We present a higher-order approach to the extraction of isosurfaces from unstructured meshes. Existing methods use linear interpolation along each mesh edge to find isosurface intersections. In contrast, our method de...
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We present a higher-order approach to the extraction of isosurfaces from unstructured meshes. Existing methods use linear interpolation along each mesh edge to find isosurface intersections. In contrast, our method determines intersections by performing barycentric interpolation over diamonds formed by the tetrahedra incident to each edge. Our method produces smoother, more accurate isosurfaces. Additionally, interpolating over diamonds, rather than linearly interpolating edge endpoints. enables us to identify up to two isosurface intersections per edge. This paper details how our new technique extracts isopoints, and presents a simple connection strategy for forming a triangle mesh isosurface.
We introduce a technique to visualize the gradual evolutionary change of the shapes of living things as a morph between known three-dimensional shapes. Given geometric computer models of anatomical shapes for some col...
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ISBN:
(纸本)0780394623
We introduce a technique to visualize the gradual evolutionary change of the shapes of living things as a morph between known three-dimensional shapes. Given geometric computer models of anatomical shapes for some collection of specimens - here the skulls of the some of the extant members of a family of monkeys - an evolutionary tree for the group implies a hypothesis about the way in which the shape changed through time. We use a statistical model which expresses the value of some continuous variable at an internal point in the tree as a weighted average of the values at the leaves. The framework of geometric morphometrics can then be used to define a shape-space, based on the correspondences of landmark points on the surfaces, within which these weighted averages can be realized as actual surfaces. Our software provides tools for performing and visualizing such an analysis in three dimensions. Beginning with laser range scans of crania, we use our landmark editor to interactively place landmark points on the surface. We use these to compute a "tree-morph" that smoothly interpolates the shapes across the tree. Each intermediate shape in the morph is a linear combination of all of the input surfaces. We create a surface model for an intermediate shape by warping all the input meshes towards the correct shape and then blending them together. To do the blending, we compute a weighted average of their associated trivariate distance functions and then extract a surface from the resulting function. We implement this idea using the squared distance function, rather than the usual signed distance function, in a novel way.
We present an approach to hierarchically encode the topology of functions over triangulated surfaces. Its Morse-Smale complex, a well known structure in computational topology, describes the topology of a function. Fo...
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We present an approach to hierarchically encode the topology of functions over triangulated surfaces. Its Morse-Smale complex, a well known structure in computational topology, describes the topology of a function. Following concepts of Morse theory, a Morse-Smale complex (and therefore a function's topology) can be simplified by successively canceling pairs of critical points. We demonstrate how cancellations can be effectively encoded to produce a highly adaptive topology-based multi-resolution representation of a given function. Contrary to the approach, we avoid encoding the complete complex in a traditional mesh hierarchy. Instead, the information is split into a new structure we call a cancellation forest and a traditional dependency graph. The combination of this new structure with a traditional mesh hierarchy proofs to be significantly more flexible than the one previously reported. In particular, we can create hierarchies that are guaranteed to be of logarithmic height.
Visualizing hierarchical data is one of the core areas of information visualization. Most of these techniques focus on single hierarchies—hierarchies with a single root element and a single path to each element. In c...
We introduce a technique to visualize the gradual evolutionary change of the shapes of living things as a morph between known three-dimensional shapes. Given geometric computer models of anatomical shapes for some col...
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We introduce a technique to visualize the gradual evolutionary change of the shapes of living things as a morph between known three-dimensional shapes. Given geometric computer models of anatomical shapes for some collection of specimens - here the skulls of the some of the extant members of a family of monkeys - an evolutionary tree for the group implies a hypothesis about the way in which the shape changed through time. We use a statistical model which expresses the value of some continuous variable at an internal point in the tree as a weighted average of the values at the leaves. The framework of geometric morphometrics can then be used to define a shape-space, based on the correspondences of landmark points on the surfaces, within which these weighted averages can be realized as actual surfaces. Our software provides tools for performing and visualizing such an analysis in three dimensions. Beginning with laser range scans of crania, we use our landmark editor to interactively place landmark points on the surface. We use these to compute a "tree-morph" that smoothly interpolates the shapes across the tree. Each intermediate shape in the morph is a linear combination of all of the input surfaces. We create a surface model for an intermediate shape by warping all the input meshes towards the correct shape and then blending them together. To do the blending, we compute a weighted average of their associated trivariate distance functions and then extract a surface from the resulting function. We implement this idea using the squared distance function, rather than the usual signed distance function, in a novel way.
This work focuses on visualizing highly cyclic hierarchical data. A user interface is discussed and its interaction is illustrated using a recipe database example. This example showcases a database with multiple categ...
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This work focuses on visualizing highly cyclic hierarchical data. A user interface is discussed and its interaction is illustrated using a recipe database example. This example showcases a database with multiple categ...
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This work focuses on visualizing highly cyclic hierarchical data. A user interface is discussed and its interaction is illustrated using a recipe database example. This example showcases a database with multiple categories for each recipe (database entry).
We introduce the piecewise-linear Haar (PLHaar) transform, a reversible n-bit to n-bit transform that is based on the Haar wavelet transform. PLHaar is continuous, while all current n-bit to n-bit methods are not, and...
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We introduce the piecewise-linear Haar (PLHaar) transform, a reversible n-bit to n-bit transform that is based on the Haar wavelet transform. PLHaar is continuous, while all current n-bit to n-bit methods are not, and is therefore uniquely usable with both lossy and lossless methods (e.g. image compression). PLHaar has both integer and continuous (i.e. non-discrete) forms. By keeping the coefficients to n bits PLHaar is particularly suited for use in hardware environments where channel width is limited, such as digital video channels and graphics hardware.
We present a variant of fuzzy c-means that allows us to find similar shapes in time series data in a scale-invariant fashion. We use data from protein mass spectrography to show how this approach finds areas of intere...
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We present a variant of fuzzy c-means that allows us to find similar shapes in time series data in a scale-invariant fashion. We use data from protein mass spectrography to show how this approach finds areas of interest without a need for ad-hoc normalizations.
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