365 research outputs found

    Exploiting lattice structures in shape grammar implementations

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    The ability to work with ambiguity and compute new designs based on both defined and emergent shapes are unique advantages of shape grammars. Realizing these benefits in design practice requires the implementation of general purpose shape grammar interpreters that support: (a) the detection of arbitrary subshapes in arbitrary shapes and (b) the application of shape rules that use these subshapes to create new shapes. The complexity of currently available interpreters results from their combination of shape computation (for subshape detection and the application of rules) with computational geometry (for the geometric operations need to generate new shapes). This paper proposes a shape grammar implementation method for three-dimensional circular arcs represented as rational quadratic BĂ©zier curves based on lattice theory that reduces this complexity by separating steps in a shape computation process from the geometrical operations associated with specific grammars and shapes. The method is demonstrated through application to two well-known shape grammars: Stiny's triangles grammar and Jowers and Earl's trefoil grammar. A prototype computer implementation of an interpreter kernel has been built and its application to both grammars is presented. The use of BĂ©zier curves in three dimensions opens the possibility to extend shape grammar implementations to cover the wider range of applications that are needed before practical implementations for use in real life product design and development processes become feasible

    A discrete methodology for controlling the sign of curvature and torsion for NURBS

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    This paper develops a discrete methodology for approximating the so-called convex domain of a NURBS curve, namely the domain in the ambient space, where a user-specified control point is free to move so that the curvature and torsion retains its sign along the NURBS parametric domain of definition. The methodology provides a monotonic sequence of convex polyhedra, converging from the interior to the convex domain. If the latter is non-empty, a simple algorithm is proposed, that yields a sequence of polytopes converging uniformly to the restriction of the convex domain to any user-specified bounding box. The algorithm is illustrated for a pair of planar and a spatial BĂ©zier configuration

    Geometric characteristics of conics in BĂ©zier form

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    In this paper, we address the calculation of geometric characteristics of conic sections (axes, asymptotes, centres, eccentricity, foci) given in BĂ©zier form in terms of their control polygons and weights, making use of real and complex projective and affine geometry and avoiding the use of coordinates

    Arbitrary topology meshes in geometric design and vector graphics

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    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

    An Efficient Trim Structure for Rendering Large B-Rep Models

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    International audienceWe present a multiresolution trim structure for fast and accurate B-Rep model visualization. To get a good tradeoff between performance and visual accuracy, we propose to use a vectorial but approximated representation of the model that allows efficient, real-time GPU exploitation. Our structure, based on a quadtree, enables us to do shallow lookups for distant fragments. For closeups, we leverage hardware tessellation. We get interactive frame rates for models that consists of hundreds of thousands of B-Rep faces, regardless of the zoom level

    Streaming of Plants in Distributed Virtual Environments

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    International audienceJust as in the real world, plants are important objects in virtual world for creating pleasant and realistic environments, especially those involving natural scenes. As such, much effort has been made in realistic modeling of plants. As the trend moves towards networked and distributed virtual environment, however, the current models are inadequate as they are not designed for progressive transmissions. In this paper, we fill in this gap by proposing a progressive representation for plants based on generalized cylinders. To facilitate the transmission of the plants, we quantify the visual contribution of each branch and use this weight in packet scheduling. We show the efficiency of our representations and effectiveness of our packet scheduler through simulations

    BoolSurf: Boolean Operations on Surfaces

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    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 BĂ©zier 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

    Multisided generalisations of Gregory patches

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    We propose two generalisations of Gregory patches to faces of any valency by using generalised barycentric coordinates in combination with two kinds of multisided BĂ©zier patches. Our first construction builds on S-patches to generalise triangular Gregory patches. The local construction of Chiyokura and Kimura providing G1 continuity between adjoining BĂ©zier patches is generalised so that the novel Gregory S-patches of any valency can be smoothly joined to one another. Our second construction makes a minor adjustment to the generalised BĂ©zier patch structure to allow for cross-boundary derivatives to be defined independently per side. We show that the corresponding blending functions have the inherent ability to blend ribbon data much like the rational blending functions of Gregory patches. Both constructions take as input a polygonal mesh with vertex normals and provide G1 surfaces interpolating the input vertices and normals. Due to the full locality of the methods, they are well suited for geometric modelling as well as computer graphics applications relying on hardware tessellation

    Interactive real-time three-dimensional visualisation of virtual textiles

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    Virtual textile databases provide a cost-efficient alternative to the use of existing hardcover sample catalogues. By taking advantage of the high performance features offered by the latest generation of programmable graphics accelerator boards, it is possible to combine photometric stereo methods with 3D visualisation methods to implement a virtual textile database. In this thesis, we investigate and combine rotation invariant texture retrieval with interactive visualisation techniques. We use a 3D surface representation that is a generic data representation that allows us to combine real-time interactive 3D visualisation methods with present day texture retrieval methods. We begin by investigating the most suitable data format for the 3D surface representation and identify relief-mapping combined with BĂ©zier surfaces as the most suitable 3D surface representations for our needs, and go on to describe how these representation can be combined for real-time rendering. We then investigate ten different methods of implementing rotation invariant texture retrieval using feature vectors. These results show that first order statistics in the form of histogram data are very effective for discriminating colour albedo information, while rotation invariant gradient maps are effective for distinguishing between different types of micro-geometry using either first or second order statistics.Engineering and physical Sciences Research (EPSRC
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