分离轴理论 - 垂直轴上的假阳性

Question

我已经使用 SAT 实现了碰撞检测，如果另一个bbox高于或低于边界框，我会得到误报。

我将边界框的每个（现在）轴对齐面投影到它自己和其他bbox角。

返回的碰撞数据是正确的(depth, stepheight)，但它为边界框上方或下方的每个对象返回碰撞的事实为ofc false。

我根据一个有效的简单aabb碰撞检查检查我的结果。

以下是代码：

//------------------------------
BoundingBoxIntersectionResult BoundingBox::IntersectionSAT(BoundingBox & other)
{

    // check shortest edge
    f32 distances[6] = {
        (other.mMaxVec.x - this->mMinVec.x),
        (this->mMaxVec.x - other.mMinVec.x),
        (other.mMaxVec.y - this->mMinVec.y),
        (this->mMaxVec.y - other.mMinVec.y),
        (other.mMaxVec.z - this->mMinVec.z),
        (this->mMaxVec.z - other.mMinVec.z)
    };

    i32 faceIndex = 0;
    Vec3 faceNormal;
    f32 collisionDepth = 0.0f;

    // for each face normal, get the minimum and maximum extens of the projection 
    // of all corner points of both shapes
    // if they dont overlap, there is no intersection

    // check each normal
    for (ui32 i = 0; i < 6; i++)
    {
        // CornerPointsWorld represents the world space corner positions
        SATReturn ret = this->SATTest(this->mNormals[i], this->mCornerPointsWorld);
        SATReturn ret2 = this->SATTest(this->mNormals[i], other.mCornerPointsWorld);

        float d1 = ret.minAlong - ret2.maxAlong;
        float d2 = ret2.minAlong - ret.maxAlong;
        if ((d1 > 0.0f) || (d2> 0.0f))
        {
            // return a false collision event, because we got a seperating axis
            return { false, 0.0f, 0.0f, Vec3(), BBOX_SIDE_LEFT };
        }
    }


    // check each normal of the other bbox
    for (ui32 i = 0; i < 6; i++)
    {
        SATReturn ret = this->SATTest(other.mNormals[i], this->mCornerPointsWorld);
        SATReturn ret2 = this->SATTest(other.mNormals[i], other.mCornerPointsWorld);

        float d1 = ret.minAlong - ret2.maxAlong;
        float d2 = ret2.minAlong - ret.maxAlong;
        if ((d1 > 0.0f) || (d2> 0.0f))
        {
            // return a false collision event, because we got a seperating axis
            return { false, 0.0f, 0.0f, Vec3(), BBOX_SIDE_LEFT };
        }

        // get collision data
        if (i == 0 || distances[i] < collisionDepth)
        {
            faceIndex = i;
            faceNormal = this->mNormals[i];
            collisionDepth = distances[i];
        }
    }

    // get step height needed to climb this object
    f32 stepHeight = other.mMaxVec.y - this->mMinVec.y;

    return { true, collisionDepth, stepHeight, faceNormal, BoundingBoxSide(faceIndex) };
}


//------------------------------
SATReturn BoundingBox::SATTest(Vec3& normal, Vector<Vec3>& corners)
{
    SATReturn ret;
    ret.maxAlong = MIN_FLOAT;
    ret.minAlong = MAX_FLOAT;

    // for each point
    for (ui32 i = 0; i < corners.GetSize(); i++)
    {
        f32 dot = Vec3::Dot(corners[i], normal);
        if (dot < ret.minAlong) ret.minAlong = dot;
        if (dot > ret.maxAlong) ret.maxAlong = dot;
    }

    return ret;
}

其中面法线定义为：

Vec3 mNormals[6] =
    {
        Vec3(1,  0,  0), // left
        Vec3(-1,  0,  0), // right
        Vec3(0,  1,  0), // up
        Vec3(0,  -1,  0), // down
        Vec3(0,  0,  1), //back
        Vec3(0,  0,  -1), // front
    };

我添加了一个屏幕截图来显示问题：

所以问题是：

它为边界框下方或上方的所有对象返回误报。