快速判断一个点是否在三角形内

 

       通过叉乘的方法实现，下面是ogre中的实现代码，只给出2维的函数，三维是同样的道理：

 

    //判断一个点是否在一个2维三角形内，通过叉乘的方法来实现
    bool Math::pointInTri2D(const Vector2& p, const Vector2& a, 
        const Vector2& b, const Vector2& c)
    {
        // Winding must be consistent from all edges for point to be inside
        Vector2 v1, v2;
        Real dot[3];
        bool zeroDot[3];

        v1 = b - a;
        v2 = p - a;

        // Note we don't care about normalisation here since sign is all we need
        // It means we don't have to worry about magnitude of cross products either
        dot[0] = v1.crossProduct(v2);
        zeroDot[0] = Math::RealEqual(dot[0], 0.0f, 1e-3);


        v1 = c - b;
        v2 = p - b;

        dot[1] = v1.crossProduct(v2);
        zeroDot[1] = Math::RealEqual(dot[1], 0.0f, 1e-3);

        // Compare signs (ignore colinear / coincident points)
        if(!zeroDot[0] && !zeroDot[1] 
        && Math::Sign(dot[0]) != Math::Sign(dot[1]))
        {
            return false;
        }

        v1 = a - c;
        v2 = p - c;

        dot[2] = v1.crossProduct(v2);
        zeroDot[2] = Math::RealEqual(dot[2], 0.0f, 1e-3);
        // Compare signs (ignore colinear / coincident points)
        if((!zeroDot[0] && !zeroDot[2] 
            && Math::Sign(dot[0]) != Math::Sign(dot[2])) ||
            (!zeroDot[1] && !zeroDot[2] 
            && Math::Sign(dot[1]) != Math::Sign(dot[2])))
        {
            return false;
        }


        return true;
    }