example, it is conventional to present literature, maps, and diagrams in 2D. Likewise, despite the intrinsic three-dimensionality of such things as fabric-weave, highway interchanges, river systems, roofs,  knots and even visual paradoxes, a two dimensional rendition sometimes has more explanatory power than a full-fledged three dimensional presentation of the thing being visualized.
Certain "3D" things are easier to visualize when drawn in 2D:
At the same time, SVG, because of its two-dimensional focus, is encumbered by a two-dimensional semantics that focuses on geometry rather than meaning, flow, or connectivity. Put simply, in SVG, objects cannot occlude parts of themselves. Nor do objects that are "linked together" semantically have any natural way, other than hierarchical grouping or shared decoration, to reflect a typical graph theoretic connection. And other than the currently quite limited options for gradients, markers and animation, the directionality of flow is not intrinsic to SVG drawings. Depicting such things as weave, underpasses, relationships, knots, and visual paradox is difficult to accomplish with SVG. This often forces authors to use much less elegant tool sets (such as animated GIF and WebGL) to visualize such domains. Examination of the source code used in such examples as these may indicate that, despite compelling reasons for using SVG, there are dogged complexities associated with these depictions.

Certain domains of discourse would seem to be natural matches for a vector-based 2D graphical standard. Over the past several years I've examined various ways that SVG falls short of the expressiveness that might be required of some of these domains. Encouraged by the existence of concise notations for certain combinatorial structures like Venn diagrams, knots, tangles, and polyominoes, this talk will summarize the findings of this inquiry as well as point toward the possibilities for creating a declarative language, like SVG, but which focuses more on topology than on geometry. In particular What are some types of things SVG doesn't do well? What are the requirements of a notation/language for the depiction of drawing and flow? What domains of connectivity, topology, activity and weave can be properly addresses by such a notation?