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Item 2D Points Curve Reconstruction Survey and Benchmark(The Eurographics Association and John Wiley & Sons Ltd., 2021) Ohrhallinger, Stefan; Peethambaran, Jiju; Parakkat, Amal Dev; Dey, Tamal Krishna; Muthuganapathy, Ramanathan; Bühler, Katja and Rushmeier, HollyCurve reconstruction from unstructured points in a plane is a fundamental problem with many applications that has generated research interest for decades. Involved aspects like handling open, sharp, multiple and non-manifold outlines, run-time and provability as well as potential extension to 3D for surface reconstruction have led to many different algorithms. We survey the literature on 2D curve reconstruction and then present an open-sourced benchmark for the experimental study. Our unprecedented evaluation of a selected set of planar curve reconstruction algorithms aims to give an overview of both quantitative analysis and qualitative aspects for helping users to select the right algorithm for specific problems in the field. Our benchmark framework is available online to permit reproducing the results and easy integration of new algorithms.Item Moment-Based Opacity Optimization(The Eurographics Association, 2020) Zeidan, Mahmoud; Rapp, Tobias; Peters, Christoph; Dachsbacher, Carsten; Frey, Steffen and Huang, Jian and Sadlo, FilipGeometric structures such as points, lines, and surfaces play a vital role in scientific visualization. However, these visualizations frequently suffer from visual clutter that hinders the inspection of important features behind dense but less important features. In the past few years, geometric cluttering and occlusion avoidance has been addressed in scientific visualization with various approaches such as opacity optimization techniques. In this paper, we present a novel approach for opacity optimization based on recent state-of-the-art moment-based techniques for signal reconstruction. In contrast to truncated Fourier series, momentbased reconstructions of feature importance and optical depth along view rays are highly accurate for sparse regions but also plausible for densely covered regions. At the same time, moment-based methods do not suffer from ringing artifacts. Moreover, this representation enables fast evaluation and compact storage, which is crucial for per-pixel optimization especially for large geometric structures. We also present a fast screen space filtering approach for optimized opacities that works directly on moment buffers. This filtering approach is suitable for real-time visualization applications, while providing comparable quality to object space smoothing. Its implementation is independent of the type of geometry such that it is general and easy to integrate. We compare our technique to recent state of the art techniques for opacity optimization and apply it to real and synthetic data sets in various applications.Item 2D Points Curve Reconstruction Survey and Benchmark(The Eurographics Association, 2022) Ohrhallinger, Stefan; Peethambaran, Jiju; Parakkat, Amal Dev; Dey, Tamal K.; Muthuganapathy, R.; Hahmann, Stefanie; Patow, Gustavo A.Curve reconstruction from unstructured points in a plane is a fundamental problem with many applications that has generated research interest for decades. Involved aspects like handling open, sharp, multiple and non-manifold outlines, run-time and provability as well as potential extension to 3D for surface reconstruction have led to many different algorithms. We survey the literature on 2D curve reconstruction and then present an open-sourced benchmark for the experimental study. Our unprecedented evaluation of a selected set of planar curve reconstruction algorithms aims to give an overview of both quantitative analysis and qualitative aspects for helping users to select the right algorithm for specific problems in the field. Our benchmark framework is available online to permit reproducing the results and easy integration of new algorithms.