Co-Planar Stereotaxic Atlas of the Human Brain—3-Dimensional Proportional System: An Approach to Cerebral Imaging, J. Talairach, P. Tournoux. Georg Thieme Verlag, New York (1988), 122 pp., 130 figs. DM 268

Monthly Notices is one of the three largest general primary astronomical research publications. It is an international journal, published by the Royal Astronomical Society. This article 1 describes its publication policy and practice.

Monthly Notices of the Royal Astronomical Society

Initial-value ordinary differential equation solution via variable order Adams method (SIVA/DIVA) package is collection of subroutines for solution of nonstiff ordinary differential equations. There are versions for single-precision and double-precision arithmetic. Requires fewer evaluations of derivatives than other variable-order Adams predictor/ corrector methods. Option for direct integration of second-order equations makes integration of trajectory problems significantly more efficient. Written in FORTRAN 77.

Solving Ordinary Differential Equations

Computational geometry

We present a sketching interface for quickly and easily designing freeform models such as stuffed animals and other rotund objects. The user draws several 2D freeform strokes interactively on the screen and the system automatically constructs plausible 3D polygonal surfaces. Our system supports several modeling operations, including the operation to construct a 3D polygonal surface from a 2D silhouette drawn by the user: it inflates the region surrounded by the silhouette making wide areas fat, and narrow areas thin. Teddy, our prototype system, is implemented as a Java™ program, and the mesh construction is done in real-time on a standard PC. Our informal user study showed that a first-time user typically masters the operations within 10 minutes, and can construct interesting 3D models within minutes.

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Teddy: a sketching interface for 3D freeform design

A comprehensive uncertainty, baseline, and noise analysis in computing 3D points using a recent L1-based triangulation algorithm is presented. This method is shown to be not only faster and more accurate than its main competitor, linear triangulation, but also more stable under noise and baseline changes. A Monte Carlo analysis of covariance and a confidence ellipsoid analysis were performed over a large range of baselines and noise levels for different camera configurations, to compare performance between angular error-based and linear triangulation. Furthermore, the effect of baseline and noise was analyzed for true multi-view triangulation versus pair wise stereo fusion. Results on real and synthetic data show that L1 angular error-based triangulation has a positive effect on confidence ellipsoids, lowers covariance values and results in more-accurate pair wise and multi-view triangulation, for varying numbers of cameras and configurations.

/pdf/uncertainty-baseline-and-noise-analysis-for-l1-error-based-gf4pma5hzp.pdf

Uncertainty, Baseline, and Noise Analysis for L1 Error-Based Multi-view Triangulation

We present a method for hierarchical data approximation using quadratic simplicial elements for domain decomposition and field approximation Higher-order simplicial elements can approximate data better than linear elements Thus, fewer quadratic elements are required to achieve similar approximation quality We use quadratic basis functions and compute best quadratic simplicial spline approximations that are C0-continuous everywhere We adaptively refine a simplicial approximation by identifying and bisecting simplicial elements with largest errors It is possible to store multiple approximation levels of increasing quality We have tested the suitability and efficiency of our hierarchical data approximation scheme by applying it to several data sets

/pdf/best-quadratic-spline-approximation-for-hierarchical-4ahi1fqf9x.pdf

Best quadratic spline approximation for hierarchical visualization

Multiresolution representation of high-dimensional scattered data is a fundamental problem in scientific visualization. This paper introduces a data hierarchy of Voronoi diagrams as a versatile Solution. Given an arbitrary set of points in the plane, our goal is the construction of an approximation hierarchy using the Voronoi diagram as the essential building block. We have implemented two Voronoi diagram-based algorithms to demonstrate their usefulness for hierarchical scattered data approximation. The first algorithm uses a constant function to approximate the data within each Voronoi cell, and the second algorithm uses the Sibson interpolant [14].

/pdf/hierarchical-data-representations-based-on-planar-voronoi-2edm1z62bq.pdf

Hierarchical Data Representations Based on Planar Voronoi Diagrams

Author(s): Bremer, Peer Timo; Porumbescu, Serban D.; Hamann, Bernd; Joy, Ken | Editor(s): Lyche, T.; Mazure, M.-L.; Schumaker, L. L. | Abstract: This paper describes a method to construct semi-regular meshes for a surface S defined by the zero set of a trivariate function F(x,y,z), representing a distance eld definition of S. An adaptive distance field (ADF) definition of S is obtained by constructing, adap- tively, an octree decomposition of F's domain. The vertices of the octree-based denition of S lie either on the positive or negative side of S (or on S). Octree cells that are intersected by S are identified, and the faces of these cells that lie on the outside of S are projected onto S. The result is a quadrilateral mesh to which various procedures are applied that lead to an improved mesh containing a much smaller number of extraordinary vertices, i.e., non-valence-four vertices.

/pdf/automatic-semi-regular-mesh-construction-from-adaptive-4r9mff61bt.pdf

Automatic Semi-Regular Mesh Construction from Adaptive Distance Fields

We present a visualization method for the exploration of three-dimensional tensor fields The representation of the tensor field on a one-parameter family of two-dimensional surfaces as stretched, compressed and bent piece of fabric reflects the physical properties of stress and strain tensor fields The texture parameters as the fiber density and fiber direction are controlled by tensor field The surface family is defined as a set of isosurfaces extracted from an additional scalar field This field can be a “connected” scalar field, for example, pressure or a scalar field representing some symmetry or inherent structure of the dataset The texture generation consists basically of three steps The first is the transformation of the tensor field into a positive definite metric In the second step, we generate a spot noise texture as input for the final fabric generation Shape and density of the spots are controlled by the eigenvalues of the tensor field This spot image incorporates the entire information defined by the three eigenvalue fields In the third step we use line integral convolution (LIC) to provide a contin- uous representation that enhances the visibility of the eigendirections This method supports an intuitive distinction between positive and negative eigenvalues and supports the additional visualization of a connected scalar field

/pdf/tensor-fields-visualization-using-a-fabric-like-texture-3ehddh452m.pdf

Kenneth I. Joy

Papers

Uncertainty, Baseline, and Noise Analysis for L1 Error-Based Multi-view Triangulation

Best quadratic spline approximation for hierarchical visualization

Hierarchical Data Representations Based on Planar Voronoi Diagrams

Automatic Semi-Regular Mesh Construction from Adaptive Distance Fields

Tensor-Fields Visualization Using a Fabric-like Texture Applied to Arbitrary Two-dimensional Surfaces