A tight inclusion function for continuous collision detection

Last update: Jan 01, 2023

Related tags

Overview

Tight-Inclusion Continuous Collision Detection

A conservative Continuous Collision Detection (CCD) method with support for minimum separation.

You can read more about this work in our ACM Transactions on Graphics paper:

"A Large Scale Benchmark and an Inclusion-Based Algorithm forContinuous Collision Detection"

@article{Wang:2021:Benchmark,
    title   = {A Large Scale Benchmark and an Inclusion-Based Algorithm for Continuous Collision Detection},
    author  = {Bolun Wang and Zachary Ferguson and Teseo Schneider and Xin Jiang and Marco Attene and Daniele Panozzo},
    year    = 2021,
    journal = {ACM Transactions on Graphics}
}

Compiling Instruction

To compile the code, first make sure CMake is installed.

To build the library on Linux or macOS:

mkdir build
cd build
cmake ../ -DCMAKE_BUILD_TYPE=Release
make

Then you can run a CCD example:

./Tight_Inclusion_bin

We also provide you an example to run the Sample Queries using our CCD method. You may need to install gmp before compiling the code. Then set the CMake option TIGHT_INCLUSION_WITH_TESTS as ON when compiling:

cmake ../ -DCMAKE_BUILD_TYPE=Release -DTIGHT_INCLUSION_WITH_TESTS=ON
make

Then you can run ./Tight_Inclusion_bin to test the handcrafted queries in the Sample Queries.

Usage

Include #include <tight_inclusion/inclusion_ccd.hpp>

To check edge-edge ccd, use bool inclusion_ccd::edgeEdgeCCD_double();

To check vertex-face ccd, use bool inclusion_ccd::vertexFaceCCD_double();

💡 If collision is detected, the ccd function will return true, otherwise, the ccd function will return false. Since our method is CONSERVATIVE, if the returned result is false, we guarantee that there is no collision happens. If the result is true, it is possible that there is no collision but we falsely report a collision, but we can guarantee that this happens only if the minimal distance between the two primitives in this time step is no larger than tolerance + ms + err. We wil explain these parameters below.

For both edge-edge ccd and vertex-face ccd, the input CCD query is presented by 8 vertices which are in the format of Eigen::Vector3d. Please read our code in tight_inclusion/inclusion_ccd.hpp for the correct input order of the vertices.

Beside the input vertices, there are some input and output parameters for users to tune the performace or to get more CCD information. Here is a list of the explanations of the parameters:

input:
    err                 The numerical filters of the x, y and z coordinates. It measures the errors introduced by floating-point calculation when solving inclusion functions.
    ms                  Minimum separation distance no less than 0. It guarantees that collision will be reported if the distance between the two primitives is less than ms.
    tolerance           User-specific solving precision. It is the target maximal x, y, and z length of the inclusion function. We suggest the user to set it as 1e-6.
    t_max               The time range [0, t_max] where we detect collisions. Since the input query implies the motion in time range [0, 1], t_max should no larger than 1.
    max_itr             The parameter to enable early termination of the algorithm. If you set max_itr < 0, early termination will be disabled, but this may cause longer runtime. We suggest to set max_itr = 1e6.
    CCD_TYPE            The parameter to choose collision detection algorithms. By default CCD_TYPE = 1. If set CCD_TYPE = 0, the code will switch to a naive conservative CCD algorithm, but lack of our advanced features. 
    
output:
    toi                 Time of impact. If multiple collisions happen in this time step, it will return the earlist collision time. If there is no collision, the returned toi value will be std::numeric_limits<double>::infinity().
    output_tolerance    The real solving precision. If early termination is enabled, the solving precision may not reach the target precision. This parameter will return the real solving precision when the code is terminated.

Tips

💡 The input parameter err is crucial to guarantee our algorithm to be a conservative method not affected by floating point rounding errors. To run a single query, you can set err = {{-1, -1, -1}} to enable a sub-function to calculate the real numerical filters when solving CCD. If you are integrating our CCD in simulators, you need to:

Include the headler: #include <tight_inclusion/interval_root_finder.hpp>.
Call std::array<double, 3> err_vf = inclusion_ccd::get_numerical_error() and std::array<double, 3> err_ee = inclusion_ccd::get_numerical_error()
Use the parameter err_ee each time you call bool inclusion_ccd::edgeEdgeCCD_double() and err_vf when you call bool inclusion_ccd::vertexFaceCCD_double().

The parameters for function inclusion_ccd::get_numerical_error() is explained below:

input:
    vertices            Vertices of the Axies-Aligned-Bounding-Box of the simulation scene. Before you run the simulation, you need to conservatively estimate the Axies-Aligned-Bounding-Box in which the meshes will located during the whole simulation process, and the vertices should be the corners of the AABB.
    check_vf            A boolean instruction showing if you are checking vertex-face or edge-edge CCD.
    using_minimum_separation    A boolean instruction. If you are using minimum-separation CCD (the input parameter ms > 0), please set it as true.

💡 For some simulators which use non-zero minimum separation distance (ms > 0) to make sure intersection-free for each time-step, we have a CMake option TIGHT_INCLUSION_WITH_NO_ZERO_TOI to avoid the returned collision time toi is 0. You need to set TIGHT_INCLUSION_WITH_NO_ZERO_TOI as ON when compiling by: cmake ../ -DCMAKE_BUILD_TYPE=Release -DTIGHT_INCLUSION_WITH_NO_ZERO_TOI=ON. Then when you use the CCD functions, the code will continue the refinement in higher precision if the output toi is 0 under the given tolerance. So, the eventually toi will not be 0.

To have a better understand, or to get more details of our Tight-Inclusion CCD algorithm, please refer to our paper.

Continuous Query Decomposition for Complex Query Answering in Incomplete Knowledge Graphs

Continuous Query Decomposition This repository contains the official implementation for our ICLR 2021 (Oral) paper, Complex Query Answering with Neura

71 Dec 29, 2022

On the model-based stochastic value gradient for continuous reinforcement learning

On the model-based stochastic value gradient for continuous reinforcement learning This repository is by Brandon Amos, Samuel Stanton, Denis Yarats, a

46 Dec 15, 2022

Continuous Diffusion Graph Neural Network

We present Graph Neural Diffusion (GRAND) that approaches deep learning on graphs as a continuous diffusion process and treats Graph Neural Networks (GNNs) as discretisations of an underlying PDE.

227 Jan 5, 2023

PyTorch implementation for MINE: Continuous-Depth MPI with Neural Radiance Fields

MINE: Continuous-Depth MPI with Neural Radiance Fields Project Page | Video PyTorch implementation for our ICCV 2021 paper. MINE: Towards Continuous D

325 Dec 29, 2022

This repository contains the source code and data for reproducing results of Deep Continuous Clustering paper

Deep Continuous Clustering Introduction This is a Pytorch implementation of the DCC algorithms presented in the following paper (paper): Sohil Atul Sh

197 Nov 29, 2022

This is the codebase for the ICLR 2021 paper Trajectory Prediction using Equivariant Continuous Convolution

Trajectory Prediction using Equivariant Continuous Convolution (ECCO) This is the codebase for the ICLR 2021 paper Trajectory Prediction using Equivar

45 Jul 22, 2022

PyTorch implementation for Stochastic Fine-grained Labeling of Multi-state Sign Glosses for Continuous Sign Language Recognition.

Stochastic CSLR This is the PyTorch implementation for the ECCV 2020 paper: Stochastic Fine-grained Labeling of Multi-state Sign Glosses for Continuou

28 Dec 19, 2022

Code for the ICASSP-2021 paper: Continuous Speech Separation with Conformer.

Continuous Speech Separation with Conformer Introduction We examine the use of the Conformer architecture for continuous speech separation. Conformer

81 Nov 28, 2022

A clean and robust Pytorch implementation of PPO on continuous action space.

PPO-Continuous-Pytorch I found the current implementation of PPO on continuous action space is whether somewhat complicated or not stable. And this is

56 Dec 16, 2022

Comments

Improved No Zero ToI
I changed the options for avoiding a zero time of impact by making the option a parameter to the CCD functions.

I also changed from a recursive algorithm to an iterative one with a maximum number of iterations.
opened by zfergus 2

a case returned 0 TOI

For the PT CCD case below, TICCD returned 0 TOI.

3.5000000000e-01 0.0000000000e+00 3.5000000000e-01
3.4604643638e-01 2.7847887896e-03 3.4658121160e-01
3.5000819263e-01 -1.5763377304e-06 3.5001214242e-01
3.4903882032e-01 -1.5866575093e-03 3.4560164356e-01
0.0000000000e+00 0.0000000000e+00 0.0000000000e+00
1.0120300789e-07 -1.4009994248e-04 -8.5653091896e-05
-9.2976239634e-07 1.4361165221e-06 5.5168830145e-07
1.1649271683e-04 -3.6172565398e-05 -4.7128237917e-05

The format is

node_x node_y node_z
traingle_node0_x traingle_node0_y traingle_node0_z
traingle_node1_x traingle_node1_y traingle_node1_z
traingle_node2_x traingle_node2_y traingle_node2_z
node_displacement_x node_displacement_y node_displacement_z
traingle_node0_displacement_x traingle_node0_displacement_y traingle_node0_displacement_z
traingle_node1_displacement_x traingle_node1_displacement_y traingle_node1_displacement_z
traingle_node2_displacement_x traingle_node2_displacement_y traingle_node2_displacement_z

I used the TICCD from the CCDWrapper repo (latest commit), and I called it like

template <class T>
bool Point_Triangle_CCD_TI(
    const Eigen::Matrix<T, 3, 1>& p, 
    const Eigen::Matrix<T, 3, 1>& t0, 
    const Eigen::Matrix<T, 3, 1>& t1,
    const Eigen::Matrix<T, 3, 1>& t2,
    const Eigen::Matrix<T, 3, 1>& dp, 
    const Eigen::Matrix<T, 3, 1>& dt0, 
    const Eigen::Matrix<T, 3, 1>& dt1,
    const Eigen::Matrix<T, 3, 1>& dt2,
    T eta, T thickness, T& toc)
{
    T toc_prev = toc;
    T output_tolerance;

    T dist2_cur;
    Point_Triangle_Distance_Unclassified(p, t0, t1, t2, dist2_cur);
    T dist_cur = std::sqrt(dist2_cur);
    if (inclusion_ccd::vertexFaceCCD_double(p, t0, t1, t2,
        p + dp, t0 + dt0, t1 + dt1, t2 + dt2, { { -1, 0, 0 } },
        eta * (dist2_cur - thickness * thickness) / (dist_cur + thickness) + thickness,
        toc, 1e-6, toc_prev, 1e6, output_tolerance, 1))
    {
        if (toc < 1.0e-6) {
            std::cout << "PT CCD tiny!" << std::endl;
            if (inclusion_ccd::vertexFaceCCD_double(p, t0, t1, t2,
                p + dp, t0 + dt0, t1 + dt1, t2 + dt2, { { -1, 0, 0 } },
                thickness, toc, 1e-6, toc_prev, 1e6, output_tolerance, 1))
            {
                toc *= (1.0 - eta);
                return true;
            }
            else {
                return false;
            }
        }
        return true;
    }
    return false;
}

printf("TICCD:\n");
largestAlpha = 1;
tstart = clock();
if (Point_Triangle_CCD_TI(x[0], x[1], x[2], x[3], x[4], x[5], x[6], x[7], 0.1, 0.0, largestAlpha)) {
    printf("%le\n", largestAlpha);
}
else {
    printf("no collision\n");
}
printf("%.1lems\n", double(clock() - tstart) / CLOCKS_PER_SEC * 1000);

The output is

TICCD:
PT CCD tiny!
0.000000e+00
1.9e+00ms

However I implemented a simpler version of TICCD according to the paper as

template <class T>
void Point_Triangle_Distance_Vector_Unclassified(
    const Eigen::Matrix<T, 3, 1>& p, 
    const Eigen::Matrix<T, 3, 1>& t0, 
    const Eigen::Matrix<T, 3, 1>& t1,
    const Eigen::Matrix<T, 3, 1>& t2,
    const Eigen::Matrix<T, 3, 1>& dp, 
    const Eigen::Matrix<T, 3, 1>& dt0, 
    const Eigen::Matrix<T, 3, 1>& dt1,
    const Eigen::Matrix<T, 3, 1>& dt2,
    T t, T lambda, T beta,
    Eigen::Matrix<T, 3, 1>& distVec)
{
    const Eigen::Matrix<T, 3, 1> tp = (1 - lambda - beta) * t0 + lambda * t1 + beta * t2;
    const Eigen::Matrix<T, 3, 1> dtp = (1 - lambda - beta) * dt0 + lambda * dt1 + beta * dt2;
    distVec = p + t * dp - (tp + t * dtp);
}

template <class T>
bool Point_Triangle_CheckInterval_Unclassified(
    const Eigen::Matrix<T, 3, 1>& p, 
    const Eigen::Matrix<T, 3, 1>& t0, 
    const Eigen::Matrix<T, 3, 1>& t1,
    const Eigen::Matrix<T, 3, 1>& t2,
    const Eigen::Matrix<T, 3, 1>& dp, 
    const Eigen::Matrix<T, 3, 1>& dt0, 
    const Eigen::Matrix<T, 3, 1>& dt1,
    const Eigen::Matrix<T, 3, 1>& dt2,
    const std::array<T, 6>& interval,
    T gap)
{
    Eigen::Matrix<T, 3, 1> distVecMax, distVecMin;
    distVecMax.setConstant(-2 * gap - 1);
    distVecMin.setConstant(2 * gap + 1);
    for (int t = 0; t < 2; ++t) {
        for (int lambda = 0; lambda < 2; ++lambda) {
            for (int beta = 0; beta < 2; ++beta) {
                if (lambda == 1 && beta == 1) {
                    continue;
                }
                Eigen::Matrix<T, 3, 1> distVec;
                Point_Triangle_Distance_Vector_Unclassified(p, t0, t1, t2, dp, dt0, dt1, dt2, 
                    interval[t], interval[2 + lambda], interval[4 + beta], distVec);
                distVecMax = distVecMax.array().max(distVec.array());
                distVecMin = distVecMin.array().min(distVec.array());
            }
        }
    }
    return (distVecMax.array() >= -gap).all() && (distVecMin.array() <= gap).all();
}
template <class T>
bool Point_Triangle_TICCD(
    const Eigen::Matrix<T, 3, 1>& p, 
    const Eigen::Matrix<T, 3, 1>& t0, 
    const Eigen::Matrix<T, 3, 1>& t1,
    const Eigen::Matrix<T, 3, 1>& t2,
    Eigen::Matrix<T, 3, 1> dp, 
    Eigen::Matrix<T, 3, 1> dt0, 
    Eigen::Matrix<T, 3, 1> dt1,
    Eigen::Matrix<T, 3, 1> dt2,
    T eta, T thickness, T& toc)
{
    T dist2_cur;
    Point_Triangle_Distance_Unclassified(p, t0, t1, t2, dist2_cur);
    T dist_cur = std::sqrt(dist2_cur);
    T gap = eta * (dist2_cur - thickness * thickness) / (dist_cur + thickness);

    T tTol = 1e-3;

    std::vector<std::array<T, 6>> roots;
    std::deque<std::array<T, 6>> intervals;
    intervals.push_back({0, toc, 0, 1, 0, 1});
    int iterAmt = 0;
    while (!intervals.empty()) {
        ++iterAmt;

        std::array<T, 6> curIV = intervals.front();
        intervals.pop_front();

        // check
        if (Point_Triangle_CheckInterval_Unclassified(p, t0, t1, t2, dp, dt0, dt1, dt2, curIV, gap)) {
            if (curIV[0] && curIV[1] - curIV[0] < tTol) {
                // root found within tTol
                roots.emplace_back(curIV);
            }
            else {
                // split interval and push back
                std::vector<T> intervalLen({curIV[1] - curIV[0], curIV[3] - curIV[2], curIV[5] - curIV[4]});
                switch (std::max_element(intervalLen.begin(), intervalLen.end()) - intervalLen.begin()) {
                case 0:
                    intervals.push_back({curIV[0], (curIV[1] + curIV[0]) / 2, curIV[2], curIV[3], curIV[4], curIV[5]});
                    intervals.push_back({(curIV[1] + curIV[0]) / 2, curIV[1], curIV[2], curIV[3], curIV[4], curIV[5]});
                    break;

                case 1:
                    intervals.push_back({curIV[0], curIV[1], curIV[2], (curIV[2] + curIV[3]) / 2, curIV[4], curIV[5]});
                    intervals.push_back({curIV[0], curIV[1], (curIV[2] + curIV[3]) / 2, curIV[3], curIV[4], curIV[5]});
                    break;

                case 2:
                    intervals.push_back({curIV[0], curIV[1], curIV[2], curIV[3], curIV[4], (curIV[4] + curIV[5]) / 2});
                    intervals.push_back({curIV[0], curIV[1], curIV[2], curIV[3], (curIV[4] + curIV[5]) / 2, curIV[5]});
                    break;
                }
            }
        }
    }
    
    if (roots.empty()) {
        printf("TICCD PT converged with %d iters\n", iterAmt);
        return false;
    }
    else {
        for (const auto& rI : roots) {
            if (toc > rI[0]) {
                toc = rI[0];
            }
        }
        printf("TICCD PT converged with %d iters\n", iterAmt);
        return true;
    }
}

and it kinds of worked on this case and output

TICCD PT converged with 6143 iters
4.882812e-04
5.3e-01ms

which with tighter convergence tolerance might be able to reach the ground truth solution -- no collision.

In my implementation, I didn't include the epsilons in formula (5) in the paper. Is it the main cause here?

opened by liminchen 2

Refactored and cleaned up code

I tested and timed it on the entire dataset. I get 0 FN, a couple of fewer FP on the handcrafted data, and the timing is a little faster on the simulation and faster on handcrafted.

opened by zfergus 0

Releases(v1.0.2)

v1.0.2(Jun 30, 2022)

Resolved compiler warnings on Linux and macOS.
Source code(tar.gz)
Source code(zip)
v1.0.1(Jun 9, 2022)

Refactor with slight performance improvement
Source code(tar.gz)
Source code(zip)
v1.0.0(Jan 28, 2022)

This is a stable release of our CCD algorithm before we refactor some of the code and make updates to the API.
Source code(tar.gz)
Source code(zip)

Owner

Continuous Collision Detection

Code for continuous collision detection methods bechmarked in "A Large Scale Benchmark and an Inclusion-Based Algorithm for Continuous Collision Detection"

GitHub Repository

NeRF visualization library under construction

NeRF visualization library using PlenOctrees, under construction pip install nerfvis Docs will be at: https://nerfvis.readthedocs.org import nerfvis s

196 Jan 04, 2023

Open source repository for the code accompanying the paper 'PatchNets: Patch-Based Generalizable Deep Implicit 3D Shape Representations'.

PatchNets This is the official repository for the project "PatchNets: Patch-Based Generalizable Deep Implicit 3D Shape Representations". For details,

16 May 22, 2022

《Image2Reverb: Cross-Modal Reverb Impulse Response Synthesis》(2021)

Image2Reverb Image2Reverb is an end-to-end neural network that generates plausible audio impulse responses from single images of acoustic environments

48 Nov 27, 2022

B-cos Networks: Attention is All we Need for Interpretability

Convolutional Dynamic Alignment Networks for Interpretable Classifications M. Böhle, M. Fritz, B. Schiele. B-cos Networks: Alignment is All we Need fo

58 Dec 23, 2022

TYolov5: A Temporal Yolov5 Detector Based on Quasi-Recurrent Neural Networks for Real-Time Handgun Detection in Video

TYolov5: A Temporal Yolov5 Detector Based on Quasi-Recurrent Neural Networks for Real-Time Handgun Detection in Video Timely handgun detection is a cr

18 Dec 26, 2022

Identifying a Training-Set Attack’s Target Using Renormalized Influence Estimation

Identifying a Training-Set Attack’s Target Using Renormalized Influence Estimation By: Zayd Hammoudeh and Daniel Lowd Paper: Arxiv Preprint Coming soo

2 Oct 08, 2022

A Python training and inference implementation of Yolov5 helmet detection in Jetson Xavier nx and Jetson nano

yolov5-helmet-detection-python A Python implementation of Yolov5 to detect head or helmet in the wild in Jetson Xavier nx and Jetson nano. In Jetson X

12 Dec 05, 2022

Detectron2 for Document Layout Analysis

Detectron2 trained on PubLayNet dataset This repo contains the training configurations, code and trained models trained on PubLayNet dataset using Det

163 Nov 21, 2022

This is the repository of our article published on MDPI Entropy "Feature Selection for Recommender Systems with Quantum Computing".

Collaborative-driven Quantum Feature Selection This repository was developed by Riccardo Nembrini, PhD student at Politecnico di Milano. See the websi

10 Apr 21, 2022

We utilize deep reinforcement learning to obtain favorable trajectories for visual-inertial system calibration.

Unified Data Collection for Visual-Inertial Calibration via Deep Reinforcement Learning Update: The lastest code will be updated in this branch. Pleas

27 Dec 29, 2022

Lolviz - A simple Python data-structure visualization tool for lists of lists, lists, dictionaries; primarily for use in Jupyter notebooks / presentations

lolviz By Terence Parr. See Explained.ai for more stuff. A very nice looking javascript lolviz port with improvements by Adnan M.Sagar. A simple Pytho

785 Dec 30, 2022

Official code base for the poster "On the use of Cortical Magnification and Saccades as Biological Proxies for Data Augmentation" published in NeurIPS 2021 Workshop (SVRHM)

Self-Supervised Learning (SimCLR) with Biological Plausible Image Augmentations Official code base for the poster "On the use of Cortical Magnificatio

8 Aug 17, 2022