如何解决AABB碰撞代码的三角形不起作用
我一直在调整和修改我的代码以针对一个三角形测试AABB，但我不确定自己做错了什么。我正在使用分离轴定理，因为我认为这是检测AABB和三角形之间碰撞的最好且唯一的方法（如果我错了或者有更好/更快的方法，请纠正我）。当前，当发生碰撞时，它什么也检测不到。
代码相对较小，每帧调用isAABBIntersectingTriangle，希望了解数学或算法的人可以对我有所帮助。该函数将边界框min和max作为两个3D向量（glm :: vec3）和三个三角形顶点（tri1，tri2，tri3）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转换，三角形通过位置旋转和比例转换）
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,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,bBoxMin.z));
float v4 = glm::dot(axis,bBoxMax.z));
float v5 = glm::dot(axis,bBoxMin.z));
float v6 = glm::dot(axis,bBoxMax.z));
float v7 = glm::dot(axis,bBoxMax.z));
float v8 = glm::dot(axis,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,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 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 tri3)
{
//AABB face normals
glm::vec3 axis1(1,0);
glm::vec3 axis2(0,1,0);
glm::vec3 axis3(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.z) - glm::vec3(bBoxMin.x,bBoxMax.z);
glm::vec3 e5 = glm::vec3(bBoxMax.x,bBoxMax.z) - glm::vec3(bBoxMax.x,bBoxMax.z);
glm::vec3 e6 = glm::vec3(bBoxMax.x,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,tri3)) return false;
if (!SATTriangleAABBCheck(axis2,tri3)) return false;
if (!SATTriangleAABBCheck(axis3,tri3)) return false;
if (!SATTriangleAABBCheck(axis4,tri3)) return false;
if (!SATTriangleAABBCheck(axis5,tri3)) return false;
if (!SATTriangleAABBCheck(axis6,tri3)) return false;
if (!SATTriangleAABBCheck(axis7,tri3)) return false;
if (!SATTriangleAABBCheck(axis8,tri3)) return false;
if (!SATTriangleAABBCheck(axis9,tri3)) return false;
if (!SATTriangleAABBCheck(axis10,tri3)) return false;
if (!SATTriangleAABBCheck(axis11,tri3)) return false;
if (!SATTriangleAABBCheck(axis12,tri3)) return false;
if (!SATTriangleAABBCheck(axis13,tri3)) return false;
return true;
}
这也是主循环中的代码，该代码计算三角形的世界位置，然后调用该函数，我认为这里没有什么不对的地方，因为它可能是最受关注的地方：
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));
mat = glm::rotate(mat,glm::radians(entities[0]->yRot),glm::vec3(0,glm::radians(entities[0]->zRot),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";
}
解决方法
测试中有一部分代码不够健壮。
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，才能对向量进行归一化。当因子平行时，叉积的长度为零。因此，如果e1,e2,e3中的任何一个与e4,e5,e6中的任何一个平行，则对应的叉积将为零长度矢量，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坐标足以使涉及该向量的任何点积评估为NaN。这确实与SATTriangleAABBCheck的尝试混淆。 （零长度向量同样会干扰函数，因此跳过归一化不是解决方案。）
该解决方案取决于叉积为零的情况下应采取的措施。在这种情况下，该零表示计算无法生成分隔轴。检查的轴数少于最大数量，因为不同的平行线永不相交。在零轴（标准化为NaN）上跳过测试。
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