arXiv subjects

Teseo Schneider

Publications and source records attributed to Teseo Schneider.

25 records · Page 2Linked to original sources

arXiv2021

A Large Scale Benchmark and an Inclusion-Based Algorithm for Continuous Collision Detection

We introduce a large scale benchmark for continuous collision detection (CCD) algorithms, composed of queries manually constructed to highlight challenging degenerate cases and automatically generated using existing simulators to cover common cases. We use the benchmark to evaluate the accuracy, correctness, and efficiency of state-of-the-art continuous collision detection algorithms, both with and without minimal separation. We discover that, despite the widespread use of CCD algorithms, existing algorithms are either: (1) correct but impractically slow, (2) efficient but incorrect, introducing false negatives which will lead to interpenetration, or (3) correct but over conservative, reporting a large number of false positives which might lead to inaccuracies when integrated in a simulator. By combining the seminal interval root finding algorithm introduced by Snyder in 1992 with modern predicate design techniques, we propose a simple and efficient CCD algorithm. This algorithm is competitive with state of the art methods in terms of runtime while conservatively reporting the time of impact and allowing explicit trade off between runtime efficiency and number of false positives reported.

cs.GR↗

arXiv2021

An Extensible Benchmark Suite for Learning to Simulate Physical Systems

Simulating physical systems is a core component of scientific computing, encompassing a wide range of physical domains and applications. Recently, there has been a surge in data-driven methods to complement traditional numerical simulations methods, motivated by the opportunity to reduce computational costs and/or learn new physical models leveraging access to large collections of data. However, the diversity of problem settings and applications has led to a plethora of approaches, each one evaluated on a different setup and with different evaluation metrics. We introduce a set of benchmark problems to take a step towards unified benchmarks and evaluation protocols. We propose four representative physical systems, as well as a collection of both widely used classical time integrators and representative data-driven methods (kernel-based, MLP, CNN, nearest neighbors). Our framework allows evaluating objectively and systematically the stability, accuracy, and computational efficiency of data-driven methods. Additionally, it is configurable to permit adjustments for accommodating other learning tasks and for establishing a foundation for future developments in machine learning for scientific computing.

cs.LG↗

arXiv2021

Robust & Asymptotically Locally Optimal UAV-Trajectory Generation Based on Spline Subdivision

Generating locally optimal UAV-trajectories is challenging due to the non-convex constraints of collision avoidance and actuation limits. We present the first local, optimization-based UAV-trajectory generator that simultaneously guarantees the validity and asymptotic optimality for known environments. \textit{Validity:} Given a feasible initial guess, our algorithm guarantees the satisfaction of all constraints throughout the process of optimization. \textit{Asymptotic Optimality:} We use an asymptotic exact piecewise approximation of the trajectory with an automatically adjustable resolution of its discretization. The trajectory converges under refinement to the first-order stationary point of the exact non-convex programming problem. Our method has additional practical advantages including joint optimality in terms of trajectory and time-allocation, and robustness to challenging environments as demonstrated in our experiments.

cs.RO↗

arXiv2020

ACORNS: An Easy-To-Use Code Generator for Gradients and Hessians

The computation of first and second-order derivatives is a staple in many computing applications, ranging from machine learning to scientific computing. We propose an algorithm to automatically differentiate algorithms written in a subset of C99 code and its efficient implementation as a Python script. We demonstrate that our algorithm enables automatic, reliable, and efficient differentiation of common algorithms used in physical simulation and geometry processing.

cs.MS↗

arXiv2020

Fast Tetrahedral Meshing in the Wild

We propose a new tetrahedral meshing method, fTetWild, to convert triangle soups into high-quality tetrahedral meshes. Our method builds on the TetWild algorithm, replacing the rational triangle insertion with a new incremental approach to construct and optimize the output mesh, interleaving triangle insertion and mesh optimization. Our approach makes it possible to maintain a valid floating-point tetrahedral mesh at all algorithmic stages, eliminating the need for costly constructions with rational numbers used by TetWild, while maintaining full robustness and similar output quality. This allows us to improve on TetWild in two ways. First, our algorithm is significantly faster, with running time comparable to less robust Delaunay-based tetrahedralization algorithms. Second, our algorithm is guaranteed to produce a valid tetrahedral mesh with floating-point vertex coordinates, while TetWild produces a valid mesh with rational coordinates which is not guaranteed to be valid after floating-point conversion. As a trade-off, our algorithm no longer guarantees that all input triangles are present in the output mesh, but in practice, as confirmed by our tests on the Thingi10k dataset, the algorithm always succeeds in inserting all input triangles.

cs.GR↗

arXiv2019

Deep Geometric Prior for Surface Reconstruction

The reconstruction of a discrete surface from a point cloud is a fundamental geometry processing problem that has been studied for decades, with many methods developed. We propose the use of a deep neural network as a geometric prior for surface reconstruction. Specifically, we overfit a neural network representing a local chart parameterization to part of an input point cloud using the Wasserstein distance as a measure of approximation. By jointly fitting many such networks to overlapping parts of the point cloud, while enforcing a consistency condition, we compute a manifold atlas. By sampling this atlas, we can produce a dense reconstruction of the surface approximating the input cloud. The entire procedure does not require any training data or explicit regularization, yet, we show that it is able to perform remarkably well: not introducing typical overfitting artifacts, and approximating sharp features closely at the same time. We experimentally show that this geometric prior produces good results for both man-made objects containing sharp features and smoother organic objects, as well as noisy inputs. We compare our method with a number of well-known reconstruction methods on a standard surface reconstruction benchmark.

cs.CV↗

arXiv2019

Poly-Spline Finite Element Method

We introduce an integrated meshing and finite element method pipeline enabling black-box solution of partial differential equations in the volume enclosed by a boundary representation. We construct a hybrid hexahedral-dominant mesh, which contains a small number of star-shaped polyhedra, and build a set of high-order basis on its elements, combining triquadratic B-splines, triquadratic hexahedra (27 degrees of freedom), and harmonic elements. We demonstrate that our approach converges cubically under refinement, while requiring around 50% of the degrees of freedom than a similarly dense hexahedral mesh composed of triquadratic hexahedra. We validate our approach solving Poisson's equation on a large collection of models, which are automatically processed by our algorithm, only requiring the user to provide boundary conditions on their surface.

math.NA↗