rasterize_triangle(const Triangle& t) in rasterizer.cpp
//Screen space rasterization
void rst::rasterizer::rasterize_triangle(const Triangle& t, const std::array<Eigen::Vector3f, 3>& view_pos)
{
// TODO: From your HW3, get the triangle rasterization code.
// TODO: Inside your rasterization loop:
// * v[i].w() is the vertex view space depth value z.
// * Z is interpolated view space depth for the current pixel
// * zp is depth between zNear and zFar, used for z-buffer
// float Z = 1.0 / (alpha / v[0].w() + beta / v[1].w() + gamma / v[2].w());
// float zp = alpha * v[0].z() / v[0].w() + beta * v[1].z() / v[1].w() + gamma * v[2].z() / v[2].w();
// zp *= Z;
// TODO: Interpolate the attributes:
// auto interpolated_color
// auto interpolated_normal
// auto interpolated_texcoords
// auto interpolated_shadingcoords
// Use: fragment_shader_payload payload( interpolated_color, interpolated_normal.normalized(), interpolated_texcoords, texture ? &*texture : nullptr);
// Use: payload.view_pos = interpolated_shadingcoords;
// Use: Instead of passing the triangle's color directly to the frame buffer, pass the color to the shaders first to get the final color;
// Use: auto pixel_color = fragment_shader(payload);
}
2. 实现投影矩阵
get_projection_matrix() in main.cpp
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
}
3. 实现 Blinn-Phong 模型计算 Fragment Color
phong_fragment_shader() in main.cpp
Eigen::Vector3f phong_fragment_shader(const fragment_shader_payload& payload)
{
Eigen::Vector3f ka = Eigen::Vector3f(0.005, 0.005, 0.005);
Eigen::Vector3f kd = payload.color;
Eigen::Vector3f ks = Eigen::Vector3f(0.7937, 0.7937, 0.7937);
auto l1 = light{{20, 20, 20}, {500, 500, 500}};
auto l2 = light{{-20, 20, 0}, {500, 500, 500}};
std::vector<light> lights = {l1, l2};
Eigen::Vector3f amb_light_intensity{10, 10, 10};
Eigen::Vector3f eye_pos{0, 0, 10};
float p = 150;
Eigen::Vector3f color = payload.color;
Eigen::Vector3f point = payload.view_pos;
Eigen::Vector3f normal = payload.normal;
Eigen::Vector3f result_color = {0, 0, 0};
for (auto& light : lights)
{
// TODO: For each light source in the code, calculate what the *ambient*, *diffuse*, and *specular*
// components are. Then, accumulate that result on the *result_color* object.
}
return result_color * 255.f;
}
4. 实现纹理映射
texture_fragment_shader() in main.cpp
在实现 Blinn-Phong 的基础上，将纹理颜色视为公式中的 kd ，实现 Texture Shading Fragment Shader。
Eigen::Vector3f texture_fragment_shader(const fragment_shader_payload &payload) {
Eigen::Vector3f return_color = {0, 0, 0};
if (payload.texture) {
// TODO: Get the texture value at the texture coordinates of the current fragment
}
Eigen::Vector3f texture_color;
texture_color << return_color.x(), return_color.y(), return_color.z();
Eigen::Vector3f ka = Eigen::Vector3f(0.005, 0.005, 0.005);
Eigen::Vector3f kd = texture_color / 255.f;
Eigen::Vector3f ks = Eigen::Vector3f(0.7937, 0.7937, 0.7937);
auto l1 = light{{20, 20, 20},
{500, 500, 500}};
auto l2 = light{{-20, 20, 0},
{500, 500, 500}};
std::vector<light> lights = {l1, l2};
Eigen::Vector3f amb_light_intensity{10, 10, 10};
Eigen::Vector3f eye_pos{0, 0, 10};
float p = 150;
Eigen::Vector3f color = texture_color;
Eigen::Vector3f point = payload.view_pos;
Eigen::Vector3f normal = payload.normal;
Eigen::Vector3f result_color = {0, 0, 0};
for (auto &light: lights) {
// TODO: For each light source in the code, calculate what the *ambient*, *diffuse*, and *specular*
// components are. Then, accumulate that result on the *result_color* object.
}
return result_color * 255.f;
}
Eigen::Vector3f bump_fragment_shader(const fragment_shader_payload &payload) {
Eigen::Vector3f ka = Eigen::Vector3f(0.005, 0.005, 0.005);
Eigen::Vector3f kd = payload.color;
Eigen::Vector3f ks = Eigen::Vector3f(0.7937, 0.7937, 0.7937);
auto l1 = light{{20, 20, 20},
{500, 500, 500}};
auto l2 = light{{-20, 20, 0},
{500, 500, 500}};
std::vector<light> lights = {l1, l2};
Eigen::Vector3f amb_light_intensity{10, 10, 10};
Eigen::Vector3f eye_pos{0, 0, 10};
float p = 150;
Eigen::Vector3f color = payload.color;
Eigen::Vector3f point = payload.view_pos;
Eigen::Vector3f normal = payload.normal;
float kh = 0.2, kn = 0.1;
// TODO: Implement bump mapping here
// Let n = normal = (x, y, z)
// Vector t = (x*y/sqrt(x*x+z*z),sqrt(x*x+z*z),z*y/sqrt(x*x+z*z))
// Vector b = n cross product t
// Matrix TBN = [t b n]
// dU = kh * kn * (h(u+1/w,v)-h(u,v))
// dV = kh * kn * (h(u,v+1/h)-h(u,v))
// Vector ln = (-dU, -dV, 1)
// Normal n = normalize(TBN * ln)
Eigen::Vector3f result_color = {0, 0, 0};
result_color = normal;
return result_color * 255.f;
}
6. 实现位移片元着色器
displacement_fragment_shader() in main.cpp
在实现 Bump mapping 的基础上，实现 displacement mapping。
Eigen::Vector3f displacement_fragment_shader(const fragment_shader_payload &payload) {
Eigen::Vector3f ka = Eigen::Vector3f(0.005, 0.005, 0.005);
Eigen::Vector3f kd = payload.color;
Eigen::Vector3f ks = Eigen::Vector3f(0.7937, 0.7937, 0.7937);
auto l1 = light{{20, 20, 20},
{500, 500, 500}};
auto l2 = light{{-20, 20, 0},
{500, 500, 500}};
std::vector<light> lights = {l1, l2};
Eigen::Vector3f amb_light_intensity{10, 10, 10};
Eigen::Vector3f eye_pos{0, 0, 10};
float p = 150;
Eigen::Vector3f color = payload.color;
Eigen::Vector3f point = payload.view_pos;
Eigen::Vector3f normal = payload.normal;
float kh = 0.2, kn = 0.1;
// TODO: Implement displacement mapping here
// Let n = normal = (x, y, z)
// Vector t = (x*y/sqrt(x*x+z*z),sqrt(x*x+z*z),z*y/sqrt(x*x+z*z))
// Vector b = n cross product t
// Matrix TBN = [t b n]
// dU = kh * kn * (h(u+1/w,v)-h(u,v))
// dV = kh * kn * (h(u,v+1/h)-h(u,v))
// Vector ln = (-dU, -dV, 1)
// Position p = p + kn * n * h(u,v)
// Normal n = normalize(TBN * ln)
Eigen::Vector3f result_color = {0, 0, 0};
for (auto &light: lights) {
// TODO: For each light source in the code, calculate what the *ambient*, *diffuse*, and *specular*
// components are. Then, accumulate that result on the *result_color* object.
}
return result_color * 255.f;
}
题解解析
1. 实现三角形渲染（HW2基础上增加颜色、法向量和纹理颜色坐标插值）
代码内容大致与HW2相同。
首先使用Bounding Box缩小渲染范围。
auto v = t.toVector4();
float min_x = std::floor(std::min({v[0].x(), v[1].x(), v[2].x()}));
float max_x = std::ceil(std::max({v[0].x(), v[1].x(), v[2].x()}));
float min_y = std::floor(std::min({v[0].y(), v[1].y(), v[2].y()}));
float max_y = std::ceil(std::max({v[0].y(), v[1].y(), v[2].y()}));
// Iterating through each pixel in the bounding box
for (float x = min_x; x <= max_x; x++) {
for (float y = min_y; y <= max_y; y++) {
......//后文代码均在此处
}
}
// Set the pixel color if it should be painted
Eigen::Vector2i p = { (float)x,(float)y};
set_pixel(p, pixel_color); //设置颜色
depth_buf[get_index(x, y)] = z_interpolated;//更新z值
2. 投影变换矩阵
HW2已经写过，这里直接抄过来。
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();
Eigen::Matrix4f M = Eigen::Matrix4f ::Identity();
float fov = 0.5*eye_fov*MY_PI/180;
float top = tan(fov) * zNear;
float bottom = -top;
float right = top * aspect_ratio;
float left = -right;
M << 2 * abs(zNear) / (right - left), 0, (right + left) / (right - left), 0,
0, 2 * abs(zNear) / (top - bottom), (top + bottom) / (top - bottom), 0,
0, 0, (abs(zNear) + abs(zFar)) / (abs(zNear) - abs(zFar)), 2 * abs(zFar * zNear) / (abs(zNear) - abs(zFar)),
0, 0, -1, 0;
return M;
}
在作业框架中，已经事先生成了ambient, diffuse, and specular 反射系数（ka, kd, ks），需要注意的是，这个反射系数包含了环境光的；两个光源的位置和强度（l1, l2），环境光强度常数（ amb_light_intensity ）。与此同时，之前光栅化的信息保存在了 payload 中，包括物体材质颜色 color ，位置信息 point 和法线 normal 。
并且创建了 result_color 用于保存Blinn-Phong处理的结果。
对于每个光源，它计算到光源的方向向量( l )和相机的方向向量( v )，以及用于高光项的半向量(h)。衰减因子（ r ），距离该点越远，光的强度就越低。代码中直接对 l 自身做一次点积处理获得向量 l 的模的平方。
// TODO: For each light source in the code, calculate what the *ambient*, *diffuse*, and *specular*
// components are. Then, accumulate that result on the *result_color* object.
auto v = eye_pos - point; //v为出射光方向（指向眼睛）
auto l = light.position - point; //l为指向入射光源方向
auto h = (v + l).normalized(); //h为半程向量即v+l归一化后的单位向量
auto r = l.dot(l); //衰减因子
auto ambient = ka.cwiseProduct(amb_light_intensity);
auto diffuse = kd.cwiseProduct(light.intensity / r) * std::max(0.0f, normal.normalized().dot(l.normalized()));
auto specular = ks.cwiseProduct(light.intensity / r) * std::pow(std::max(0.0f, normal.normalized().dot(h)), p);
result_color += (ambient + diffuse + specular);
4. 完成纹理映射
这个部分和上part基本一致，只是改变了 漫反射系数 的 kd 数值。
我们只需要填充这个部分：
if (payload.texture) {
// TODO: Get the texture value at the texture coordinates of the current fragment
return_color = payload.texture->getColor(payload.tex_coords.x(), payload.tex_coords.y());
}
Eigen::Vector3f getColor(float u, float v)
{
if (u < 0) {u = 0;}
if (u > 1) {u = 1;}
if (v < 0) {v = 0;}
if (v > 1) {v = 1;}
auto u_img = u * width;
auto v_img = (1 - v) * height;
auto color = image_data.at<cv::Vec3b>(v_img, u_img);
return Eigen::Vector3f(color[0], color[1], color[2]);
}
至于原因目前还没深入研究 // TODO
5. 实现凹凸贴图
首先将贴图改回「hmap.jpg」，渲染函数改为「bump_fragment_shader」：
auto texture_path = "hmap.jpg";
// auto texture_path = "spot_texture.png";
...
std::function<Eigen::Vector3f(fragment_shader_payload)> active_shader = bump_fragment_shader;
在Phong模型的基础上，通过TBN矩阵实现凹凸反射。、
什么是TBN：
将纹理坐标对应到模型空间的矩阵
The acronym TBN stands for Tangent, Bitangent, Normal, and it's used in the context of bump mapping or normal mapping in 3D computer graphics, including the fragment shader.
Tangent: A vector that is perpendicular to the surface of the object and aligned with the direction of increasing texture U-coordinate (along the width of the texture).
Bitangent (or Binormal): A vector perpendicular to the surface of the object and aligned with the direction of increasing texture V-coordinate (along the height of the texture).
Normal: A vector pointing directly out from the surface of the object, it is perpendicular to both the Tangent and Bitangent vectors.
// TODO: Implement bump mapping here
// Let n = normal = (x, y, z)
// Vector t = (x*y/sqrt(x*x+z*z),sqrt(x*x+z*z),z*y/sqrt(x*x+z*z))
// Vector b = n cross product t
// Matrix TBN = [t b n]
// dU = kh * kn * (h(u+1/w,v)-h(u,v))
// dV = kh * kn * (h(u,v+1/h)-h(u,v))
// Vector ln = (-dU, -dV, 1)
// Normal n = normalize(TBN * ln)
构建TBN矩阵：
auto x = normal.x();
auto y = normal.y();
auto z = normal.z();
Eigen::Vector3f t(x*y/sqrt(x*x+z*z),sqrt(x*x+z*z),z*y/sqrt(x*x+z*z));
Eigen::Vector3f b = normal.cross(t);
Eigen::Matrix3f TBN; //TBN矩阵: 将纹理坐标对应到模型空间中
TBN <<
t.x(), b.x(), normal.x(),
t.y(), b.y(), normal.y(),
t.z(), b.z(), normal.z();
(u + 1.0f / w, v) 对当前点稍微右边的纹理进行采样， (u, v) 对当前点的纹理进行采样。 dV 同理。
kh,kn 用于控制纹理高度的变化。定义： float kh = 0.2, kn = 0.1; 。
auto u = payload.tex_coords.x();
auto v = payload.tex_coords.y();
auto w = payload.texture->width;
auto h = payload.texture->height;
auto dU = kh*kn*(payload.texture->getColor(u + 1.0f / w, v).norm() - payload.texture->getColor(u, v).norm());
auto dV = kh*kn*(payload.texture->getColor(u, v + 1.0f / h).norm() - payload.texture->getColor(u, v).norm());
位移片元着色器则会获取模型的顶点，然后通过 kn * normal * payload.texture->getColor(u, v).norm() 抬高或压低顶点 point ，方向是法向量的方向。
......
auto dV = kh * kn * (payload.texture->getColor(u, v + 1.0f / h).norm() - payload.texture->getColor(u, v).norm());
Eigen::Vector3f ln{ -dU,-dV,1.0f };
//将物体表面拉高
point += (kn * normal * payload.texture->getColor(u, v).norm());
normal = TBN * ln;
normal.normalized();
Eigen::Vector3f result_color = {0, 0, 0};
for (auto &light: lights) {
......
接下来，使用Blinn-Phong Reflection Model处理所有光线。
auto v = eye_pos - point; //v为出射光方向（指向眼睛）
auto l = light.position - point; //l为指向入射光源方向
auto h = (v + l).normalized(); //h为半程向量即v+l归一化后的单位向量
auto r = l.dot(l); //衰减因子
auto ambient = ka.cwiseProduct(amb_light_intensity);
auto diffuse = kd.cwiseProduct(light.intensity / r) * std::max(0.0f, normal.normalized().dot(l.normalized()));
auto specular = ks.cwiseProduct(light.intensity / r) * std::pow(std::max(0.0f, normal.normalized().dot(h)), p);
result_color += (ambient + diffuse + specular);
