c++ - AABB碰撞代码的三角形不起作用

Question

我一直在调整和修改我的代码，以针对一个三角形测试AABB，但不确定自己做错了什么。我正在使用分离轴定理，因为我认为这是检测AABB和三角形之间碰撞的最好且唯一的方法(如果我错了或者有更好/更快的方法，请纠正我)。当前，当发生碰撞时，它什么也检测不到。
代码相对较小，每帧都调用isAABBIntersectingTriangle，希望了解数学或算法的人可以对我有所帮助。该函数将边界框min和max作为两个3D vector (glm::vec3)和三个三角形顶点(tri1，tri2，tri3)作为glm::vec3s。这些坐标都在世界空间中(AABB坐标仅通过位置和比例转换，三角形通过位置旋转和比例转换)

bool SATTriangleAABBCheck(glm::vec3 axis, glm::vec3 bboxMin, glm::vec3 bboxMax, glm::vec3 tri1, glm::vec3 tri2, glm::vec3 tri3)
{
    //Dot triangle vertices
    float triVert1 = glm::dot(axis, tri1);
    float triVert2 = glm::dot(axis, tri2);
    float triVert3 = glm::dot(axis, tri3);

    float triMin = glm::min(glm::min(triVert1, triVert2), triVert3);
    float triMax = glm::max(glm::max(triVert1, triVert2), triVert3);

    //Dot cube vertices
    float v1 = glm::dot(axis, glm::vec3(bboxMin.x, bboxMin.y, bboxMin.z));
    float v2 = glm::dot(axis, glm::vec3(bboxMax.x, bboxMax.y, bboxMax.z));
    float v3 = glm::dot(axis, glm::vec3(bboxMax.x, bboxMax.y, bboxMin.z));
    float v4 = glm::dot(axis, glm::vec3(bboxMax.x, bboxMin.y, bboxMax.z));
    float v5 = glm::dot(axis, glm::vec3(bboxMax.x, bboxMin.y, bboxMin.z));
    float v6 = glm::dot(axis, glm::vec3(bboxMin.x, bboxMax.y, bboxMax.z));
    float v7 = glm::dot(axis, glm::vec3(bboxMin.x, bboxMin.y, bboxMax.z));
    float v8 = glm::dot(axis, glm::vec3(bboxMin.x, bboxMax.y, bboxMin.z));

    float aabbMin = glm::min(glm::min(glm::min(glm::min(glm::min(glm::min(glm::min(v1, v2), v3), v4), v5), v6), v7) ,v8);
    float aabbMax = glm::max(glm::max(glm::max(glm::max(glm::max(glm::max(glm::max(v1, v2), v3), v4), v5), v6), v7), v8);

    if ((triMin < aabbMax && triMin > aabbMin) || (triMax < aabbMax && triMax > aabbMin))
        return true;
    if ((aabbMin < triMax && aabbMin > triMin) || (aabbMax < triMax && aabbMax > triMin))
        return true;

    return false;
}

glm::vec3 CalcSurfaceNormal(glm::vec3 tri1, glm::vec3 tri2, glm::vec3 tri3)
{
    glm::vec3 u = tri2 - tri1;
    glm::vec3 v = tri3 - tri1;
    glm::vec3 nrmcross = glm::normalize(glm::cross(u, v));
    return nrmcross;
}

bool isAABBIntersectingTriangle(glm::vec3 bboxMin, glm::vec3 bboxMax, glm::vec3 tri1, glm::vec3 tri2,  glm::vec3 tri3)
{   
    //AABB face normals
    glm::vec3 axis1(1, 0, 0);
    glm::vec3 axis2(0, 1, 0);
    glm::vec3 axis3(0, 0, 1);

    //Triangle face normal
    glm::vec3 axis4 = CalcSurfaceNormal(tri1, tri2, tri3);

    //Edge normals
    glm::vec3 e1 = tri2 - tri1;
    glm::vec3 e2 = tri3 - tri1;
    glm::vec3 e3 = tri3 - tri2;
    glm::vec3 e4 = glm::vec3(bboxMax.x, bboxMax.y, bboxMax.z) - glm::vec3(bboxMin.x, bboxMax.y, bboxMax.z);
    glm::vec3 e5 = glm::vec3(bboxMax.x, bboxMax.y, bboxMax.z) - glm::vec3(bboxMax.x, bboxMin.y, bboxMax.z);
    glm::vec3 e6 = glm::vec3(bboxMax.x, bboxMax.y, bboxMax.z) - glm::vec3(bboxMax.x, bboxMax.y, bboxMin.z);

    //Cross products of each edge
    glm::vec3 axis5 = glm::normalize(glm::cross(e1, e4));
    glm::vec3 axis6 = glm::normalize(glm::cross(e1, e5));
    glm::vec3 axis7 = glm::normalize(glm::cross(e1, e6));
    glm::vec3 axis8 = glm::normalize(glm::cross(e2, e4));
    glm::vec3 axis9 = glm::normalize(glm::cross(e2, e5));
    glm::vec3 axis10 = glm::normalize(glm::cross(e2, e6));
    glm::vec3 axis11 = glm::normalize(glm::cross(e3, e4));
    glm::vec3 axis12 = glm::normalize(glm::cross(e3, e5));
    glm::vec3 axis13 = glm::normalize(glm::cross(e3, e6));


    //If no overlap on all axes
    if (!SATTriangleAABBCheck(axis1, bboxMin, bboxMax, tri1, tri2, tri3)) return false;
    if (!SATTriangleAABBCheck(axis2, bboxMin, bboxMax, tri1, tri2, tri3)) return false;
    if (!SATTriangleAABBCheck(axis3, bboxMin, bboxMax, tri1, tri2, tri3)) return false;
    if (!SATTriangleAABBCheck(axis4, bboxMin, bboxMax, tri1, tri2, tri3)) return false;
    if (!SATTriangleAABBCheck(axis5, bboxMin, bboxMax, tri1, tri2, tri3)) return false;
    if (!SATTriangleAABBCheck(axis6, bboxMin, bboxMax, tri1, tri2, tri3)) return false;
    if (!SATTriangleAABBCheck(axis7, bboxMin, bboxMax, tri1, tri2, tri3)) return false;
    if (!SATTriangleAABBCheck(axis8, bboxMin, bboxMax, tri1, tri2, tri3)) return false;
    if (!SATTriangleAABBCheck(axis9, bboxMin, bboxMax, tri1, tri2, tri3)) return false;
    if (!SATTriangleAABBCheck(axis10, bboxMin, bboxMax, tri1, tri2, tri3)) return false;
    if (!SATTriangleAABBCheck(axis11, bboxMin, bboxMax, tri1, tri2, tri3)) return false;
    if (!SATTriangleAABBCheck(axis12, bboxMin, bboxMax, tri1, tri2, tri3)) return false;
    if (!SATTriangleAABBCheck(axis13, bboxMin, bboxMax, tri1, tri2, tri3)) return false;

    return true;
}

这也是主循环中的代码，该代码计算三角形的世界位置然后调用该函数，我认为这里没有什么不对的地方，因为它可能已得到最多的关注:

glm::vec3 tri1 = glm::vec3(entities[0]->model.meshes[0].vertices[entities[0]->model.meshes[0].indices[0]].position.x * entities[0]->scale, entities[0]->model.meshes[0].vertices[entities[0]->model.meshes[0].indices[0]].position.y * entities[0]->scale, entities[0]->model.meshes[0].vertices[entities[0]->model.meshes[0].indices[0]].position.z * entities[0]->scale);
    glm::vec3 tri2 = glm::vec3(entities[0]->model.meshes[0].vertices[entities[0]->model.meshes[0].indices[1]].position.x * entities[0]->scale, entities[0]->model.meshes[0].vertices[entities[0]->model.meshes[0].indices[1]].position.y * entities[0]->scale, entities[0]->model.meshes[0].vertices[entities[0]->model.meshes[0].indices[1]].position.z * entities[0]->scale);
    glm::vec3 tri3 = glm::vec3(entities[0]->model.meshes[0].vertices[entities[0]->model.meshes[0].indices[2]].position.x * entities[0]->scale, entities[0]->model.meshes[0].vertices[entities[0]->model.meshes[0].indices[2]].position.y * entities[0]->scale, entities[0]->model.meshes[0].vertices[entities[0]->model.meshes[0].indices[2]].position.z * entities[0]->scale);

    //Translate these tris by the model matrix
    glm::mat4 mat(1.0f);
    mat = glm::translate(mat, glm::vec3(entities[0]->xPos, entities[0]->yPos, entities[0]->zPos));
    mat = glm::rotate(mat, glm::radians(entities[0]->xRot), glm::vec3(1, 0, 0));
    mat = glm::rotate(mat, glm::radians(entities[0]->yRot), glm::vec3(0, 1, 0));
    mat = glm::rotate(mat, glm::radians(entities[0]->zRot), glm::vec3(0, 0, 1));
    mat = glm::scale(mat, glm::vec3(entities[0]->scale, entities[0]->scale, entities[0]->scale));
    glm::vec4 tri11 = mat * glm::vec4(tri1.x, tri1.y, tri1.z, 1.0f);
    glm::vec4 tri22 = mat * glm::vec4(tri2.x, tri2.y, tri2.z, 1.0f);
    glm::vec4 tri33 = mat * glm::vec4(tri3.x, tri3.y, tri3.z, 1.0f);


    if (isAABBIntersectingTriangle(entities[3]->bboxMin, entities[3]->bboxMax, glm::vec3(tri11.x, tri11.y, tri11.z), glm::vec3(tri22.x, tri22.y, tri22.z), glm::vec3(tri33.x, tri33.y, tri33.z)))
    {
        std::cout << "AABB Tri collision\n";
    }

Answer 1

测试中有一部分代码不够健壮。

glm::vec3 axis5 = glm::normalize(glm::cross(e1, e4));
glm::vec3 axis6 = glm::normalize(glm::cross(e1, e5));
glm::vec3 axis7 = glm::normalize(glm::cross(e1, e6));
glm::vec3 axis8 = glm::normalize(glm::cross(e2, e4));
glm::vec3 axis9 = glm::normalize(glm::cross(e2, e5));
glm::vec3 axis10 = glm::normalize(glm::cross(e2, e6));
glm::vec3 axis11 = glm::normalize(glm::cross(e3, e4));
glm::vec3 axis12 = glm::normalize(glm::cross(e3, e5));
glm::vec3 axis13 = glm::normalize(glm::cross(e3, e6));

这些计算是无条件进行的。但是，仅当 vector 的长度不为零时，才能对 vector 进行归一化。当因子平行时，叉积的长度为零。因此，如果e1, e2, e3中的任何一个与e4, e5, e6中的任何一个平行，则对应的叉积将是零长度 vector ，并且归一化的坐标将是NaN。
NaN的一个大问题是，它会“毒化”所有计算。特别是， vector 中的单个NaN坐标足以使涉及该 vector 的任何点积评估为NaN。这确实与SATTriangleAABBCheck尝试执行的操作弄混了。 (零长度 vector 将类似地使函数混乱，因此跳过归一化不是解决方案。)
解决方案取决于叉积为零的情况下应采取的措施。在这种情况下，该零表示计算无法生成分隔轴。检查的轴数少于最大数量，因为不同的平行线永不相交。在零轴(已归一化为NaN)上跳过测试。