// generate 8 points around this point, from a certain factor
std::vector<Vec3Df> getPointsCircle(Vec3Df const point,
                                    int const dimensions,
                                    float const factor = 0.08f)
{
    using namespace std;

    vector<Vec3Df> points;
    Vec3Df p0, p2;

    for (int dimLevel = 1; dimLevel < dimensions + 1; dimLevel++) {
        // set up the box
        for (int i = 0; i < 3; ++i)
            p0[i] = point[i] + (dimLevel * factor * -0.5f);

        p2[0] = point[0];
        p2[1] = point[1] + (dimLevel * factor * 0.5f);
        p2[2] = point[2] + (dimLevel * factor * 0.5f);

        BoundingBox triBoxed(p0, p2);

        // take the eight points around it and put them in a list
        Vec3Df A, B, C, D, E, F, G, H;
        triBoxed.allPoints(A, B, C, D, E, F, G, H);

        for (Vec3Df boxPoint : {
                    A, B, C, D, E, F, G, H
                })
            points.push_back(boxPoint);
    }

    return points;
}

float hardShadow(Vec3Df& isctPoint,
                 Vec3Df& normal)
{
    using namespace std;

    float total = 0.f;

    isctPoint += .01f * normal;

    for (int i = 0; i < MyLightPositions.size(); i++) {

        Vec3Df tempLight = MyLightPositions[i];
        Vec3Df lightDir = getRay(isctPoint, tempLight);

        Vec3Df potentialIsct, n, color;
        float t, tMin = FLT_MAX;
        bool hitTriangle = rootNode.hit(&rootNode, isctPoint, lightDir, t,
                                        tMin, n, color, potentialIsct);

        if (!hitTriangle)
            return 1.f;
    }

    return 0.f;
}

float softShadow(Vec3Df& isctPoint,
                 Vec3Df& normal)
{
    using namespace std;

    float total = 0.f;

    int dimensions = 5;

    isctPoint += .01f * normal;

    for (int i = 0; i < MyLightPositions.size(); i++) {

        vector<Vec3Df> lightList = getPointsCircle(MyLightPositions[i], dimensions);
//		vector<Vec3Df> lightList = generateRandomPoints(MyLightPositions[i], 8);
        Vec3Df tempLight;

        for (int i = 0; i < lightList.size(); i++) {
            tempLight = lightList[i];
            Vec3Df lightDir = getRay(isctPoint, tempLight);
            float lightDist = lightDir.getLength();

            // see if there is anything in the way by comparing lengths
            Vec3Df potentialIsct, n, color;
            float t, tMin = FLT_MAX;
            bool hitTriangle = rootNode.hit(&rootNode, isctPoint, lightDir, t,
                                            tMin, n, color, potentialIsct);

            if (!hitTriangle)
                total += 1;
        }
    }
    float positions = MyLightPositions.size();
    float res = total / (dimensions * 8.f * positions);
    return res;
}