使用以下函数来检查AABB和扫描胶囊体之间的相交:

bool TestAABBSweptSphereIntersection(const Vector3& aabbMin, const Vector3& aabbMax, const Vector3& capsuleStart, const Vector3& capsuleEnd, float capsuleRadius)
{
    // 计算胶囊体的包围盒
    Vector3 capsuleMin = Vector3::Min(capsuleStart, capsuleEnd) - Vector3::One * capsuleRadius;
    Vector3 capsuleMax = Vector3::Max(capsuleStart, capsuleEnd) + Vector3::One * capsuleRadius;

    // 检查AABB是否和胶囊体的包围盒相交
    if (!TestAABBAABBIntersection(aabbMin, aabbMax, capsuleMin, capsuleMax))
        return false;

    // 在胶囊体路径上检查AABB是否和胶囊体相交
    float capsuleLength = (capsuleEnd - capsuleStart).Length();
    Vector3 capsuleDir = (capsuleEnd - capsuleStart).Normalized();
    Vector3 capsuleRight = Vector3::Cross(Vector3::Up, capsuleDir).Normalized();
    Vector3 capsuleUp = Vector3::Cross(capsuleRight, capsuleDir).Normalized();
    Vector3 capsuleCenter;
    for (float t = 0; t <= capsuleLength; t += capsuleRadius)
    {
        capsuleCenter = capsuleStart + (capsuleDir * t);

        Vector3 capRectMin = capsuleCenter - capsuleRight * capsuleRadius - capsuleUp * capsuleRadius;
        Vector3 capRectMax = capsuleCenter + capsuleRight * capsuleRadius + capsuleUp * capsuleRadius;

        if (TestAABBAABBIntersection(aabbMin, aabbMax, capRectMin, capRectMax))
            return true;
    }

    return false;
}

其中，TestAABBAABBIntersection()是用来检查AABB与AABB之间的相交。检查AABB与胶囊体之间的相交是通过检查胶囊体路径上多个包围盒与AABB之间的相交实现的。