c++ - Simple Oriented Bounding Box OBB 碰撞检测解释

Question

我可以实现 AABB 方法来检测碰撞，它既简单又便宜，但我想实现 OBB 以获得更高的准确性，所以我使用模型初始化创建了边界框，它由 8 个边界顶点和中心组成，我变换的每一帧所有具有适合定向边界框的变换矩阵的顶点，但我无法理解检测两个 OBB 之间碰撞的方法，我找不到一个简单明了的教程来解释算法的代码观点而不是数学，因为我不是数学家。

如果我有

struct Box {
    glm::vec3 vertices[8];
    Box() {
        for (int i = 0; i < 8; i++) {
            vertices[i] = glm::vec3(0);
        }
    }
    glm::vec3 max;
    glm::vec3 min;
    glm::vec3 origin;

    void reCompute() {
        max = vertices[0];
        min = vertices[0];
        for (int i = 1; i < 8; i++) {
            max.x = max.x > vertices[i].x ? max.x : vertices[i].x;
            max.y = max.y > vertices[i].y ? max.y : vertices[i].y;
            max.z = max.z > vertices[i].z ? max.z : vertices[i].z;

            min.x = min.x < vertices[i].x ? min.x : vertices[i].x;
            min.y = min.y < vertices[i].y ? min.y : vertices[i].y;
            min.z = min.z < vertices[i].z ? min.z : vertices[i].z;
        }
        origin = glm::vec3((max.x + min.x) / 2.0f, (max.y + min.y) / 2.0f, (max.z + min.z) / 2.0f);
    }
//AABB intersection
    bool intersects(const Box &b) const {
        return (min.x < b.max.x) && (max.x > b.min.x) && (min.y < b.max.y) && (max.y > b.min.y) && (min.z < b.max.z) && (max.z > b.min.z) && *this != b;
    }

    bool operator==(const Box& b) const {
        return (max.x == b.max.x && max.y == b.max.y && max.z == b.max.z && min.x == b.min.x && min.y == b.min.y && min.z == b.min.z);
    }
    bool operator!=(const Box& b) const {
        return (max.x != b.max.x) || (max.y != b.max.y) || (max.z != b.max.z) || (min.x != b.min.x) || (min.y != b.min.y) || (min.z != b.min.z);
    }
};

在模型初始化时我创建了盒子

    box.vertices[0] = glm::vec3(meshMinX, meshMinY, meshMinZ);
    box.vertices[1] = glm::vec3(meshMaxX, meshMinY, meshMinZ);
    box.vertices[2] = glm::vec3(meshMinX, meshMaxY, meshMinZ);
    box.vertices[3] = glm::vec3(meshMaxX, meshMaxY, meshMinZ);
    box.vertices[4] = glm::vec3(meshMinX, meshMinY, meshMaxZ);
    box.vertices[5] = glm::vec3(meshMaxX, meshMinY, meshMaxZ);
    box.vertices[6] = glm::vec3(meshMinX, meshMaxY, meshMaxZ);
    box.vertices[7] = glm::vec3(meshMaxX, meshMaxY, meshMaxZ);

每一帧我用模型的变换矩阵重新计算框

for (int n = 0; n < 8; n++) {
        boxs[j].vertices[n] = glm::vec3(matrix * glm::vec4(box.vertices[n], 1));
    }
boxs[j].reCompute();

Answer 1

用于两个 3D OBB 之间简单碰撞检测的分离轴定理的 C++ 代码实现如下:

#include <iostream>

// define the operations to be used in our 3D vertices
struct vec3
{
    float x, y, z;
    vec3 operator- (const vec3 & rhs) const { return{ x - rhs.x, y - rhs.y, z - rhs.z }; }
    float operator* (const vec3 & rhs) const { return{ x * rhs.x + y * rhs.y + z * rhs.z }; } // DOT PRODUCT
    vec3 operator^ (const vec3 & rhs) const { return{ y * rhs.z - z * rhs.y, z * rhs.x - x * rhs.z, x * rhs.y - y * rhs.x }; } // CROSS PRODUCT
    vec3 operator* (const float& rhs)const { return vec3{ x * rhs, y * rhs, z * rhs }; }
};

// set the relevant elements of our oriented bounding box
struct OBB
{
    vec3 Pos, AxisX, AxisY, AxisZ, Half_size;
};

// check if there's a separating plane in between the selected axes
bool getSeparatingPlane(const vec3& RPos, const vec3& Plane, const OBB& box1, const OBB&box2)
{
    return (fabs(RPos*Plane) > 
        (fabs((box1.AxisX*box1.Half_size.x)*Plane) +
        fabs((box1.AxisY*box1.Half_size.y)*Plane) +
        fabs((box1.AxisZ*box1.Half_size.z)*Plane) +
        fabs((box2.AxisX*box2.Half_size.x)*Plane) + 
        fabs((box2.AxisY*box2.Half_size.y)*Plane) +
        fabs((box2.AxisZ*box2.Half_size.z)*Plane)));
}

// test for separating planes in all 15 axes
bool getCollision(const OBB& box1, const OBB&box2)
{
    static vec3 RPos;
    RPos = box2.Pos - box1.Pos;

    return !(getSeparatingPlane(RPos, box1.AxisX, box1, box2) ||
        getSeparatingPlane(RPos, box1.AxisY, box1, box2) ||
        getSeparatingPlane(RPos, box1.AxisZ, box1, box2) ||
        getSeparatingPlane(RPos, box2.AxisX, box1, box2) ||
        getSeparatingPlane(RPos, box2.AxisY, box1, box2) ||
        getSeparatingPlane(RPos, box2.AxisZ, box1, box2) ||
        getSeparatingPlane(RPos, box1.AxisX^box2.AxisX, box1, box2) ||
        getSeparatingPlane(RPos, box1.AxisX^box2.AxisY, box1, box2) ||
        getSeparatingPlane(RPos, box1.AxisX^box2.AxisZ, box1, box2) ||
        getSeparatingPlane(RPos, box1.AxisY^box2.AxisX, box1, box2) ||
        getSeparatingPlane(RPos, box1.AxisY^box2.AxisY, box1, box2) ||
        getSeparatingPlane(RPos, box1.AxisY^box2.AxisZ, box1, box2) ||
        getSeparatingPlane(RPos, box1.AxisZ^box2.AxisX, box1, box2) ||
        getSeparatingPlane(RPos, box1.AxisZ^box2.AxisY, box1, box2) ||
        getSeparatingPlane(RPos, box1.AxisZ^box2.AxisZ, box1, box2));
}

// a quick test to see the code working
int _tmain(int argc, _TCHAR* argv[])
{
    // create two obbs
    OBB A, B;

    // set the first obb's properties
    A.Pos = { 0.f, 0.f, 0.f }; // set its center position

    // set the half size
    A.Half_size.x = 10.f; 
    A.Half_size.y = 1.f; 
    A.Half_size.z = 1.f;

    // set the axes orientation
    A.AxisX = { 1.f, 0.f, 0.f };
    A.AxisY = { 0.f, 1.f, 0.f };
    A.AxisZ = { 0.f, 0.f, 1.f };

    // set the second obb's properties
    B.Pos = { 20.f, 0.f, 0.f }; // set its center position

    // set the half size
    B.Half_size.x = 10.f;
    B.Half_size.y = 1.f;
    B.Half_size.z = 1.f;

    // set the axes orientation
    B.AxisX = { 1.f, 0.f, 0.f };
    B.AxisY = { 0.f, 1.f, 0.f };
    B.AxisZ = { 0.f, 0.f, 1.f };

    // run the code and get the result as a message
    if (getCollision(A, B)) std::cout << "Collision!!!" << std::endl;
    else std::cout << "No collision." << std::endl;

    // pause and quit
    std::cout << std::endl;
    system("pause");
    return 0;
}