2,325 research outputs found
Gap Processing for Adaptive Maximal Poisson-Disk Sampling
In this paper, we study the generation of maximal Poisson-disk sets with
varying radii. First, we present a geometric analysis of gaps in such disk
sets. This analysis is the basis for maximal and adaptive sampling in Euclidean
space and on manifolds. Second, we propose efficient algorithms and data
structures to detect gaps and update gaps when disks are inserted, deleted,
moved, or have their radius changed. We build on the concepts of the regular
triangulation and the power diagram. Third, we will show how our analysis can
make a contribution to the state-of-the-art in surface remeshing.Comment: 16 pages. ACM Transactions on Graphics, 201
Multi-objective optimization of a wing fence on an unmanned aerial vehicle using surrogate-derived gradients
In this paper, the multi-objective, multifidelity optimization of a wing fence on an unmanned aerial vehicle (UAV) near stall is presented. The UAV under consideration is characterized by a blended wing body (BWB), which increases its efficiency, and a tailless design, which leads to a swept wing to ensure longitudinal static stability. The consequence is a possible appearance of a nose-up moment, loss of lift initiating at the tips, and reduced controllability during landing, commonly referred to as tip stall. A possible solution to counter this phenomenon is wing fences: planes placed on top of the wing aligned with the flow and developed from the idea of stopping the transverse component of the boundary layer flow. These are optimized to obtain the design that would fence off the appearance of a pitch-up moment at high angles of attack, without a significant loss of lift and controllability. This brings forth a constrained multi-objective optimization problem. The evaluations are performed through unsteady Reynolds-Averaged Navier-Stokes (URANS) simulations. However, since controllability cannot be directly assessed through computational fluid dynamics (CFD), surrogate-derived gradients are used. An efficient global optimization framework is developed employing surrogate modeling, namely regressive co-Kriging, updated using a multi-objective formulation of the expected improvement. The result is a wing fence design that extends the flight envelope of the aircraft, obtained with a feasible computational budget
Variational blue noise sampling
Blue noise point sampling is one of the core algorithms in computer graphics. In this paper, we present a new and versatile variational framework for generating point distributions with high-quality blue noise characteristics while precisely adapting to given density functions. Different from previous approaches based on discrete settings of capacity-constrained Voronoi tessellation, we cast the blue noise sampling generation as a variational problem with continuous settings. Based on an accurate evaluation of the gradient of an energy function, an efficient optimization is developed which delivers significantly faster performance than the previous optimization-based methods. Our framework can easily be extended to generating blue noise point samples on manifold surfaces and for multi-class sampling. The optimization formulation also allows us to naturally deal with dynamic domains, such as deformable surfaces, and to yield blue noise samplings with temporal coherence. We present experimental results to validate the efficacy of our variational framework. Finally, we show a variety of applications of the proposed methods, including nonphotorealistic image stippling, color stippling, and blue noise sampling on deformable surfaces. © 1995-2012 IEEE.published_or_final_versio
Non-Euclidean Sliced Optimal Transport Sampling
In machine learning and computer graphics, a fundamental task is the
approximation of a probability density function through a well-dispersed
collection of samples. Providing a formal metric for measuring the distance
between probability measures on general spaces, Optimal Transport (OT) emerges
as a pivotal theoretical framework within this context. However, the associated
computational burden is prohibitive in most real-world scenarios. Leveraging
the simple structure of OT in 1D, Sliced Optimal Transport (SOT) has appeared
as an efficient alternative to generate samples in Euclidean spaces. This paper
pushes the boundaries of SOT utilization in computational geometry problems by
extending its application to sample densities residing on more diverse
mathematical domains, including the spherical space Sd , the hyperbolic plane
Hd , and the real projective plane Pd . Moreover, it ensures the quality of
these samples by achieving a blue noise characteristic, regardless of the
dimensionality involved. The robustness of our approach is highlighted through
its application to various geometry processing tasks, such as the intrinsic
blue noise sampling of meshes, as well as the sampling of directions and
rotations. These applications collectively underscore the efficacy of our
methodology.Comment: 14 page
- …