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**11 - 17**of**17**### EFFICIENT MULTIFRAGMENT EFFECTS ON GRAPHICS PROCESSING UNITS

, 2007

"... has been read by each member of the following supervisory committee and by majority vote has been found to be satisfactory. ..."

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has been read by each member of the following supervisory committee and by majority vote has been found to be satisfactory.

### GPU-Accelerated Volume Splatting With Elliptical RBFs

"... Radial Basis Functions (RBFs) have become a popular rendering primitive, both in surface and in volume rendering. This paper focuses on volume visualization, giving rise to 3D kernels. RBFs are especially convenient for the representation of scattered and irregularly distributed point samples, where ..."

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Radial Basis Functions (RBFs) have become a popular rendering primitive, both in surface and in volume rendering. This paper focuses on volume visualization, giving rise to 3D kernels. RBFs are especially convenient for the representation of scattered and irregularly distributed point samples, where the RBF kernel is used as a blending function for the space in between samples. Common representations employ radially symmetric RBFs, and various techniques have been introduced to render these, also with efficient implementations on programmable graphics hardware (GPUs). In this paper, we extend the existing work to more generalized, ellipsoidal RBF kernels, for the rendering of scattered volume data. We devise a post-shaded kernel-centric rendering approach, specifically designed to run efficiently on GPUs, and we demonstrate our renderer using datasets from subdivision volumes and computational science. Categories and Subject Descriptors (according to ACM CSS): I.3.3 [Computer Graphics]: Display Algorithms 1.

### Direct Isosurface Extraction from Scattered Volume Data

"... Isosurface extraction is a standard visualization method for scalar volume data and has been subject to research for decades. Nevertheless, to our knowledge, no isosurface extraction method exists that directly extracts surfaces from scattered volume data without 3D mesh generation or reconstruction ..."

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Isosurface extraction is a standard visualization method for scalar volume data and has been subject to research for decades. Nevertheless, to our knowledge, no isosurface extraction method exists that directly extracts surfaces from scattered volume data without 3D mesh generation or reconstruction over a structured grid. We propose a method based on spatial domain partitioning using a kd-tree and an indexing scheme for efcient neighbor search. Our approach consists of a geometry extraction and a rendering step. The geometry extraction step computes points on the isosurface by linearly interpolating between neighboring pairs of samples. The neighbor information is retrieved by partitioning the 3D domain into cells using a kd-tree. The cells are merely described by their index and bitwise index operations allow for a fast determination of potential neighbors. We use an angle criterion to select appropriate neighbors from the small set of candidates. The output of the geometry step is a point cloud representation of the isosurface. The nal rendering step uses point-based rendering techniques to visualize the point cloud. Our direct isosurface extraction algorithm for scattered volume data produces results of quality close to the results from standard isosurface extraction algorithms for gridded volume data (like marching cubes). In comparison to 3D mesh generation algorithms (like Delaunay tetrahedrization), our algorithm is about one order of magnitude faster for the examples used in this paper.

### ABSTRACT On The Simplification Of Radial Basis Function Fields For Volume Rendering: Some Practical Insights

"... Volume rendering with splatting most commonly decomposes a volume dataset into a field of overlapping radial basis function (RBF) kernels, such as Gaussians. The rendering effort is directly related to the number of RBFs in the volume and the degree of RBF overlap in the rasterization phase. Much wo ..."

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Volume rendering with splatting most commonly decomposes a volume dataset into a field of overlapping radial basis function (RBF) kernels, such as Gaussians. The rendering effort is directly related to the number of RBFs in the volume and the degree of RBF overlap in the rasterization phase. Much work has been done that seeks to lower the number of RBFs by replacing a neighborhood of kernels with a single, wider kernel of the same family. The most regular decomposition for this is the octree. We argue in this paper that this simplification can adversely change the characteristics of the volume, as this substitution results in a different reconstruction of the local volume function. To cope, we propose a special kernel, called AG-splat (AGglutinative splat), which is designed to faithfully encode the local set of RBFs it seeks to replace. At the same time, AG-splats are amenable to the same expedient rendering mechanisms than the regular RBFs. Apart from the rendering primitive itself, we also give a local algorithm, based on statistical fitting, for its encoding of homogenous and ramp-like volume areas. 1

### Ray-Driven Dynamic Working Set Rendering For Complex Volume Scene Graphs Involving Large Point Clouds

"... Abstract Ray tracing a volume scene graph composed of multiple point-based volume objects (PBVO) can produce high quality images with effects such as shadows and constructive operations. A naive approach, however, would demand an overwhelming amount of memory to accommodate all point datasets and th ..."

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Abstract Ray tracing a volume scene graph composed of multiple point-based volume objects (PBVO) can produce high quality images with effects such as shadows and constructive operations. A naive approach, however, would demand an overwhelming amount of memory to accommodate all point datasets and their associated control structures such as octrees. This paper describes an out-of-core system for rendering such a scene graph in a scalable manner. In order to address the difficulty in pre-determining the order of data caching, we introduce a technique based on a dynamic, in-core working set. We present a ray-driven algorithm for predicting the working set automatically. This allows both the data and the control structures required for ray tracing to be dynamically pre-fetched according to access patterns determined based on captured knowledge of ray-data intersection. We have conducted a series of experiments on the scalability of the technique using working sets and datasets of different sizes. With the aid of both qualitative and quantitative analysis, we demonstrate that this approach allows the rendering of multiple large PBVOs in a volume scene graph be performed on desktop computers. Keywords out-of-core · very large dataset visualization · octree · point-based modeling · point-based rendering · ray tracing · volume scene graph

### Visualization of Cosmological Particle-Based Datasets

"... Abstract—We describe our visualization process for a particle-based simulation of the formation of the first stars and their impact on cosmic history. The dataset consists of several hundred time-steps of point simulation data, with each time-step containing approximately two million point particles ..."

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Abstract—We describe our visualization process for a particle-based simulation of the formation of the first stars and their impact on cosmic history. The dataset consists of several hundred time-steps of point simulation data, with each time-step containing approximately two million point particles. For each time-step, we interpolate the point data onto a regular grid using a method taken from the radiance estimate of photon mapping [21]. We import the resulting regular grid representation into ParaView [24], with which we extract isosurfaces across multiple variables. Our images provide insights into the evolution of the early universe, tracing the cosmic transition from an initially homogeneous state to one of increasing complexity. Specifically, our visualizations capture the build-up of regions of ionized gas around the first stars, their evolution, and their complex interactions with the surrounding matter. These observations will guide the upcoming James Webb Space Telescope, the key astronomy mission of the next decade. Index Terms—Interpolation, Isosurface, Astronomy, Cosmology. 1