Update(2020/7/9)
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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。
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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.
}
结果
两者对比结果如下：
| without_MSAA | with_MSAA |
|---|---|
 |
 |