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A new measure of the accuracy of an isosurface produced by marching isosurfacing algorithms (e.g., Marching Cubes) is described. This metric has a low computational cost yet well-approximates a computationally-expensive, common assessment of produced ...

In volume rendering, most optical models currently in use are based on the assumptions that a volumetric object is a collection of particles and that the macro behavior of particles, when they interact with light rays, can be predicted based on the ...

The reconstruction of a continuous function from discrete data is a basic task in many applications such as the visualization of 3D volumetric data sets. We use a local approximation method for quadratic C1 splines on uniform tetrahedrat partitions to ...

We present a new technique for providing interpolation within cell-centered Adaptive Mesh Refinement (AMR) data that achieves C^0 continuity throughout the 3D domain. Our technique improves on earlier work in that it does not require that adjacent ...

Uncertainty is ubiquitous in science, engineering and medicine. Drawing conclusions from uncertain data is the normal case, not an exception. While the field of statistical graphics is well established, only a few 2D and 3D visualization and feature ...

Molecular dynamics simulations are a principal tool in the study of molecules. The efficient investigation of the structure and dynamics of the simulated molecular systems benefits from interactive high-quality visualizations. Molecular surfaces are ...

Two alternatives to the standard (central differencing) method for estimating normals of Marching Cubes isosurfaces are considered. The methods are based on higher order approximations of dataset gradients. Of primary concern here are the effects of ...

This paper introduces an efficient algorithm for computing the Reeb graph of a scalar function f defined on a volumetric mesh M in R^3. We introduce a procedure called "loop surgery" that transforms M into a mesh M' by a sequence of cuts and guarantees ...

Representational accuracy of the isosurface meshes produced by well-known marching isosurfacing methods is considered. Accuracy is determined versus the isosurface given by trilinear interpolation and quantified using a new measure of volumetric ...

Implicit modelling is a powerful technique to design geometric shapes, where a geometric object is described by a real function. In general, the real functions used in implicit modelling are unbounded and can take any values in space R. In general, the ...

In this paper, we present a new visibility-based feature extraction algorithm from discrete models as dense point clouds resulting from laser scans. Based on the observation that one can characterize local properties of the surface by what can be seen ...

We describe a new technique for fitting noisy scattered point cloud data. The fitting surface is determined as zero level isosurface of a trivariate model which is an implicit least squares fit of the data based upon Radial Hermite Operators (RHO). We ...

In this paper, we show that histograms represent spatial function distributions with a nearest neighbour interpolation. We confirm that this results in systematic underrepresentation of transitional features of the data, and provide new insight why this ...

Many applications require the extraction of isolines and isosurfaces from scalar functions defined on regular grids. These scalar functions may have many different origins: from MRI and CT scan data to terrain data or results of a simulation. As a ...

In this paper, we propose the utilization of a kd-tree based hierarchy as an implicit object representation. Compared to an octree, the kd-tree based hierarchy is superior in terms of adaptation to the object surface. In consequence, we obtain ...

In this paper we propose a novel visibility-culling technique for optimizing the computation and rendering of opaque isosurfaces. Given a continuous scalar field f(x) over a domain D and an iso-value w, our technique exploits the continuity of f to ...

We describe a new technique for fitting scattered point cloud data. Given a scattered point cloud of 3D data points and associated normal vectors, our new method produces an implicit volume model whose zero level isosurface interpolates the given points ...

We present the definition and computational algorithms for a new class of surfaces which are dual to the isosurface produced by the widely used marching cubes (MC) algorithm. These new isosurfaces have the same separating properties as the MC surfaces ...

We propose an interpolating refinement method for two- and three-dimensional scalar fields defined on hexahedral grids. Iterative fairing of the underlying contours (isosurfaces) provides the function values of new grid points. Our method can be ...

Heart diseases cause considerable morbidity and the prognosis after heart failure is poor. An improved understanding of cardiac mechanics is necessary to advance the diagnosis and treatment of heart diseases. This paper presents techniques for ...