我目前正在尝试将https://mollyrocket.com/849中提供的简化GJK算法实现到我的C ++游戏中。
然而，我在第二和第三维中遇到了奇怪的行为：有时候（通常在每秒多次调用时）算法会陷入案例循环中。例如，调试消息一遍又一遍地将以下内容打印到std :: cout：
3ACxAB
4AB
3ABxAC
4ABD
4AD
如果您查看我的代码，您会看到这些行代表算法允许的情况。例如。 3ACxAB 表示单纯形当前是一个三角形，并且原点位于面的voronoi区域，在交叉积 AC x AB 的方向上（可以解释） as＆＃34;在＆＃34;或＆＃34;在＆＃34;下面＆＃34;三角形）。情况 4AB 表示单纯形是四面体，原点位于边 AB 的voronoi区域。
A 始终是新添加的点。在代码中， A 始终是simplex的最大索引。 （^ simplex [1]`如果它是一条线，如果是三角形则为2，在a的情况下为3）四面体。
即使经过几天的搜索错误（我发现了一些错误，但仍有一个或多个错误），该算法仍无法正常工作。
您是否在代码中看到任何问题？因为我和我的两个朋友都没有。
PS：我没有从凯西的视频中复制任何计算（例如方向向量的交叉产品）。看完之后，我自己决定了，所以潜在的问题可能存在，特别是在第三个方面，凯西故意没有谈论。
我的支持功能：
//hullA/B: convex hull of A resp. B; baseA/B: location of A/B
Vector3f gjkSupport(Vector3f direction,
std::vector<GLfloat> hullA, std::vector<GLfloat> baseA,
std::vector<GLfloat> hullB, std::vector<GLfloat> baseB) {
//Initialize
GLfloat maxDotP = -std::numeric_limits<GLfloat>::max();
Vector3f furthestPointA, furthestPointB;
//Get furthest point in given direction out of hullA by getting the maximum dot
//product of the direction vector and a hull vertex's position vector
for (GLuint i = 0; i < hullA.size(); i += 3) {
Vector3f current (hullA[i]+baseA[0], hullA[i+1]+baseA[1], hullA[i+2]+baseA[2]);
// * = dot product
GLfloat dotP = direction * current;
if (dotP > maxDotP) {
maxDotP = dotP;
furthestPointA = current;
}
}
maxDotP = -std::numeric_limits<GLfloat>::max();
//Get furthest point in negative of the given direction out of hullB
for (GLuint i = 0; i < hullB.size(); i += 3) {
Vector3f current (hullB[i]+baseB[0], hullB[i+1]+baseB[1], hullB[i+2]+baseB[2]);
GLfloat dotP = -direction * current;
if (dotP > maxDotP) {
maxDotP = dotP;
furthestPointB = current;
}
}
//Furthest Minkowski Difference point is difference of d*A[i]-(-d)*B[j]
return furthestPointA - furthestPointB;
}
我的单纯函数：
bool gjkSimplex(std::vector<Vector3f> &simplex, Vector3f &direction) {
GLuint simplexSize = simplex.size();
std::cout << simplexSize;
switch (simplexSize) {
//If the simplex is a line segment
case 2:
//Point is closest feature
if ((simplex[0]-simplex[1])*-simplex[1] < 0) {
std::cout << "A";
simplex = {simplex[1]};
//direction = A0
direction = -simplex[1];
//Line is closest feature
} else {
std::cout << "AB";
//direction = AB x (A0 x AB)
// ^ = cross product
direction = (simplex[0]-simplex[1]) ^ ((-simplex[1]) ^ (simplex[0]-simplex[1]));
}
break;
//If the simplex is a triangle
case 3:
//Point is closest feature
if ((simplex[0]-simplex[2])*(-simplex[2]) < 0 && (simplex[1]-simplex[2])*(-simplex[2]) < 0) {
std::cout << "A";
//direction = A0
direction = -simplex[2];
simplex = {simplex[1]};
//Line to second-latest point is closest feature
} else if ((((simplex[0]-simplex[2])^(simplex[1]-simplex[2]))^(simplex[1]-simplex[2]))*-simplex[2] > 0) {
std::cout << "AB";
//direction = AB x (A0 x AB)
direction = (simplex[1]-simplex[2]) ^ ((-simplex[2]) ^ (simplex[1]-simplex[2]));
simplex = {simplex[1], simplex[2]};
//Line to oldest point is closest feature
} else if (((simplex[0]-simplex[2])^((simplex[0]-simplex[2])^(simplex[1]-simplex[2])))*-simplex[2] > 0) {
std::cout << "AC";
//direction = AC x (A0 x AC)
direction = (simplex[0]-simplex[2]) ^ ((-simplex[2]) ^ (simplex[0]-simplex[2]));
simplex = {simplex[0], simplex[2]};
//Face is closest feature
} else {
//Origin is in direction AC x AB
if (((simplex[1]-simplex[2]) ^ (simplex[0]-simplex[2])) * (-simplex[2]) < 0) {
std::cout << "ACxAB";
//direction = AC x AB
direction = (simplex[0]-simplex[2]) ^ (simplex[1]-simplex[2]);
//origin is in direction AB x AC (other side of the face)
} else {
std::cout << "ABxAC";
//direction = AB x AC
direction = (simplex[1]-simplex[2]) ^ (simplex[0]-simplex[2]);
simplex = {simplex[1], simplex[0], simplex[2]};
}
}
break;
//If the simplex is a tetrahedron
case 4:
//Newest point is closest feature
if ((simplex[0]-simplex[3])*(-simplex[3]) < 0 && (simplex[1]-simplex[3])*(-simplex[3]) < 0 &&
(simplex[2]-simplex[3])*(-simplex[3]) < 0) {
std::cout << "A";
//direction = A0
direction = -simplex[3];
simplex = {simplex[3]};
//Edge between newest and second-newest point is closest feature
} else if ((((simplex[2]-simplex[3]) ^ ((simplex[1]-simplex[3]) ^ (simplex[2]-simplex[3]))) * (-simplex[2]) < 0) &&
((((simplex[1]-simplex[3]) ^ (simplex[0]-simplex[3])) ^ (simplex[2]-simplex[3])) * (-simplex[2]) < 0)) {
std::cout << "AB";
//direction = AB x (A0 x AB)
direction = (simplex[2]-simplex[3]) ^ ((-simplex[3]) ^ (simplex[2]-simplex[3]));
simplex = {simplex[2], simplex[3]};
//Edge between newest and third-newest vertex is closest feature
} else if ((((simplex[1]-simplex[3]) ^ ((simplex[0]-simplex[3]) ^ (simplex[1]-simplex[3]))) * (-simplex[2]) < 0) &&
((((simplex[0]-simplex[3]) ^ (simplex[2]-simplex[3])) ^ (simplex[1]-simplex[3])) * (-simplex[2]) < 0)) {
std::cout << "AC";
//direction = AC x (A0 x AC)
direction = (simplex[1]-simplex[3]) ^ ((-simplex[3]) ^ (simplex[1]-simplex[3]));
simplex = {simplex[1], simplex[3]};
//Edge between newest and oldest point is closest feature
} else if ((((simplex[0]-simplex[3]) ^ ((simplex[2]-simplex[3]) ^ (simplex[0]-simplex[3]))) * (-simplex[2]) < 0) &&
((((simplex[2]-simplex[3]) ^ (simplex[1]-simplex[3])) ^ (simplex[0]-simplex[3])) * (-simplex[2]) < 0)) {
std::cout << "AD";
//direction = AD x (A0 x AD)
direction = (simplex[0]-simplex[3]) ^ ((-simplex[3]) ^ (simplex[0]-simplex[3]));
simplex = {simplex[0], simplex[3]};
//Face between the three newest points is closest feature
} else if (((simplex[1]-simplex[3]) ^ (simplex[2]-simplex[3])) * (-simplex[3]) > 0) {
std::cout << "ABC";
//direction = AC x AB (outer normal of face)
direction = (simplex[1]-simplex[3]) ^ (simplex[2]-simplex[3]);
simplex = {simplex[1], simplex[3], simplex[2]};
//Face between newest, second-newest and oldest point is closest feature
} else if (((simplex[2]-simplex[3]) ^ (simplex[0]-simplex[3])) * (-simplex[3]) > 0) {
std::cout << "ABD";
//direction = AB x AD
direction = (simplex[2]-simplex[3]) ^ (simplex[0]-simplex[3]);
simplex = {simplex[0], simplex[2], simplex[3]};
//Face between newest, second-oldest and oldest point is closest feature
} else if (((simplex[0]-simplex[3]) ^ (simplex[1]-simplex[3])) * (-simplex[3]) > 0) {
std::cout << "ACD";
//direction = AD x AC
direction = (simplex[0]-simplex[3]) ^ (simplex[1]-simplex[3]);
simplex = {simplex[0], simplex[3], simplex[1]};
//Origin is encased by simplex
} else {
//Collision detected
std::cout << "ABCD";
return true;
}
break;
default:
direction = {1,1,1};
simplex = {};
break;
}
std::cout << "\n";
return false;
};
GJK主循环：
//Narrow Phase collision function using GJK
bool SolidObject::collidesWith(SolidObject *object) {
//Initialize by using an arbitrary direction
Vector3f direction (1,1,1);
std::vector<Vector3f> simplex;
Vector3f point = gjkSupport(direction,
this->meshes[0].getConvexHull(), this->base, object->meshes[0].getConvexHull(), object->base);
simplex = {point};
//Set direction to the negative of the resulting point
direction = -point;
bool originInSimplex = false;
while (!originInSimplex) {
//Get furthest point in new direction
point = gjkSupport(direction,
this->meshes[0].getConvexHull(), this->base, object->meshes[0].getConvexHull(), object->base);
//The furthest point in the negative direction is not in the opposing octant
// => no collision
if (point*direction < 0) {
return false;
}
//Add point to the simplex
simplex.push_back(point);
//Update simplex and direction, and return whether the simplex contains the origin
originInSimplex = gjkSimplex(simplex, direction);
}
std::cout << "\n";
return true;
}
答案 0 :(得分：1)
只是一个猜测：
case 2:
//Point is closest feature
if ((simplex[0]-simplex[1])*-simplex[1] < 0) {
std::cout << "A";
simplex = {simplex[1]};
//direction = A0
direction = -simplex[1];
//Line is closest feature
在设置direction之前，您应该设置simplex吗？否则，您将尝试访问长度为1的向量的第2个元素。
此外，您编写的函数gjkSupport()接受std::vector个对象而不是std::vector&个对象。这可能会降低性能，因为每次调用函数时向量都会被复制构造。
答案 1 :(得分：1)
在三角形的情况下：
//Point is closest feature
if ((simplex[0]-simplex[2])*(-simplex[2]) < 0 && (simplex[1]-simplex[2])*(-simplex[2]) < 0) {
std::cout << "A";
//direction = A0
direction = -simplex[2];
simplex = {simplex[1]};
}
应该是
simplex = {simplex[2]};
在四面体案例中：
所有边缘检查均使用simplex[2]执行点prodocut，但他们应使用最新点simplex[3]。
我认为你的第一个边缘检查对第二个条件使用了错误的面，所以不是
if ((((simplex[2]-simplex[3]) ^ ((simplex[1]-simplex[3]) ^ (simplex[2]-simplex[3]))) * (-simplex[2]) < 0) &&
((((simplex[1]-simplex[3]) ^ (simplex[0]-simplex[3])) ^ (simplex[2]-simplex[3])) * (-simplex[2]) < 0)) {
std::cout << "AB";
//direction = AB x (A0 x AB)
direction = (simplex[2]-simplex[3]) ^ ((-simplex[3]) ^ (simplex[2]-simplex[3]));
simplex = {simplex[2], simplex[3]};
}
应该是
if ((((simplex[2]-simplex[3]) ^ ((simplex[1]-simplex[3]) ^ (simplex[2]-simplex[3]))) * (-simplex[3]) < 0) &&
((((simplex[2]-simplex[3]) ^ (simplex[0]-simplex[3])) ^ (simplex[2]-simplex[3])) * (-simplex[3]) < 0)) {
std::cout << "AB";
//direction = AB x (A0 x AB)
direction = (simplex[2]-simplex[3]) ^ ((-simplex[3]) ^ (simplex[2]-simplex[3]));
simplex = {simplex[2], simplex[3]};
}
同样适用于第二次边缘检查的第二个条件，它应该是：
((((simplex[1]-simplex[3]) ^ (simplex[2]-simplex[3])) ^ (simplex[1]-simplex[3])) * (-simplex[3]) < 0)
和第三次边缘检查的第二个条件：
((((simplex[0]-simplex[3]) ^ (simplex[1]-simplex[3])) ^ (simplex[0]-simplex[3])) * (-simplex[3]) < 0)
我还修复了三角形检查的输出simplexe。输入单形的最后一点应始终是输出单形的最后一点。此外，点的排序应该是一致的并且与计算的方向匹配。
这是完整的固定功能：
bool gjkSimplex(std::vector<Vector3f> &simplex, Vector3f &direction) {
GLuint simplexSize = simplex.size();
std::cout << simplexSize;
switch (simplexSize) {
//If the simplex is a line segment
case 2:
//Point is closest feature
if ((simplex[0]-simplex[1])*-simplex[1] < 0) {
std::cout << "A";
//direction = A0
direction = -simplex[1];
simplex = {simplex[1]};
//Line is closest feature
} else {
std::cout << "AB";
//direction = AB x (A0 x AB)
// ^ = cross product
direction = (simplex[0]-simplex[1]) ^ ((-simplex[1]) ^ (simplex[0]-simplex[1]));
}
break;
//If the simplex is a triangle
case 3:
//Point is closest feature
if ((simplex[0]-simplex[2])*(-simplex[2]) < 0 && (simplex[1]-simplex[2])*(-simplex[2]) < 0) {
std::cout << "A";
//direction = A0
direction = -simplex[2];
simplex = {simplex[2]};
//Line to second-latest point is closest feature
} else if ((((simplex[0]-simplex[2])^(simplex[1]-simplex[2]))^(simplex[1]-simplex[2]))*-simplex[2] > 0) {
std::cout << "AB";
//direction = AB x (A0 x AB)
direction = (simplex[1]-simplex[2]) ^ ((-simplex[2]) ^ (simplex[1]-simplex[2]));
simplex = {simplex[1], simplex[2]};
//Line to oldest point is closest feature
} else if (((simplex[0]-simplex[2])^((simplex[0]-simplex[2])^(simplex[1]-simplex[2])))*-simplex[2] > 0) {
std::cout << "AC";
//direction = AC x (A0 x AC)
direction = (simplex[0]-simplex[2]) ^ ((-simplex[2]) ^ (simplex[0]-simplex[2]));
simplex = {simplex[0], simplex[2]};
//Face is closest feature
} else {
//Origin is in direction AC x AB
if (((simplex[1]-simplex[2]) ^ (simplex[0]-simplex[2])) * (-simplex[2]) < 0) {
std::cout << "ACxAB";
//direction = AC x AB
direction = (simplex[0]-simplex[2]) ^ (simplex[1]-simplex[2]);
//origin is in direction AB x AC (other side of the face)
} else {
std::cout << "ABxAC";
//direction = AB x AC
direction = (simplex[1]-simplex[2]) ^ (simplex[0]-simplex[2]);
simplex = {simplex[1], simplex[0], simplex[2]};
}
}
break;
//If the simplex is a tetrahedron
case 4:
//Newest point is closest feature
if ((simplex[0]-simplex[3])*(-simplex[3]) < 0 && (simplex[1]-simplex[3])*(-simplex[3]) < 0 &&
(simplex[2]-simplex[3])*(-simplex[3]) < 0) {
std::cout << "A";
//direction = A0
direction = -simplex[3];
simplex = {simplex[3]};
//Edge between newest and second-newest point is closest feature
} else if ((((simplex[2]-simplex[3]) ^ ((simplex[1]-simplex[3]) ^ (simplex[2]-simplex[3]))) * (-simplex[3]) < 0) &&
((((simplex[2]-simplex[3]) ^ (simplex[0]-simplex[3])) ^ (simplex[2]-simplex[3])) * (-simplex[3]) < 0)) {
std::cout << "AB";
//direction = AB x (A0 x AB)
direction = (simplex[2]-simplex[3]) ^ ((-simplex[3]) ^ (simplex[2]-simplex[3]));
simplex = {simplex[2], simplex[3]};
//Edge between newest and third-newest vertex is closest feature
} else if ((((simplex[1]-simplex[3]) ^ ((simplex[0]-simplex[3]) ^ (simplex[1]-simplex[3]))) * (-simplex[3]) < 0) &&
((((simplex[1]-simplex[3]) ^ (simplex[2]-simplex[3])) ^ (simplex[1]-simplex[3])) * (-simplex[3]) < 0)) {
std::cout << "AC";
//direction = AC x (A0 x AC)
direction = (simplex[1]-simplex[3]) ^ ((-simplex[3]) ^ (simplex[1]-simplex[3]));
simplex = {simplex[1], simplex[3]};
//Edge between newest and oldest point is closest feature
} else if ((((simplex[0]-simplex[3]) ^ ((simplex[2]-simplex[3]) ^ (simplex[0]-simplex[3]))) * (-simplex[3]) < 0) &&
((((simplex[0]-simplex[3]) ^ (simplex[1]-simplex[3])) ^ (simplex[0]-simplex[3])) * (-simplex[3]) < 0)) {
std::cout << "AD";
//direction = AD x (A0 x AD)
direction = (simplex[0]-simplex[3]) ^ ((-simplex[3]) ^ (simplex[0]-simplex[3]));
simplex = {simplex[0], simplex[3]};
//Face between the three newest points is closest feature
} else if (((simplex[1]-simplex[3]) ^ (simplex[2]-simplex[3])) * (-simplex[3]) > 0) {
std::cout << "ABC";
//direction = AC x AB (outer normal of face)
direction = (simplex[1]-simplex[3]) ^ (simplex[2]-simplex[3]);
simplex = {simplex[1], simplex[2], simplex[3]};
//Face between newest, second-newest and oldest point is closest feature
} else if (((simplex[2]-simplex[3]) ^ (simplex[0]-simplex[3])) * (-simplex[3]) > 0) {
std::cout << "ABD";
//direction = AB x AD
direction = (simplex[2]-simplex[3]) ^ (simplex[0]-simplex[3]);
simplex = {simplex[2], simplex[0], simplex[3]};
//Face between newest, second-oldest and oldest point is closest feature
} else if (((simplex[0]-simplex[3]) ^ (simplex[1]-simplex[3])) * (-simplex[3]) > 0) {
std::cout << "ACD";
//direction = AD x AC
direction = (simplex[0]-simplex[3]) ^ (simplex[1]-simplex[3]);
simplex = {simplex[0], simplex[1], simplex[3]};
//Origin is encased by simplex
} else {
//Collision detected
std::cout << "ABCD";
return true;
}
break;
default:
direction = {1,1,1};
simplex = {};
break;
}
std::cout << "\n";
return false;
};