A tight inclusion function for continuous collision detection

Last update: Jan 01, 2023

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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.

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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"

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