game101作业3

虚拟机代码
本文参考的文章链接:
重心坐标插值推导
代码参考
理论

规范纹理坐标
Texture.hpp中的getColor（）
规范纹理的坐标到[0,1]之间，这一步不做，在虚拟机中运行到bump计算dV的时候会出现错误，以防万一，改下保险。

Eigen::Vector3f getColor(float u, float v){if(u>1) u = 1;if(u<0) u=0;if(v>1) v=1;if(v<0) v=0;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]);}

心坐标插值法
根据重心坐标插值法得到插值的颜色，纹理坐标，法线，物体坐标，深度
公式推导可看找个链接
rasterize_triangle()

void rst::rasterizer::rasterize_triangle(const Triangle& t, const std::array<Eigen::Vector3f, 3>& view_pos)
{// transform matrixauto v = t.toVector4();// bounding boxfloat minx = std::min({v[0][0], v[1][0], v[2][0]});float miny = std::min({v[0][1], v[1][1], v[2][1]});float maxx = std::max({v[0][0], v[1][0], v[2][0]});float maxy = std::max({v[0][1], v[1][1], v[2][1]});// Interateminx = std::floor(minx);miny = std::floor(miny);maxx = std::ceil(maxx);maxy = std::ceil(maxy);for (int x = minx; x <= maxx;x++) {for (int y = miny; y <= maxy;y++) {if (insideTriangle((float) x + 0.5, (float) y + 0.5, t.v)) {//    * 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-bufferauto tp = computeBarycentric2D((float)x + 0.5, (float)y + 0.5, t.v);float alpha ,beta, gamma;std::tie(alpha, beta, gamma) = tp;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;// 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);if (zp<depth_buf[get_index(x, y)]) {auto interpolated_color = interpolate(alpha,beta,gamma,t.color[0],t.color[1],t.color[2], 1.0);auto interpolated_normal = interpolate(alpha,beta,gamma,t.normal[0],t.normal[1],t.normal[2], 1.0 );auto interpolated_texcoords = interpolate(alpha,beta,gamma,t.tex_coords[0],t.tex_coords[1],t.tex_coords[2], 1.0);// obeject coordinateauto interpolated_shadingcoords = interpolate(alpha, beta,gamma,view_pos[0],view_pos[1],view_pos[2],  1.0);fragment_shader_payload payload( interpolated_color, interpolated_normal.normalized(), interpolated_texcoords, texture ? &*texture : nullptr);payload.view_pos = interpolated_shadingcoords;auto pixel_color = fragment_shader(payload);depth_buf[get_index(x,y)] = zp;// using coordinate from originalset_pixel(Eigen::Vector2i(x, y), pixel_color);}}}}// 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);}

phong光照模型
phong_fragment_shader（）

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.// ambientEigen::Vector3f ambient = ka.cwiseProduct(amb_light_intensity);// diffuse// lightdirEigen::Vector3f lightdir = light.position - point;float r2 = lightdir.dot(lightdir);Eigen::Vector3f diffuse = kd.cwiseProduct(light.intensity/r2);diffuse *= std::max(0.0f, lightdir.normalized().dot(normal.normalized()));// specularEigen::Vector3f eyedir = eye_pos - point;Eigen::Vector3f specular = ks.cwiseProduct(light.intensity/r2);specular *= std::pow(std::max(0.0f, normal.normalized().dot((eyedir + lightdir).normalized())), p);result_color += ambient + diffuse  + specular;}return result_color * 255.f;
}

纹理贴图
就是将kd用纹理颜色代替，而不是一个单调的RGB色，说白了就是将一张“布”铺在一个物体的表面
texture_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// get texCoordinate color return_color = payload.texture->getColor(payload.tex_coords[0],payload.tex_coords[1]);}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){// get  lightdirEigen::Vector3f lightdir = light.position - point;// get viewdirEigen::Vector3f viewdir = eye_pos - point;// get decay/corrode parametersfloat r2 = lightdir.dot(lightdir);// ambientEigen::Vector3f ambient = ka.cwiseProduct(amb_light_intensity);// diffuseEigen::Vector3f diffuse = kd.cwiseProduct(light.intensity/r2);diffuse *= std::max(0.0f, lightdir.normalized().dot(normal.normalized()));// specularEigen::Vector3f h = lightdir + viewdir;Eigen::Vector3f specular = ks.cwiseProduct(light.intensity/r2);specular*= std::pow(std::max(0.0f, h.normalized().dot(normal.normalized())),p);result_color += ambient + specular + diffuse;         }return result_color * 255.f;
}

模型法线展示
normal_fragment_shader（）

Eigen::Vector3f normal_fragment_shader(const fragment_shader_payload& payload)
{Eigen::Vector3f return_color = (payload.normal.head<3>().normalized() + Eigen::Vector3f(1.0f, 1.0f, 1.0f)) / 2.f;Eigen::Vector3f result;result << return_color.x() * 255, return_color.y() * 255, return_color.z() * 255;return result;
}

法线贴图（凹凸贴图）
这里用颜色来显示出被扰动的法线，可以和normal_fragment_shader的结果做对比，normal_fragment_shader的法线就是一个三角形碎片使用一个方向的法线
单独说下里面的参数含义：
1，kh kn ：x方向和y方向梯度的一个权重因子
2，du, dv ：TBN空间中法线的 x y ，（-du,dv,1.0）组成TBN空间中的法线。
3，TBN：从切线空间变换到世界空间
4，TODO里面已经给出了公式，具体咋推导不太清楚

bump_fragment_shader()

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)float x = normal.x();float y = normal.y();float z = normal.z();Eigen::Vector3f t{ x * y / std::sqrt(x * x + z * z), std::sqrt(x * x + z * z), z*y / std::sqrt(x * x + z * z) };Eigen::Vector3f b = normal.cross(t);Eigen::Matrix3f TBN;TBN << t.x(), b.x(), normal.x(),t.y(), b.y(), normal.y(),t.z(), b.z(), normal.z();float u = payload.tex_coords.x();float v = payload.tex_coords.y();float w = payload.texture->width;float h = payload.texture->height;float dU = kh * kn * (payload.texture->getColor(u + 1.0f / w , v).norm() - payload.texture->getColor(u, v).norm());float 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 };normal = (TBN * ln).normalized();// 归一化Eigen::Vector3f result_color = normal;return result_color * 255.f;}

法线贴图 + phong光照模型
就是将上面可视化出来的法线贴图的法线分布图和光照模型一起运用起来，也可以添加纹理的操作
displacement_fragment_shader()

Eigen::Vector3f displacement_fragment_shader(const fragment_shader_payload& payload)
{// 添加纹理的效果/*Eigen::Vector3f return_color = {0, 0, 0};if (payload.texture){// TODO: Get the texture value at the texture coordinates of the current fragment// get texCoordinate color return_color = payload.texture->getColor(payload.tex_coords[0],payload.tex_coords[1]);}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);*/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)float x = normal.x();float y = normal.y();float z = normal.z();Eigen::Vector3f t{ x * y / std::sqrt(x * x + z * z), std::sqrt(x * x + z * z), z*y / std::sqrt(x * x + z * z) };Eigen::Vector3f b = normal.cross(t);Eigen::Matrix3f TBN;TBN << t.x(), b.x(), normal.x(),t.y(), b.y(), normal.y(),t.z(), b.z(), normal.z();float u = payload.tex_coords.x();float v = payload.tex_coords.y();float w = payload.texture->width;float h = payload.texture->height;float dU = kh * kn * (payload.texture->getColor(u + 1.0f / w , v).norm() - payload.texture->getColor(u, v).norm());float 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 };// Position p = p + kn * n * h(u,v)normal = (TBN * ln).normalized();point += kn * normal * payload.texture->getColor(u, v).norm();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.Eigen::Vector3f ambient = ka.cwiseProduct(amb_light_intensity);// diffuse// lightdirEigen::Vector3f lightdir = light.position - point;float r2 = lightdir.dot(lightdir);Eigen::Vector3f diffuse = kd.cwiseProduct(light.intensity/r2);diffuse *= std::max(0.0f, lightdir.normalized().dot(normal.normalized()));// specularEigen::Vector3f eyedir = eye_pos - point;Eigen::Vector3f specular = ks.cwiseProduct(light.intensity/r2);specular *= std::pow(std::max(0.0f, normal.normalized().dot((eyedir + lightdir).normalized())), p);result_color += ambient + diffuse  + specular;}return result_color * 255.f;
}

和纹理一起用

双线性插值
步骤
1，找到某个点周围的4个点
2，对四个点进行水平的两次插值，
3，对水平插值出来的两个点进行垂直方向的插值
图解：

在Texture类中添加 getColorBilinear（）方法，其写法就是参照上面的公式

 Eigen::Vector3f getColorBilinear(float u, float v){if(u>1) u = 1;if(u<0) u=0;if(v>1) v=1;if(v<0) v=0;float u_img = u * width;float v_img = (1 - v) * height;float u_min = std::floor(u_img);float v_min = std::floor(v_img);float u_max = std::ceil(u_img);float v_max = std::ceil(v_img);auto U01 = image_data.at<cv::Vec3b>(u_min,v_min);auto U11 = image_data.at<cv::Vec3b>(u_max,v_min);auto U00 = image_data.at<cv::Vec3b>(u_min,v_max);auto U10 = image_data.at<cv::Vec3b>(u_max,v_max);float h = (u_img -u_min)/(u_max-u_min);float ve = (v_img-v_min)/(v_max-v_min);auto bottom = U00 + h * (U10 - U00);auto top = U01 + h * (U11 - U01);auto Vertical = bottom + ve *(top-bottom);return Eigen::Vector3f(Vertical[0], Vertical[1], Vertical[2]);}

效果图：
使用的是100 x 100的纹理图像

纹理图像（100 X100）

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