1

我一直在调整和修改我的代码以针对三角形测试 AABB，但我不确定我做错了什么。我正在使用分离轴定理，因为我相信这是用于检测 AABB 和三角形之间碰撞的最佳且唯一的方法（如果我错了或有更好/更快的方法，请纠正我）。目前，当发生碰撞时，它不会检测到任何东西。

代码比较小，每帧都调用isAABBIntersectingTriangle，希望懂数学或者算法的人能帮帮我。该函数将边界框 min 和 max 作为两个 3D 向量 (glm::vec3) 和三角形顶点 (tri1, tri2, tri3) 中的 3 个作为 glm::vec3s。这些坐标都在世界空间中（AABB 坐标仅通过位置和比例平移，三角形通过位置旋转和比例平移）

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;
}

这里也是主循环中的代码，它计算三角形的世界位置，然后调用函数，我不相信这里有什么问题，因为它可能被检查得最多：

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";
    }
4

1 回答 1

0

测试中有一段代码不健壮。

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，仅当向量的长度不为零时，对向量进行归一化才有效。当因子平行时，叉积的长度为零。因此，如果其中任何一个e1, e2, e3与任何一个平行e4, e5, e6，则相应的叉积将是一个零长度向量，并且归一化的坐标将为NaN。

NaN 的一个大问题是它会“毒化”所有计算。特别是，向量中的单个 NaN 坐标足以导致涉及该向量的任何点积计算为 NaN。这真的与SATTriangleAABBCheck试图做的事情混淆了。（零长度向量同样会与函数混淆，因此跳过标准化不是解决方案。）

解决方案取决于在叉积为零的情况下应该做什么。在这种情况下，该零表示计算未能产生分离轴。要检查的轴数少于最大数量，因为不同的平行线永远不会相交。跳过零轴上的测试（归一化为 NaN）。

于 2020-10-04T22:52:58.497 回答