Scientific visualization is a discipline that transforms raw data into meaningful representations, enhancing our understanding of underlying phenomena. Through visualization, domain experts, scientists, engineers, and even novice users can gain valuable insights into processes such as scientific simulations and real-world systems.

Vector field visualization is an active area of research that supports experts across many disciplines — including biology, chemistry, and medicine — in exploring critical phenomena and identifying salient features within flow data. Geometric primitives such as points, lines, and surfaces are fundamental to representing flow structures. However, these visualizations often suffer from visual clutter, which can obscure important features beneath dense or less relevant elements. Recent advances such as streamline selection and opacity optimization aim to reduce this clutter, but most such techniques remain too computationally demanding for real-time and interactive settings.

In parallel, understanding large-scale particle simulations of the universe has become increasingly important for physicists, astrophysicists, and other domain scientists. Cosmological structures, galaxy formation, and the evolution of the universe are explored using dynamic particle simulations — such as smoothed particle hydrodynamics (SPH) — executed on large compute clusters. As simulation outputs reach tera-, peta-, and even exascale, interactively visualizing such massive datasets becomes a significant challenge, particularly for maintaining responsiveness during data exploration.

This dissertation addresses these challenges and proposes efficient solutions for the rendering and understanding of complex datasets, spanning vector field visualization and large-scale particle rendering. All proposed solutions leverage the massively parallel architecture of modern GPUs to enable fast, interactive rendering.

Glyph-based Flow Visualization. Line integral convolution (LIC) is a standard method for texture-based vector field visualization, but 3D texture-based methods are computationally demanding due to convolution and volume rendering. Geometry-based techniques instead generate glyphs conveying attributes such as rotation or divergence, but typically require different glyph types for different phenomena. This thesis presents a geometry-based visualization technique that unifies and extends prior approaches within a flexible, GPU-accelerated framework, mapping characteristic lines to a variety of interpolated glyph cross-sections and approximating the appearance of 3D LIC, achieving fast rendering at high resolutions with moderate memory usage.

Moment-based Opacity Optimization. Geometric occlusion is a common challenge in flow visualization. This thesis introduces a novel opacity optimization approach based on moment-based signal reconstruction, which — unlike truncated Fourier series — yields accurate results in sparse regions, remains plausible in dense areas, avoids ringing artifacts, and supports compact storage and fast per-pixel evaluation. A screen-space filtering technique operating directly on moment buffers further smooths optimized opacities at quality comparable to object-space smoothing.

Out-of-Core Large Particle Visualization. This thesis also presents a visualization method for large particle datasets based on level-of-detail (LoD) structures and GPU-based out-of-core (OOC) paging. A GPU-friendly indexing tree manages large-scale particle data to support LoD construction and interactive rendering, enabling millions of particles to be rendered at interactive frame rates entirely on the GPU. The approach is demonstrated on the Illustris dataset, a large-scale cosmological simulation of galaxy formation and the evolution of the universe.