Vector Graphics Complexes

International audienceBasic topological modeling, such as the ability to have several faces share a common edge, has been largely absent from vector graphics. We introduce the vector graphics complex (VGC) as a simple data structure to support fundamental topological modeling operations for vector graphics illustrations. The VGC can represent any arbitrary non-manifold topology as an immersion in the plane, unlike planar maps which can only represent embeddings. This allows for the direct representation of incidence relationships between objects and can therefore more faithfully capture the intended semantics of many illustrations, while at the same time keeping the geometric flexibility of stacking-based systems. We describe and implement a set of topological editing operations for the VGC, including glue, unglue, cut, and uncut. Our system maintains a global stacking order for all faces, edges, and vertices without requiring that components of an object reside together on a single layer. This allows for the coordinated editing of shared vertices and edges even for objects that have components distributed across multiple layers. We introduce VGC-specific methods that are tailored towards quickly achieving desired stacking orders for faces, edges, and vertices

Vector Graphics Animation with Time-Varying Topology

International audienceWe introduce the Vector Animation Complex (VAC), a novel data structure for vector graphics animation, designed to support themodeling of time-continuous topological events. This allows features of a connected drawing to merge, split, appear, or disappear atdesired times via keyframes that introduce the desired topological change. Because the resulting space-time complex directly capturesthe time-varying topological structure, features are readily edited in both space and time in a way that reflects the intent of the drawing.A formal description of the data structure is provided, along with topological and geometric invariants. We illustrate our modelingparadigm with experimental results on various examples

Topological modeling for vector graphics

In recent years, with the development of mobile phones, tablets, and web technologies, we have seen an ever-increasing need to generate vector graphics content, that is, resolution-independent images that support sharp rendering across all devices, as well as interactivity and animation. However, the tools and standards currently available to artists for authoring and distributing such vector graphics content have many limitations. Importantly, basic topological modeling, such as the ability to have several faces share a common edge, is largely absent from current vector graphics technologies. In this thesis, we address this issue with three major contributions. First, we develop theoretical foundations of vector graphics topology, grounded in algebraic topology. More specifically, we introduce the concept of Point-Curve-Surface complex (PCS complex) as a formal tool that allows us to interpret vector graphics illustrations as non-manifold, non-planar, non-orientable topological spaces immersed in R2, unlike planar maps which can only represent embeddings. Second, based on this theoretical understanding, we introduce the vector graphics complex (VGC) as a simple data structure that supports fundamental topological modeling operations for vector graphics illustrations. It allows for the direct representation of incidence relationships between objects, while at the same time keeping the geometric flexibility of stacking-based systems, such as the ability to have edges and faces overlap each others. Third and last, based on the VGC, we introduce the vector animation complex (VAC), a data structure for vector graphics animation, designed to support the modeling of time-continuous topological events, which are common in 2D hand-drawn animation. This allows features of a connected drawing to merge, split, appear, or disappear at desired times via keyframes that introduce the desired topological change. Because the resulting space-time complex directly captures the time-varying topological structure, features are readily edited in both space and time in a way that reflects the intent of the drawing.Science, Faculty ofComputer Science, Department ofGraduat