Local Optimization for Robust Signed Distance Field Collision

2020 ◽  
Vol 3 (1) ◽  
pp. 1-17
Author(s):  
Miles Macklin ◽  
Kenny Erleben ◽  
Matthias Müller ◽  
Nuttapong Chentanez ◽  
Stefan Jeschke ◽  
...  
Keyword(s):  
Shape Representation ◽  
Golden Section ◽  
Rigid Bodies ◽  
Local Optimization ◽  
Signed Distance ◽  
Contact Points ◽  
Distance Fields ◽  
Wide Range ◽  
Sharp Point ◽  
Projected Gradient Descent

Signed distance fields (SDFs) are a popular shape representation for collision detection. This is due to their query efficiency, and the ability to provide robust inside/outside information. Although it is straightforward to test points for interpenetration with an SDF, it is not clear how to extend this to continuous surfaces, such as triangle meshes. In this paper, we propose a per-element local optimization to find the closest points between the SDF isosurface and mesh elements. This allows us to generate accurate contact points between sharp point-face pairs, and handle smoothly varying edge-edge contact. We compare three numerical methods for solving the local optimization problem: projected gradient descent, Frank-Wolfe, and golden-section search. Finally, we demonstrate the applicability of our method to a wide range of scenarios including collision of simulated cloth, rigid bodies, and deformable solids.

Improved Corners with Multi-Channel Signed Distance Fields

2017 ◽  
Vol 37 (1) ◽  
pp. 273-287
Author(s):  
V. Chlumský ◽  
J. Sloup ◽  
I. Šimeček
Keyword(s):  
Signed Distance ◽  
Distance Fields

Unraveling Paradoxical Theories for Rigid Body Collisions

1991 ◽  
Vol 58 (4) ◽  
pp. 1049-1055 ◽  
Author(s):  
W. J. Stronge
Keyword(s):  
Frictional Force ◽  
Contact Point ◽  
Tangential Velocity ◽  
Velocity Slip ◽  
Rigid Bodies ◽  
Contact Points ◽  
Before And After ◽  
Limited Applicability ◽  
Work Done ◽  
Impulsive Reaction

A collision between two rigid bodies has a normal impulsive reaction at the contact point (CP). If the bodies are slightly rough and the contact points have a relative tangential velocity (slip), there is also a frictional force that opposes slip. Small initial slip can halt before contact terminates; when slip halts the frictional force changes and the collision process is separated into periods before and after halting. An energetically consistent theory for collisions with slip that halts is based on the work done by normal (nonfrictional) forces during restitution and compression phases. This theory clearly separates dissipation due to frictional forces from that due to internal irreversible deformation. With this theory, both normal and tangential components of the impulsive reaction always dissipate energy during collisions. In contrast, Newton’s impact law results in calculations of paradoxical increases in energy for collisions where slip reverses. This law relates normal components of relative velocity for the CP at separation and incidence by a constant (the coefficient of restitution e). Newton’s impact law is a kinematic definition for e that generally depends on the slip process and friction; consequently it has limited applicability.

scholarly journals Geometric Distance Fields of Plane Curves

2021 ◽  
Author(s):  
Róbert Bán ◽  
Gábor Valasek
Keyword(s):  
Approximation Order ◽  
Higher Order ◽  
Plane Curves ◽  
Geometric Distance ◽  
Signed Distance ◽  
Distance Fields

This paper introduces a geometric generalization of signed distance fields for plane curves. We propose to store simplified geometric proxies to the curve at every sample. These proxies are constructed based on the differential geometric quantities of the represented curve and are used for queries such as closest point and distance calculations. We investigate the theoretical approximation order of these constructs and provide empirical comparisons between geometric and algebraic distance fields of higher order. We apply our results to font representation and rendering.

scholarly journals Distributionally Adversarial Attack

2019 ◽  
Vol 33 ◽  
pp. 2253-2260 ◽  
Author(s):  
Tianhang Zheng ◽  
Changyou Chen ◽  
Kui Ren
Keyword(s):  
Data Distribution ◽  
Original Data ◽  
First Order ◽  
Risk Optimization ◽  
Wide Range ◽  
Data Points ◽  
Adversarial Attack ◽  
Projected Gradient Descent ◽  
Original Objective ◽  
Direct Dependency

Recent work on adversarial attack has shown that Projected Gradient Descent (PGD) Adversary is a universal first-order adversary, and the classifier adversarially trained by PGD is robust against a wide range of first-order attacks. It is worth noting that the original objective of an attack/defense model relies on a data distribution p(x), typically in the form of risk maximization/minimization, e.g., max/min Ep(x) L(x) with p(x) some unknown data distribution and L(·) a loss function. However, since PGD generates attack samples independently for each data sample based on L(·), the procedure does not necessarily lead to good generalization in terms of risk optimization. In this paper, we achieve the goal by proposing distributionally adversarial attack (DAA), a framework to solve an optimal adversarial-data distribution, a perturbed distribution that satisfies the L∞ constraint but deviates from the original data distribution to increase the generalization risk maximally. Algorithmically, DAA performs optimization on the space of potential data distributions, which introduces direct dependency between all data points when generating adversarial samples. DAA is evaluated by attacking state-of-the-art defense models, including the adversarially-trained models provided by MIT MadryLab. Notably, DAA ranks the first place on MadryLab’s white-box leaderboards, reducing the accuracy of their secret MNIST model to 88.56% (with l∞ perturbations of ε = 0.3) and the accuracy of their secret CIFAR model to 44.71% (with l∞ perturbations of ε = 8.0). Code for the experiments is released on https://github.com/tianzheng4/Distributionally-Adversarial-Attack.

scholarly journals Complex Bogie Modeling Incorporating Advanced Friction Wedge Components

2009 ◽  
Author(s):  
Brian Sperry ◽  
Corina Sandu ◽  
Brent Ballew
Keyword(s):  
Dynamic Behavior ◽  
Degrees Of Freedom ◽  
Model Simulation ◽  
Surface Friction ◽  
Rigid Bodies ◽  
Operating Conditions ◽  
Normal Operation ◽  
Contact Points ◽  
Modeling Software ◽  
Simulation Results

This research focuses on the dynamic behavior of the three-piece bogie that supports the freight train car bodies. While the system is relatively simple, in that there are very few parts involved, the behavior of the bogie is somewhat more complex. Our research focuses primarily on the behavior of the friction wedges under different operating conditions that are seen under normal operation. The Railway Technologies Laboratory (RTL) at Virginia Tech has been developing a model to better capture the dynamic behavior of friction wedges using 3-D modeling software. In previous years, a quarter-truck model, and half-truck variably damped model have been developed using MathWorks MATLAB®. This year, research has focused on the development of a half-truck variably damped model with a new (curved surface) friction wedge, and a half-truck constantly damped model, both using the MATLAB® based software program. Currently a full-truck variably damped model has been created using LMS Virtual.Lab. This software allows for a model that is more easily created and modified, as well as allowing for a much shorter simulation time, which became a necessity as more contact points, and more complex inputs were needed to increase the accuracy of the simulation results. The new model consists of seven rigid bodies: the bolster, two sideframes, and four wedges. We have also implemented full spring nests on each sideframe, where in previous models equivalent spring forces were used. The model allows six degrees-of-freedom for the wedges and bolster: lateral, longitudinal, and vertical translations, as well as pitch, roll, and yaw. The sideframes are constrained to two degrees-of-freedom: vertical and longitudinal translations. The inputs to the model are vertical and longitudinal translations or forces on the sideframes, which can be set completely independent of each other. The model simulation results have been compared with results from NUCARS®, an industrially-used train modeling software developed by the Transportation Technology Center, Inc. (TTCI), a wholly owned subsidiary of the Association of American Railroads (AAR), for similar inputs, as well as experimental data from warping tests performed at TTCI.

A joint-constraint model for human joints using signed distance-fields

2012 ◽  
Vol 28 (1-2) ◽  
pp. 69-81 ◽  
Author(s):  
Morten Engell-Nørregård ◽  
Sarah Niebe ◽  
Kenny Erleben
Keyword(s):  
Signed Distance ◽  
Distance Fields ◽  
Human Joints ◽  
Constraint Model
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