Computing the minimum distance between a point and a clamped B-spline surface

International audienceThe computation of the minimum distance between a point and a surface is important for the applications such as CAD/CAM, NC verification, robotics and computer graphics. This paper presents a spherical clipping method to compute the minimum distance between a point and a clamped B-spline surface. The surface patches outside the clipping sphere which do not contain the nearest point are eliminated. Another exclusion criterion whether the nearest point is on the boundary curves of the surface is employed, which is proved to be superior to previous comparable criteria. Examples are also shown to illustrate efficiency and correctness of the new method

Method of trimming PDE surfaces

A method for trimming surfaces generated as solutions to Partial Differential Equations (PDEs) is presented. The work we present here utilises the 2D parameter space on which the trim curves are defined whose projection on the parametrically represented PDE surface is then trimmed out. To do this we define the trim curves to be a set of boundary conditions which enable us to solve a low order elliptic PDE on the parameter space. The chosen elliptic PDE is solved analytically, even in the case of a very general complex trim, allowing the design process to be carried out interactively in real time. To demonstrate the capability for this technique we discuss a series of examples where trimmed PDE surfaces may be applicable

Computing the minimum distance between two Bézier curves

International audienceA sweeping sphere clipping method is presented for computing the minimum distance between two Bézier curves. The sweeping sphere is constructed by rolling a sphere with its center point along a curve. The initial radius of the sweeping sphere can be set as the minimum distance between an end point and the other curve. The nearest point on a curve must be contained in the sweeping sphere along the other curve, and all of the parts outside the sweeping sphere can be eliminated. A simple sufficient condition when the nearest point is one of the two end points of a curve is provided, which turns the curve/curve case into a point/curve case and leads to higher efficiency. Examples are shown to illustrate efficiency and robustness of the new method

Hybrid model for vascular tree structures

This paper proposes a new representation scheme of the cerebral blood vessels. This model provides information on the semantics of the vascular structure: the topological relationships between vessels and the labeling of vascular accidents such as aneurysms and stenoses. In addition, the model keeps information of the inner surface geometry as well as of the vascular map volume properties, i.e. the tissue density, the blood flow velocity and the vessel wall elasticity. The model can be constructed automatically in a pre-process from a set of segmented MRA images. Its memory requirements are optimized on the basis of the sparseness of the vascular structure. It allows fast queries and efficient traversals and navigations. The visualizations of the vessel surface can be performed at different levels of detail. The direct rendering of the volume is fast because the model provides a natural way to skip over empty data. The paper analyzes the memory requirements of the model along with the costs of the most important operations on it.Postprint (published version

Cornsweet surfaces for selective contrast enhancement

A typical goal when enhancing the contrast of images is to increase the perceived contrast without altering the original feel of the image. Such contrast enhancement can be achieved by modelling Cornsweet profiles into the image. We demonstrate that previous methods aiming to model Cornsweet profiles for contrast enhancement, often employing the unsharp mask operator, are not robust to image content. To achieve robustness, we propose a fundamentally di erent vector-centric approach with Cornsweet surfaces. Cornsweet surfaces are parametrised 3D surfaces (2D in space, 1D in luminance enhancement) that are extruded or depressed in the luminance dimension to create countershading that respects image structure. In contrast to previous methods, our method is robust against the topology of the edges to be enhanced and the relative luminance across those edges. In user trials, our solution was significantly preferred over the most related contrast enhancement method.Kosinka was funded by EPSRC grant EP/H024816/1. Lieng was funded by a scholarship from the Norwegian Government.This is the accepted manuscript. The final version is available from Elsevier at http://www.sciencedirect.com/science/article/pii/S0097849314000405

BoolSurf: Boolean Operations on Surfaces

We port Boolean set operations between 2D shapes to surfaces of any genus, with any number of open boundaries. We combine shapes bounded by sets of freely intersecting loops, consisting of geodesic lines and cubic Bézier splines lying on a surface. We compute the arrangement of shapes directly on the surface and assign integer labels to the cells of such arrangement. Differently from the Euclidean case, some arrangements on a manifold may be inconsistent. We detect inconsistent arrangements and help the user to resolve them. Also, we extend to the manifold setting recent work on Boundary-Sampled Halfspaces, thus supporting operations more general than standard Booleans, which are well defined on inconsistent arrangements, too. Our implementation discretizes the input shapes into polylines at an arbitrary resolution, independent of the level of resolution of the underlying mesh. We resolve the arrangement inside each triangle of the mesh independently and combine the results to reconstruct both the boundaries and the interior of each cell in the arrangement. We reconstruct the control points of curves bounding cells, in order to free the result from discretization and provide an output in vector format. We support interactive usage, editing shapes consisting up to 100k line segments on meshes of up to 1M triangles

A novel parallel algorithm for surface editing and its FPGA implementation

A thesis submitted to the University of Bedfordshire in partial fulfilment of the requirements for the degree of Doctor of PhilosophySurface modelling and editing is one of important subjects in computer graphics. Decades of research in computer graphics has been carried out on both low-level, hardware-related algorithms and high-level, abstract software. Success of computer graphics has been seen in many application areas, such as multimedia, visualisation, virtual reality and the Internet. However, the hardware realisation of OpenGL architecture based on FPGA (field programmable gate array) is beyond the scope of most of computer graphics researches. It is an uncultivated research area where the OpenGL pipeline, from hardware through the whole embedded system (ES) up to applications, is implemented in an FPGA chip. This research proposes a hybrid approach to investigating both software and hardware methods. It aims at bridging the gap between methods of software and hardware, and enhancing the overall performance for computer graphics. It consists of four parts, the construction of an FPGA-based ES, Mesa-OpenGL implementation for FPGA-based ESs, parallel processing, and a novel algorithm for surface modelling and editing. The FPGA-based ES is built up. In addition to the Nios II soft processor and DDR SDRAM memory, it consists of the LCD display device, frame buffers, video pipeline, and algorithm-specified module to support the graphics processing. Since there is no implementation of OpenGL ES available for FPGA-based ESs, a specific OpenGL implementation based on Mesa is carried out. Because of the limited FPGA resources, the implementation adopts the fixed-point arithmetic, which can offer faster computing and lower storage than the floating point arithmetic, and the accuracy satisfying the needs of 3D rendering. Moreover, the implementation includes Bézier-spline curve and surface algorithms to support surface modelling and editing. The pipelined parallelism and co-processors are used to accelerate graphics processing in this research. These two parallelism methods extend the traditional computation parallelism in fine-grained parallel tasks in the FPGA-base ESs. The novel algorithm for surface modelling and editing, called Progressive and Mixing Algorithm (PAMA), is proposed and implemented on FPGA-based ES’s. Compared with two main surface editing methods, subdivision and deformation, the PAMA can eliminate the large storage requirement and computing cost of intermediated processes. With four independent shape parameters, the PAMA can be used to model and edit freely the shape of an open or closed surface that keeps globally the zero-order geometric continuity. The PAMA can be applied independently not only FPGA-based ESs but also other platforms. With the parallel processing, small size, and low costs of computing, storage and power, the FPGA-based ES provides an effective hybrid solution to surface modelling and editing