Ronald J. Balsys

Refinement of the structure of Na0.74CoO2 using neutron powder diffraction

Abstract Refinement of the structure of Na 0.74(2) CoO 2 was carried out using neutron diffraction data. The material was indexed using the hexagonal P6 3 /mmc space group with lattice parameters a = 2.840(1) A and c = 10.811(1) A. High resolution neutron powder diffraction data of the layered metal oxide were analysed ab initio to reveal a structure with alternating sodium layers intercalated between octahedral sheets of cobalt oxide (CoO 6 ). The two sites available for occupancy by the sodium ion in the sodium layer of the unit cell are ( 2 3 , 1 3 , 1 4 ) and (0, 0, 1 4 ). The sodium ions occupy the two available sites unequally (the probability of finding sodium ions at one site being approximately twice that for the other site) due to the influence of second nearest neighbour cobalt ions.

Visualisation of implicit surfaces

Abstract We discuss the polygonisation and rendering of implicit surfaces through the adaptive subdivision of octree nodes. Three new algorithms which form part of this process, are discussed. The first algorithm removes the cracks that form on the surfaces between adjacent nodes that are subdivided to different depths in the octree. This algorithm fixes the cracks for arbitrary differences in depth between the adjacent nodes. The second algorithm allows user specified selected polygon outlines to be drawn on the surfaces, instead of drawing all the outlines, or no outlines. The third algorithm fixes the gaps that can appear in the polygon outlines when only selected outlines are drawn. We also investigated the use of an exact calculation of the curvature of the implicit surfaces to drive the adaptive subdivision. We conclude that this is not worthwhile doing, and give reasons.

The structure of Li0.43Na0.36CoO1.96 using neutron powder diffraction

Abstract A new layered alkali-transition metal oxide was prepared by the solid state reaction of LiCoO 2 and Na 0.7 CoO 1.96 in air at 850°C. Its chemical formula is Li 0.43 Na 0.35 CoO 1.96 as determined by atomic absorption spectrophotometry and high resolution neutron powder diffraction. X-ray and neutron diffraction data of the material were indexed using the hexagonal P6 3 mc space group with lattice parameters a = 2.839(4) A and c = 20.36(3) A . High resolution neutron powder diffraction data of the layered metal oxide were analysed ab initio to reveal a structure with alternating lithium and sodium layers intercalated between octahedral sheets oxide (CoO 6 ). The lithium ions are sited within an octahedral oxygen framework whereas the sodium ions are within a trigonal prismatic oxygen environment (between the CoO 6 layers). The sodium ions occupy two available sites unequally (the probability of finding sodium ions at one site being approximately twice that for the other site) due to the influence of second nearest neighbour cobalt ions.

Adaptive polygonisation of non-manifold implicit surfaces

We discuss the polygonisation and rendering of non-manifold implicit surfaces using adaptive octree subdivision and interval arithmetic for surface exclusion in octree nodes. We present a new algorithm that polygonises some surfaces that self intersect, or have other non-manifold features such as separate sections that meet at points. Gradient information is used to resolve ambiguous polygonisations in plotting nodes. A line-stitching algorithm is discussed that allows for multiple polygons to be in a plotting node. We illustrate the algorithm with a number of surfaces that demonstrate its capabilities and limitations.

Point-Based Rendering of Non-Manifold Surfaces

We are concerned with producing high‐quality images of parametric and implicit surfaces, in particular those with non‐manifold features. We present a point‐based technique for rendering implicit surfaces that uses octree spatial subdivision with a natural interval exclusion test that guarantees that no parts of the surface are missed. This allows us to render non‐manifold implicit surfaces at speeds comparable to parametric surfaces. We also derive criteria that guarantee complete pixel coverage of the surface. The point‐based method allows for hidden surface elimination using a z‐buffer, and shadow casting using a shadow buffer. We illustrate the technique with a number of surfaces, and discuss its advantages and disadvantages.

Point based rendering of non-manifold surfaces with contours

We present point based rendering techniques that render various types of contours as constant width slabs on surfaces. The techniques requires evaluations of the surface functions and gradients to render shaded images. We use slabs parallel to the principle planes, slabs located along a principal axis and rotated by arbitrary steps, slabs consisting of concentric spheres and slabs of constant Gaussian and mean curvatures. We also use the technique to render curvature maps of surfaces. We illustrate the techniques with a number of parametric and implicit surfaces, and discuss their advantages and disadvantages compared to other rendering techniques.

Applying Fractal and Chaos Theory to Animation in the Chinese Literati Tradition

This paper describes and tests the hypothesis that that which ancient Chinese philosophy searched for, the Tao, is the same principle as that found in modern Chaos and Fractal Theories. An elucidation of several key principles and notions of Chinese art theory is offered, coupled with fractal notions from Chaos theory. It is argued that Chinese art is an abstract form of symbolic brush-strokes, which elicit intrinsic mathematic values. An example of a modern evolving (animated) fractal form based on this notion is given to test our hypothesis

Ray Tracing Surfaces with Contours

ACM CSS: I.3.7 3D Graphics and Realism, I.3.3 Picture/Image Generation

Visualizing Nonmanifold and Singular Implicit Surfaces with Point Clouds

We use octree spatial subdivision to generate point clouds on complex nonmanifold implicit surfaces in order to visualize them. The new spatial subdivision scheme only uses point sampling and an interval exclusion test. The algorithm includes a test for pruning the resulting plotting nodes so that only points in the closest nodes to the surface are used in rendering. This algorithm results in improved image quality compared to the naive use of intervals or affine arithmetic when rendering implicit surfaces, particularly in regions of high curvature. We discuss and compare CPU and GPU versions of the algorithm. We can now render nonmanifold features such as rays, ray-like tubes, cusps, ridges, thin sections that are at arbitrary angles to the octree node edges, and singular points located within plot nodes, all without artifacts. Our previous algorithm could not render these without severe aliasing. The algorithm can render the self-intersection curves of implicit surfaces by exploiting the fact that surfaces are singular where they self-intersect. It can also render the intersection curves of two implicit surfaces. We present new image space and object space algorithms for rendering these intersection curves as contours on one of the surfaces. These algorithms are better at rendering high curvature contours than our previous algorithms. To demonstrate the robustness of the node pruning algorithm we render a number of complex implicit surfaces such as high order polynomial surfaces and Gaussian curvature surfaces. We also compare the algorithm with ray casting in terms of speed and image quality. For the surfaces presented here, the point clouds can be computed in seconds to minutes on a typical Intel based PC. Once this is done, the surfaces can be rendered at much higher frame rates to allow some degree of interactive visualization.

Real-Time Antialiasing of Edges and Contours of Point Rendered Implicit Surfaces

We present various algorithms for antialiasing silhouette edges of manifold and non-manifold implicit surfaces.The algorithms are: object space, edge blur, super-sampling, adaptive pixel-tracing, and jitter-based antialiasing. We discuss the strengths and weaknesses of the approaches and compare the results. We also discuss the antialiasing of contours rendered on implicit surfaces. The algorithms for antialiasing and rendering contours take place in the GPU and so are performed in real time. This allows us, for instance, to animate contours on a surface in real time by changing contour parameters. We give examples showing the results of our antialiasing techniques for various types of contours rendered on surfaces.