Representing rational curve segments and surface patches using semi-algebraic sets

We provide a framework for representing segments of rational planar curves or patches of rational tensor product surfaces with no singularities using semi-algebraic sets. Given a rational planar curve segment or a rational tensor product surface patch with no singularities, we find the implicit equation of the corresponding unbounded curve or surface and then construct an algebraic box defined by some additional equations and inequalities associated to the implicit equation. This algebraic box is proved to include only the given curve segment or surface patch without any extraneous parts of the unbounded curve or surface. We also explain why it is difficult to construct such an algebraic box if the curve segment or surface patch includes some singular points such as self-intersections. In this case, we show how to isolate a neighborhood of these special points from the corresponding curve segment or surface patch and to represent these special points with small curve segments or surface patches. This framework allows us to dispense with expensive approximation methods such as voxels for representing surface patches.National Natural Science Foundation of ChinaMinisterio de Ciencia, Innovación y Universidade

Distributed camera subsystem for obstacle detection

This work focuses on improving a camera system for sensing a workspace in which dynamic obstacles need to be detected. The currently available state-of-the-art solution (MoveIt!) processes data in a centralized manner from cameras that have to be registered before the system starts. Our solution enables distributed data processing and dynamic change in the number of sensors at runtime. The distributed camera data processing is implemented using a dedicated control unit on which the filtering is performed by comparing the real and expected depth images. Measurements of the processing speed of all sensor data into a global voxel map were compared between the centralized system (MoveIt!) and the new distributed system as part of a performance benchmark. The distributed system is more flexible in terms of sensitivity to a number of cameras, better framerate stability and the possibility of changing the camera number on the go. The effects of voxel grid size and camera resolution were also compared during the benchmark, where the distributed system showed better results. Finally, the overhead of data transmission in the network was discussed where the distributed system is considerably more efficient. The decentralized system proves to be faster by 38.7% with one camera and 71.5% with four cameras.Web of Science2212art. no. 458

Configraphics:

This dissertation reports a PhD research on mathematical-computational models, methods, and techniques for analysis, synthesis, and evaluation of spatial configurations in architecture and urban design. Spatial configuration is a technical term that refers to the particular way in which a set of spaces are connected to one another as a network. Spatial configuration affects safety, security, and efficiency of functioning of complex buildings by facilitating certain patterns of movement and/or impeding other patterns. In cities and suburban built environments, spatial configuration affects accessibilities and influences travel behavioural patterns, e.g. choosing walking and cycling for short trips instead of travelling by cars. As such, spatial configuration effectively influences the social, economic, and environmental functioning of cities and complex buildings, by conducting human movement patterns. In this research, graph theory is used to mathematically model spatial configurations in order to provide intuitive ways of studying and designing spatial arrangements for architects and urban designers. The methods and tools presented in this dissertation are applicable in: arranging spatial layouts based on configuration graphs, e.g. by using bubble diagrams to ensure certain spatial requirements and qualities in complex buildings; and analysing the potential effects of decisions on the likely spatial performance of buildings and on mobility patterns in built environments for systematic comparison of designs or plans, e.g. as to their aptitude for pedestrians and cyclists. The dissertation reports two parallel tracks of work on architectural and urban configurations. The core concept of the architectural configuration track is the ‘bubble diagram’ and the core concept of the urban configuration track is the ‘easiest paths’ for walking and cycling. Walking and cycling have been chosen as the foci of this theme as they involve active physical, cognitive, and social encounter of people with built environments, all of which are influenced by spatial configuration. The methodologies presented in this dissertation have been implemented in design toolkits and made publicly available as freeware applications

Adaptive 3D web-based environment for heterogeneous volume objects.

The Internet was growing fast on the last decade. Interaction and visualisation became an essential feature online. The demand for online modelling and rendering in a real-time, adaptive and interactive manner exceeded the growth and development of the hardware resources including computational power and memories. Building up and accessing an instant 3D Web-based and plugin-free platform started to be a must in order to generate 3D volumes. Modelling and rendering complicated heterogeneous volumes using online applications requires good Internet bandwidth and high computational power. A large number of 3D modelling tools designed to create complicated models in an interactive manner are now available online, the problem of using such tools is that the user needs to acquire a certain level of modelling knowledge In this work, we identify the problem, introduce the theoretical background and discuss the theory about Web-based modelling and rendering, including client- server approach, scenario optimization by solving constraint satisfaction problem, and complexity analysis. We address the challenges of designing, implementing and testing an online, Web-based, instant 3D modelling and rendering environment and we discuss some of its characteristics including adaptivity, platform independence, interactivity, and easy-to-use after presenting the theoretical part of implementing such an environment. We also introduce platform-independent modelling and rendering environment for complicated heterogeneous volumes with colour attributes based on client- server architecture. The work includes analysis and implementation for different rendering approaches suitable for different kind of users. We also discuss the performance of the proposed environment by comparing the rendering approaches. As an additional feature of our modelling system, we discuss aspects of securing the model transferring between client and the server