Polyline Drawings with Topological Constraints

Let G be a simple topological graph and let Gamma be a polyline drawing of G. We say that Gamma partially preserves the topology of G if it has the same external boundary, the same rotation system, and the same set of crossings as G. Drawing Gamma fully preserves the topology of G if the planarization of G and the planarization of Gamma have the same planar embedding. We show that if the set of crossing-free edges of G forms a connected spanning subgraph, then G admits a polyline drawing that partially preserves its topology and that has curve complexity at most three (i.e., at most three bends per edge). If, however, the set of crossing-free edges of G is not a connected spanning subgraph, the curve complexity may be Omega(sqrt{n}). Concerning drawings that fully preserve the topology, we show that if G has skewness k, it admits one such drawing with curve complexity at most 2k; for skewness-1 graphs, the curve complexity can be reduced to one, which is a tight bound. We also consider optimal 2-plane graphs and discuss trade-offs between curve complexity and crossing angle resolution of drawings that fully preserve the topology

Extending Orthogonal Planar Graph Drawings Is Fixed-Parameter Tractable

The task of finding an extension to a given partial drawing of a graph while adhering to constraints on the representation has been extensively studied in the literature, with well-known results providing efficient algorithms for fundamental representations such as planar and beyond-planar topological drawings. In this paper, we consider the extension problem for bend-minimal orthogonal drawings of planar graphs, which is among the most fundamental geometric graph drawing representations. While the problem was known to be NP-hard, it is natural to consider the case where only a small part of the graph is still to be drawn. Here, we establish the fixed-parameter tractability of the problem when parameterized by the size of the missing subgraph. Our algorithm is based on multiple novel ingredients which intertwine geometric and combinatorial arguments. These include the identification of a new graph representation of bend-equivalent regions for vertex placement in the plane, establishing a bound on the treewidth of this auxiliary graph, and a global point-grid that allows us to discretize the possible placement of bends and vertices into locally bounded subgrids for each of the above regions

Toward semantic model generation from sketch and multi-touch interactions

Designers usually start their design process by exploring and evolving their ideas rapidly through sketching since this helps them to make numerous attempts at creating, practicing, simulating, and representing ideas. Creativity inherent in solving the ill-defined problems (Eastman, 1969) often emerges when designers explore potential solutions while sketching in the design process (Schön, 1992). When using computer programs such as CAD or Building Information Modeling (BIM) tools, designers often preplan the tasks prior to executing commands instead of engaging in the process of designing. Researchers argue that these programs force designers to focus on how to use a tool (i.e. how to execute series of commands) rather than how to explore a design, and thus hinder creativity in the early stages of the design process (Goel, 1995; Dorta, 2007). Since recent design and documentation works have been computer-generated using BIM software, transitions between ideas in sketches and those in digital CAD systems have become necessary. By employing sketch interactions, we argue that a computer system can provide a rapid, flexible, and iterative method to create 3D models with sufficient data for facilitating smooth transitions between designers’ early sketches and BIM programs. This dissertation begins by describing the modern design workflows and discussing the necessary data to be exchanged in the early stage of design. It then briefly introduces the modern cognitive theories, including embodiment (Varela, Rosch, & Thompson, 1992), situated action (Suchman, 1986), and distributed cognition (Hutchins, 1995). It continues by identifying problems in current CAD programs used in the early stage of the design process, using these theories as lenses. After reviewing modern attempts, including sketch tools and design automation tools, we describe the design and implementation of a sketch and multi-touch program, SolidSketch, to facilitate and augment our abilities to work on ill-defined problems in the early stage of design. SolidSketch is a parametric modeling program that enables users to construct 3D parametric models rapidly through sketch and multi-touch interactions. It combines the benefits of traditional design tools, such as physical models and pencil sketches (i.e. rapid, low-cost, and flexible methods), with the computational power offered by digital modeling tools, such as CAD. To close the gap between modern BIM and traditional sketch tools, the models created with SolidSketch can be read by other BIM programs. We then evaluate the programs with comparisons to the commercial CAD programs and other sketch programs. We also report a case study in which participants used the system for their design explorations. Finally, we conclude with the potential impacts of this new technology and the next steps for ultimately bringing greater computational power to the early stages of design.Ph.D

Pop-tech-flat-fab

This paper for the EAAE / ARCC 2008 addresses the theme of simultaneity between the digitaland analogue by examining the production of two projects. These are: a pair of prototype busstops built in Sioux City1 and a shade structure for downtown Phoenix in the USA. The conceptual basis for both these projects coincides with the question of how "phenomenon attached toa certain locality”2 might be created through advanced methods of digital fabrication. Both projects offer an apology for rapid prototyping techniques applied to an understanding of "contextualism”3.Both projects are presented first as a contextual and symbolic response to an interpretation of"locality” and then re-appraised in technical terms. In both projects these technical aspects aim to advance not only the methods of physical production but also the transition of design methodsto 1:1 fabrication. In the case of the Sioux City Bus Stops this idea is represented throughan analysis of two-dimensional cutting techniques and developable surfaces. In the case of thePhoenix Shade project this idea is then developed through fully associative digital models. Togetherthese projects attempt to accelerate the physical production of their symbolic and contextualcontent through a discussion on parametric modeling that allows an efficient productionof a set of different permutations. By associating the symbolic/contextual with the parametricthese projects suggest and alternative procedure to the traditional and prevalent trope of "digitalarchitecture” and its co-dependence upon explicitly biomorphic, computational and quasinaturalistic language.

Pop-tech-flat-fab

This paper for the EAAE / ARCC 2008 addresses the theme of simultaneity between the digital and analogue by examining the production of two projects. These are: a pair of prototype bus stops built in Sioux City1 and a shade structure for downtown Phoenix in the USA. The conceptual basis for both these projects coincides with the question of how "phenomenon attached to a certain locality”2 might be created through advanced methods of digital fabrication. Both projects offer an apology for rapid prototyping techniques applied to an understanding of "contextualism”3. Both projects are presented first as a contextual and symbolic response to an interpretation of "locality” and then re-appraised in technical terms. In both projects these technical aspects aim to advance not only the methods of physical production but also the transition of design methods to 1:1 fabrication. In the case of the Sioux City Bus Stops this idea is represented through an analysis of two-dimensional cutting techniques and developable surfaces. In the case of the Phoenix Shade project this idea is then developed through fully associative digital models. Together these projects attempt to accelerate the physical production of their symbolic and contextual content through a discussion on parametric modeling that allows an efficient production of a set of different permutations. By associating the symbolic/contextual with the parametric these projects suggest and alternative procedure to the traditional and prevalent trope of "digital architecture” and its co-dependence upon explicitly biomorphic, computational and quasinaturalistic language