Shape manipulation using physically based wire deformations

This paper develops an efficient, physically based shape manipulation technique. It defines a 3D model with profile curves, and uses spine curves generated from the profile curves to control the motion and global shape of 3D models. Profile and spine curves are changed into profile and spine wires by specifying proper material and geometric properties together with external forces. The underlying physics is introduced to deform profile and spine wires through the closed form solution to ordinary differential equations for axial and bending deformations. With the proposed approach, global shape changes are achieved through manipulating spine wires, and local surface details are created by deforming profile wires. A number of examples are presented to demonstrate the applications of our proposed approach in shape manipulation

A Fast and Scalable System to Visualize Contour Gradient from Spatio-temporal Data

Changes in geological processes that span over the years may often go unnoticed due to their inherent noise and variability. Natural phenomena such as riverbank erosion, and climate change in general, is invisible to humans unless appropriate measures are taken to analyze the underlying data. Visualization helps geological sciences to generate scientific insights into such long-term geological events. Commonly used approaches such as side-by-side contour plots and spaghetti plots do not provide a clear idea about the historical spatial trends. To overcome this challenge, we propose an image-gradient based approach called ContourDiff. ContourDiff overlays gradient vector over contour plots to analyze the trends of change across spatial regions and temporal domain. Our approach first aggregates for each location, its value differences from the neighboring points over the temporal domain, and then creates a vector field representing the prominent changes. Finally, it overlays the vectors (differential trends) along the contour paths, revealing the differential trends that the contour lines (isolines) experienced over time. We designed an interface, where users can interact with the generated visualization to reveal changes and trends in geospatial data. We evaluated our system using real-life datasets, consisting of millions of data points, where the visualizations were generated in less than a minute in a single-threaded execution. We show the potential of the system in detecting subtle changes from almost identical images, describe implementation challenges, speed-up techniques, and scope for improvements. Our experimental results reveal that ContourDiff can reliably visualize the differential trends, and provide a new way to explore the change pattern in spatiotemporal data. The expert evaluation of our system using real-life WRF (Weather Research and Forecasting) model output reveals the potential of our technique to generate useful insights on the spatio-temporal trends of geospatial variables

Non-isometric 3D shape registration.

3D shape registration is an important task in computer graphics and computer vision. It has been widely used in the area of film industry, 3D animation, video games and AR/VR assets creation. Manually creating the 3D model of a character from scratch is tedious and time consuming, and it can only be completed by professional trained artists. With the development of 3D geometry acquisition technology, it becomes easier and cheaper to capture high-resolution and highly detailed 3D geometries. However, the scanned data are often incomplete or noisy and therefore cannot be employed directly. To deal with the above two problems, one typical and efficient solution is to deform an existing high-quality model (template) to fit the scanned data (target). Shape registration as an essential technique to do so has been arousing intensive attention. In last decades, various shape registration approaches have been proposed for accurate template fitting. However, there are still some remaining challenges. It is well known that the template can be largely different with the target in respect of size and pose. With the large (usually non-isometric) deformation between them, the shear distortion can easily occur, which may lead to poor results, such as degenerated triangles, fold-overs. Before deforming the template towards the target, reliable correspondences between them should be found first. Incorrect correspondences give the wrong deformation guidance, which can also easily produce fold-overs. As mentioned before, the target always comes with noise. This is the part we want to filter out and try not to fit the template on it. Hence, non-isometric shape registration robust to noise is highly desirable in the scene of geometry modelling from the scanned data. In this PhD research, we address existing challenges in shape registration, including how to prevent the deformation distortion, how to reduce the foldover occurrence and how to deal with the noise in the target. Novel methods including consistent as-similar as-possible surface deformation and robust Huber-L1 surface registration are proposed, which are validated through experimental comparison with state-of-the-arts. The deformation technique plays an important role in shape registration. In this research, a consistent as similar-as-possible (CASAP) surface deformation approach is proposed. Starting from investigating the continuous deformation energy, we analyse the existing term to make the discrete energy converge to the continuous one, whose property we called as energy consistency. Based on the deformation method, a novel CASAP non-isometric surface registration method is proposed. The proposed registration method well preserves the angles of triangles in the template surface so that least distortion is introduced during the surface deformation and thus reduce the risk of fold-over and self-intersection. To reduce the noise influence, a Huber-L1 based non-isometric surface registration is proposed, where a Huber-L1 regularized model constrained on the transformation variation and position difference. The proposed method is robust to noise and produces piecewise smooth results while still preserving fine details on the target. We evaluate and validate our methods through extensive experiments, whose results have demonstrated that the proposed methods in this thesis are more accurate and robust to noise in comparison of the state-of-the arts and enable us to produce high quality models with little efforts

Arbitrary topology meshes in geometric design and vector graphics

Meshes are a powerful means to represent objects and shapes both in 2D and 3D, but the techniques based on meshes can only be used in certain regular settings and restrict their usage. Meshes with an arbitrary topology have many interesting applications in geometric design and (vector) graphics, and can give designers more freedom in designing complex objects. In the first part of the thesis we look at how these meshes can be used in computer aided design to represent objects that consist of multiple regular meshes that are constructed together. Then we extend the B-spline surface technique from the regular setting to work on extraordinary regions in meshes so that multisided B-spline patches are created. In addition, we show how to render multisided objects efficiently, through using the GPU and tessellation. In the second part of the thesis we look at how the gradient mesh vector graphics primitives can be combined with procedural noise functions to create expressive but sparsely defined vector graphic images. We also look at how the gradient mesh can be extended to arbitrary topology variants. Here, we compare existing work with two new formulations of a polygonal gradient mesh. Finally we show how we can turn any image into a vector graphics image in an efficient manner. This vectorisation process automatically extracts important image features and constructs a mesh around it. This automatic pipeline is very efficient and even facilitates interactive image vectorisation

Optimization and Communication in UAV Networks

UAVs are becoming a reality and attract increasing attention. They can be remotely controlled or completely autonomous and be used alone or as a fleet and in a large set of applications. They are constrained by hardware since they cannot be too heavy and rely on batteries. Their use still raises a large set of exciting new challenges in terms of trajectory optimization and positioning when they are used alone or in cooperation, and communication when they evolve in swarm, to name but a few examples. This book presents some new original contributions regarding UAV or UAV swarm optimization and communication aspects

Hybrid modelling of heterogeneous volumetric objects.

Heterogeneous multi-material volumetric modelling is an emerging and rapidly developing field. A Heterogeneous object is a volumetric object with interior structure where different physically-based attributes are defined. The attributes can be of different nature: material distributions, density, microstructures, optical properties and others. Heterogeneous objects are widely used where the presence of the interior structures is an important part of the model. Computer-aided design (CAD), additive manufacturing, physical simulations, visual effects, medical visualisation and computer art are examples of such applications. In particular, digital fabrication employing multi-material 3D printing techniques is becoming omnipresent. However, the specific methods and tools for representation, modelling, rendering, animation and fabrication of multi-material volumetric objects with attributes are only starting to emerge. The need for adequate unifying theoretical and practical framework has been obvious. Developing adequate representational schemes for heterogeneous objects is in the core of research in this area. The most widely used representations for defining heterogeneous objects are boundary representation, distance-based representations, function representation and voxels. These representations work well for modelling homogeneous (solid) objects but they all have significant drawbacks when dealing with heterogeneous objects. In particular, boundary representation, while maintaining its prevailing role in computer graphics and geometric modelling, is not inherently natural for dealing with heterogeneous objects especially in the con- text of additive manufacturing and 3D printing, where multi-material properties are paramount as well as in physical simulation where the exact representation rather than an approximate one can be important. In this thesis, we introduce and systematically describe a theoretical and practical framework for modelling volumetric heterogeneous objects on the basis of a novel unifying functionally-based hybrid representation called HFRep. It is based on the function representation (FRep) and several distance-based representations, namely signed distance fields (SDFs), adaptively sampled distance fields (ADFs) and interior distance fields (IDFs). It embraces advantages and circumvents disadvantages of the initial representations. A mathematically substantiated theoretical description of the HFRep with an emphasis on defining functions for HFRep objects’ geometry and attributes is provided. This mathematical framework serves as the basis for developing efficient algorithms for the generation of HFRep objects taking into account both their geometry and attributes. To make the proposed approach practical, a detailed description of efficient algorithmic procedures has been developed. This has required employing a number of novel techniques of different nature, separately and in combination. In particular, an extension of a fast iterative method (FIM) for numerical solving of the eikonal equation on hierarchical grids was developed. This allowed for efficient computation of smooth distance-based attributes. To prove the concept, the main elements of the framework have been implemented and used in several applications of different nature. It was experimentally shown that the developed methods and tools can be used for generating objects with complex interior structure, e.g. microstructures, and different attributes. A special consideration has been devoted to applications of dynamic nature. A novel concept of heterogeneous space-time blending (HSTB) method with an automatic control for metamorphosis of heterogeneous objects with textures, both in 2D and 3D, has been introduced, algorithmised and implemented. We have applied the HSTB in the context of ‘4D Cubism’ project. There are plans to use the developed methods and tools for many other applications