In this paper, we present a subdivision-based approach to rasterize implicit surfaces embedded in volumetric Bezier patches undergoing a nonlinear deformation. Subdividing a given patch into simpler patches to perform...
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In this paper, we present a subdivision-based approach to rasterize implicit surfaces embedded in volumetric Bezier patches undergoing a nonlinear deformation. Subdividing a given patch into simpler patches to perform the surface rasterization task is numerically robust, and allows guaranteeing visual accuracy even in the presence of geometric degeneracies. However, due to its memory requirements and slow convergence rates, subdivision is challenging to be used in an interactive environment. Unlike previous methods employing subdivision, our approach is based on the idea where for a given patch only one subdivision tree is maintained and shared among pixels. Furthermore, as the geometry of the object changes from frame to frame, a flexible data structure is proposed to manage the geometrically varying Bezier patches. The resulting algorithm is general and maps well to parallel computing platforms such as CUDA. We demonstrate on a variety of representative graphics and visualization examples that our GPU scheme scales well and achieves up to real-time performance on consumer-level graphics cards by guaranteeing visual accuracy. (C) 2014 Elsevier Ltd. All rights reserved.
We present a non-rigid surface registration technique that can align surfaces with sizes and shapes that are different from each other, while avoiding mesh distortions during deformation. The registration is constrain...
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We present a non-rigid surface registration technique that can align surfaces with sizes and shapes that are different from each other, while avoiding mesh distortions during deformation. The registration is constrained locally as conformal as possible such that the angles of triangle meshes are preserved, yet local scales are allowed to change. Based on our conformal registration technique, we devise an automatic registration and interactive registration technique, which can reduce user interventions during template fitting. We demonstrate the versatility of our technique on a wide range of surfaces.
Many man-made objects, in particular building facades, exhibit dominant structural relations such as symmetry and regularity. When editing these shapes, a common objective is to preserve these relations. However, ofte...
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Many man-made objects, in particular building facades, exhibit dominant structural relations such as symmetry and regularity. When editing these shapes, a common objective is to preserve these relations. However, often there are numerous plausible editing results that all preserve the desired structural relations of the input, creating ambiguity. We propose an interactive facade editing framework that explores this structural ambiguity. We first analyze the input in a semi-automatic manner to detect different groupings of the facade elements and the relations among them. We then provide an incremental editing process where a set of variations that preserve the detected relations in a particular grouping are generated at each step. Starting from one input example, our system can quickly generate various facade configurations.
Multifluid simulations often create volume fraction data, representing fluid volumes per region or cell of a fluid data set. Accurate and visually realistic extraction of fluid boundaries is a challenging and essentia...
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Multifluid simulations often create volume fraction data, representing fluid volumes per region or cell of a fluid data set. Accurate and visually realistic extraction of fluid boundaries is a challenging and essential task for efficient analysis of multifluid data. In this work, we present a new material interface reconstruction method for such volume fraction data. Within each cell of the data set, our method utilizes a gradient field approximation based on trilinearly blended Coons-patches to generate a volume fraction function, representing the change in volume fractions over the cells. A continuously varying isovalue field is applied to this function to produce a smooth interface that preserves the given volume fractions well. Further, the method allows user-controlled balance between volume accuracy and physical plausibility of the interface. The method works on two-and three-dimensional Cartesian grids, and handles multiple materials. Calculations are performed locally and utilize only the one-ring of cells surrounding a given cell, allowing visualizations of the material interfaces to be easily generated on a GPU or in a large-scale distributed parallel environment. Our results demonstrate the robustness, accuracy, and flexibility of the developed algorithms.
We present a method for computing "choking" loops-a set of surface loops that describe the narrowing of the volumes inside/outside of the surface and extend the notion of surface homology and homotopy loops....
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We present a method for computing "choking" loops-a set of surface loops that describe the narrowing of the volumes inside/outside of the surface and extend the notion of surface homology and homotopy loops. The intuition behind their definition is that a choking loop represents the region where an offset of the original surface would get pinched. Our generalized loops naturally include the usual 2g handles/tunnels computed based on the topology of the genus-g surface, but also include loops that identify chokepoints or bottlenecks, i.e., boundaries of small membranes separating the inside or outside volume of the surface into disconnected regions. Our definition is based on persistent homology theory, which gives a measure to topological structures, thus providing resilience to noise and a well-defined way to determine topological feature size. More precisely, the persistence computed here is based on the lower star filtration of the interior or exterior 3D domain with the distance field to the surface being the associated 3D Morse function.
We present a new circular-arc cartogram model in which countries are drawn as polygons with circular arcs instead of straight-line segments. Given a political map and values associated with each country in the map, a ...
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ISBN:
(纸本)9781467347976
We present a new circular-arc cartogram model in which countries are drawn as polygons with circular arcs instead of straight-line segments. Given a political map and values associated with each country in the map, a cartogram is a distorted map in which the areas of the countries are proportional to the corresponding values. In the circular-arc cartogram model straight-line segments can be replaced by circular arcs in order to modify the areas of the polygons, while the corners of the polygons remain fixed. The countries in circular-arc cartograms have the aesthetically pleasing appearance of clouds or snowflakes, depending on whether their edges are bent outwards or inwards. This makes it easy to determine whether a country has grown or shrunk, just by its overall shape. We show that determining whether a given map and given area-values can be realized as a circular-arc cartogram is an NP-hard problem. Next we describe a heuristic method for constructing circular-arc cartograms,
In this paper, we presented a method for fitting large B-spline topological surfaces on freeform polygon mesh generated from cloud data of objects. The mesh has been manually segmented and large surfaces are fitted on...
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In this paper, we presented a method for fitting large B-spline topological surfaces on freeform polygon mesh generated from cloud data of objects. The mesh has been manually segmented and large surfaces are fitted on segments in a hybrid approach, i.e., combination of geometric subdivision and non-uniform rational B-spline (NURBS) interpolation which is an emerging research space. An interpolation method has been proposed to parameterize dense cloud data of any complexity level with capability of handling occluded regions. All junctions are treated with trimming of NURBS surfaces with C (0) and C (1) continuities between adjacent patches. This scheme amalgamated process knowledge of reconstruction on segmented and subdivided point cloud data, various NURBS geometry options and junction treatment resulting in faster high-quality reconstruction. Apart from manual segmentation, almost the entire process is automatic which generated superior quality surface models. Pawn, Stanford Bunny, and human head clouds with occluded surface zones are used for tryout and resulting shapes are recorded in initial graphics exchange specification (IGES) files.
The rapid development of 3D acquisition technology has brought with itself the need to perform standard signal processing operations such as filters on 3D data. It has been shown that the eigenfunctions of the Laplace...
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ISBN:
(纸本)9783642338632;9783642338625
The rapid development of 3D acquisition technology has brought with itself the need to perform standard signal processing operations such as filters on 3D data. It has been shown that the eigenfunctions of the Laplace-Beltrami operator (manifold harmonics) of a surface play the role of the Fourier basis in the Euclidean space;it is thus possible to formulate signal analysis and synthesis in the manifold harmonics basis. In particular, geometry filtering can be carried out in the manifold harmonics domain by decomposing the embedding coordinates of the shape in this basis. However, since the basis functions depend on the shape itself, such filtering is valid only for weak (near all-pass) filters, and produces severe artifacts otherwise. In this paper, we analyze this problem and propose the fractional filtering approach, wherein we apply iteratively weak fractional powers of the filter, followed by the update of the basis functions. Experimental results show that such a process produces more plausible and meaningful results.
This paper considers the problem of interactively finding the cutting contour to extract components from an existing mesh. First, we propose a constrained random walks algorithm that can add constraints to the random ...
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This paper considers the problem of interactively finding the cutting contour to extract components from an existing mesh. First, we propose a constrained random walks algorithm that can add constraints to the random walks procedure and thus allows for a variety of intuitive user inputs. Second, we design an optimization process that uses the shortest graph path to derive a nice cut contour. Then a new mesh cutting algorithm is developed based on the constrained random walks plus the optimization process. Within the same computational framework, the new algorithm provides a novel user interface for interactive mesh cutting that supports three typical user inputs and also their combinations: 1) foreground/background seed inputs: the user draws strokes specifying seeds for "foreground" (i.e., the part to be cut out) and "background" (i.e., the rest);2) soft constraint inputs: the user draws strokes on the mesh indicating the region which the cuts should be made nearby;and 3) hard constraint inputs: the marks which the cutting contour must pass. The algorithm uses feature sensitive metrics that are based on surface geometric properties and cognitive theory. The integration of the constrained random walks algorithm, the optimization process, the feature sensitive metrics, and the varieties of user inputs makes the algorithm intuitive, flexible, and effective as well. The experimental examples show that the proposed cutting method is fast, reliable, and capable of producing good results reflecting user intention and geometric attributes.
This paper addresses the definition, contouring, and visualization of scalar functions on unorganized point sets, which are sampled from a surface in 3D space;the proposed framework builds on moving least-squares tech...
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This paper addresses the definition, contouring, and visualization of scalar functions on unorganized point sets, which are sampled from a surface in 3D space;the proposed framework builds on moving least-squares techniques and implicit modeling. Given a scalar function f : P -> R, defined on a point set P, the idea behind our approach is to exploit the local connectivity structure of the k-nearest neighbor graph of P and mimic the contouring of scalar functions defined on triangle meshes. Moving least-squares and implicit modeling techniques are used to extend f from P to the surface M underlying P. To this end, we compute an analytical approximation (f) over tilde of f that allows us to provide an exact differential analysis of (f) over tilde, draw its iso-contours, visualize its behavior on and around M, and approximate its critical points. We also compare moving least-squares and implicit techniques for the definition of the scalar function underlying f and discuss their numerical stability and approximation accuracy. Finally, the proposed framework is a starting point to extend those processing techniques that build on the analysis of scalar functions on 2-manifold surfaces to point sets. (c) 2010 Elsevier Ltd. All rights reserved.
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