Games101--Assignment2

Update(2020/7/9)

之前得到了倒置三角形，正置需要修改近平面为负值，因为框架中使用的是左手系。
void rst::rasterizer::rasterize_triangle(const Triangle& t) 中包围盒上边界计算书写错误，应该为MAX而非MIN。

修改后的投影矩阵：

Eigen::Matrix4f get_projection_matrix(float eye_fov, float aspect_ratio, float zNear, float zFar)
{
    // TODO: Use the same projection matrix from the previous assignments
    Eigen::Matrix4f projection = Eigen::Matrix4f::Identity();
    float n=zNear,f=zFar;
    float t=-n*tan(eye_fov/2.0);//Use -n because the left-hand coordinate used in the framework 
    // float t=fabs(n)*tan(eye_fov/2.0); //即为倒置三角形
    float r=t*aspect_ratio;
    float b=-t,l=-r;
    projection<<(2.0*n)/(r-l),0,(r+l)/(l-r),0,
    0,(2.0*n)/(t-b),(t+b)/(b-t),0,
    0,0,(n+f)/(n-f),(2.0*n*f)/(f-n),
    0,0,1,0;
    
    return projection;
}

要求

Gams101的Assignment2的要求如下：

修改函数rasterize_triangle(const Triangle& t)。
该函数的内部工作流程如下：

创建三角形的2 维bounding box。
遍历此bounding box 内的所有像素（使用其整数索引）。然后，使用像素中
心的屏幕空间坐标来检查中心点是否在三角形内。
如果在内部，则将其位置处的插值深度值(interpolated depth value) 与深度
缓冲区(depth buffer) 中的相应值进行比较。
如果当前点更靠近相机，请设置像素颜色并更新深度缓冲区(depth buffer)。

需要修改的函数如下：
• rasterize_triangle(): 执行三角形栅格化算法
• static bool insideTriangle(): 测试点是否在三角形内。

判断点是否在三角形内，只要用叉积来判断方向即可。

static bool insideTriangle(float x, float y, const Vector3f* _v)
{   
    // TODO : Implement this function to check if the point (x, y) is inside the triangle represented by _v[0], _v[1], _v[2]
    float a=_v[0].x(),b=_v[0].y(),c=_v[1].x(),d=_v[1].y(),e=_v[2].x(),f=_v[2].y();
    float t1=(c-a)*(y-b)-(d-b)*(x-a);
    float t2=(e-c)*(y-d)-(f-d)*(x-c);
    float t3=(a-e)*(y-f)-(b-f)*(x-e);
    bool x1=true?t1>0.0:false,x2=true?t2>0.0:false,x3=true?t3>0.0:false;
    bool ret=false;
    if((x1 &x2&x3) || (!x1)&(!x2)&(!x3)) ret=true;
    return ret;
}

rasterize_triangle()，使用MSAA，用的是4x4的supersampling。

//Screen space rasterization
void rst::rasterizer::rasterize_triangle(const Triangle& t) {
    auto v = t.toVector4();
    
    // TODO : Find out the bounding box of current triangle.
    // iterate through the pixel and find if the current pixel is inside the triangle
    int left=MIN(v[0].x(),MIN(v[1].x(),v[2].x()))-1;
    int right=MAX(v[0].x(),MAX(v[1].x(),v[2].x()))+1;
    int bottom=MIN(v[0].y(),MIN(v[1].y(),v[2].y()))-1;
    int top=MAX(v[0].y(),MAX(v[1].y(),v[2].y()))+1;
    //修正top计算书写错误，应该取最大值 
    bool MSAA=true;
    //4x4 SuperSampling
    float dir[16][2]={
        {0.125,0.125},
        {0.125,0.375},
        {0.125,0.625},
        {0.125,0.875},
        {0.375,0.125},
        {0.375,0.375},
        {0.375,0.625},
        {0.375,0.875},
        {0.625,0.125},
        {0.625,0.375},
        {0.625,0.625},
        {0.625,0.875},
        {0.875,0.125},
        {0.875,0.375},
        {0.875,0.625},
        {0.875,0.875},
    };
    if(MSAA){

    for(int x=left;x<=right;x++){
        for(int y=bottom;y<=top;y++){
            float min_dep=0x7f7ffff;
            int count=0;
            for(int i=0;i<16;i++){
                if(insideTriangle(x+dir[i][0],y+dir[i][1],t.v)){
                    count++;
                    std::tuple<float, float, float> alpha= computeBarycentric2D(x, y, t.v);
                    float w_reciprocal = 1.0/(std::get<0>(alpha) / v[0].w() + std::get<1>(alpha) / v[1].w() + std::get<2>(alpha) / v[2].w());
                    float z_interpolated = std::get<0>(alpha)* v[0].z() / v[0].w() + std::get<1>(alpha) * v[1].z() / v[1].w() + std::get<2>(alpha) * v[2].z() / v[2].w();
                    z_interpolated *= w_reciprocal;
                    min_dep=MIN(min_dep,z_interpolated);
                }
            }
            if(count==0)continue;
            if(min_dep < depth_buf[get_index(x,y)]){
                depth_buf[get_index(x,y)]=min_dep;
                set_pixel(Vector3f(x,y,min_dep),t.getColor()*count/16.0);
            }
        }
    }

    }
    else
    {
        for(int x=left;x<=right;x++){
            for(int y=bottom;y<=top;y++){
                if(insideTriangle(x,y,t.v)){
                    std::tuple<float, float, float> alpha= computeBarycentric2D(x, y, t.v);
                    float w_reciprocal = 1.0/(std::get<0>(alpha) / v[0].w() + std::get<1>(alpha) / v[1].w() + std::get<2>(alpha) / v[2].w());
                    float z_interpolated = std::get<0>(alpha)* v[0].z() / v[0].w() + std::get<1>(alpha) * v[1].z() / v[1].w() + std::get<2>(alpha) * v[2].z() / v[2].w();
                    z_interpolated *= w_reciprocal;
                    if(z_interpolated<depth_buf[get_index(x,y)]){
                        depth_buf[get_index(x,y)]=z_interpolated;
                        set_pixel(Vector3f(x,y,z_interpolated),t.getColor());
                    }
                }
            }   
        }
    }
    // If so, use the following code to get the interpolated z value.
    //auto tpp = computeBarycentric2D(x, y, t.v);
    //float alpha, beta, gamma;
    //std::tie(alpha, beta, gamma)=tpp;
    //float w_reciprocal = 1.0/(alpha / v[0].w() + beta / v[1].w() + gamma / v[2].w());
    //float z_interpolated = alpha * v[0].z() / v[0].w() + beta * v[1].z() / v[1].w() + gamma * v[2].z() / v[2].w();
    //z_interpolated *= w_reciprocal;

    // TODO : set the current pixel (use the set_pixel function) to the color of the triangle (use getColor function) if it should be painted.
}

如果不用MSAA，则代码如下：

//Screen space rasterization
void rst::rasterizer::rasterize_triangle(const Triangle& t) {
    auto v = t.toVector4();
    
    // TODO : Find out the bounding box of current triangle.
    // iterate through the pixel and find if the current pixel is inside the triangle
    int left=MIN(v[0].x(),MIN(v[1].x(),v[2].x()))-1;
    int right=MAX(v[0].x(),MAX(v[1].x(),v[2].x()))+1;
    int bottom=MIN(v[0].y(),MIN(v[1].y(),v[2].y()))-1;
    int top=MAX(v[0].y(),MIN(v[1].y(),v[2].y()))+1;
    for(int x=left;x<=right;x++)
    {
        for(int y=bottom;y<=top;y++)
        {
           if(insideTriangle(x,y,t.v))
           {
               std::tuple<float, float, float> alpha= computeBarycentric2D(x, y, t.v);
               float w_reciprocal = 1.0/(std::get<0>(alpha) / v[0].w() + std::get<1>(alpha) / v[1].w() + std::get<2>(alpha) / v[2].w());
                float z_interpolated = std::get<0>(alpha)* v[0].z() / v[0].w() + std::get<1>(alpha) * v[1].z() / v[1].w() + std::get<2>(alpha) * v[2].z() / v[2].w();
                z_interpolated *= w_reciprocal;
                if(z_interpolated<depth_buf[get_index(x,y)])
                {
                    depth_buf[get_index(x,y)]=z_interpolated;
                    set_pixel(Vector3f(x,y,z_interpolated),t.getColor());
                }
            }
        }   
    }
    // If so, use the following code to get the interpolated z value.
    //auto tpp = computeBarycentric2D(x, y, t.v);
    //float alpha, beta, gamma;
    //std::tie(alpha, beta, gamma)=tpp;
    //float w_reciprocal = 1.0/(alpha / v[0].w() + beta / v[1].w() + gamma / v[2].w());
    //float z_interpolated = alpha * v[0].z() / v[0].w() + beta * v[1].z() / v[1].w() + gamma * v[2].z() / v[2].w();
    //z_interpolated *= w_reciprocal;

    // TODO : set the current pixel (use the set_pixel function) to the color of the triangle (use getColor function) if it should be painted.
}