bugfix: fix transformed texture coordinates.

src/common.h

@@ -15,9 +15,9 @@ using TransformMatrix = Eigen::Matrix<double, 4, 4>;
 
 typedef struct Vertex {
   Vertex(const Point3d &p, const Vector3d &n, const Point2d &tex_coor)
-      : position(p), normal(n), texture_coordinate(tex_coor) {}
+      : position(p), normal(n), texture_coordinate({tex_coor, 1.}) {}
 
   Point3d position;
   Vector3d normal;
-  Point2d texture_coordinate;
+  std::pair<Point2d, double> texture_coordinate;
 } Vertex;

src/main.cc

@@ -19,6 +19,7 @@ int main(int argc, char *argv[]) {
   spdlog::set_level(spdlog::level::trace);
 
   const std::string obj_path{argv[1]};
+  const std::string texture_path{argv[2]};
 
   const int resolution_width = 640;
   const int resolution_height = 320;
@@ -93,7 +94,7 @@ int main(int argc, char *argv[]) {
 
   Camera camera{Vector3d{0, 1, 0}};
   MinusRenderer renderer{near, far, fov, aspect_ratio};
-  renderer.load_mesh(obj_path);
+  renderer.load_mesh(obj_path, {texture_path});
   TransformMatrix translate{
       {1., 0., 0., 3.}, {0., 1., 0., 3.}, {0., 0., 1., -4.}, {0., 0., 0., 1.}};
   renderer.model_transform(translate);

src/mesh.cc

@@ -16,7 +16,13 @@ Mesh::Mesh(const std::vector<std::shared_ptr<Vertex>> &vertices,
            const std::shared_ptr<PhoneMaterial> &phone_material)
     : vertices_(vertices), primitives_(primitives), material_(phone_material) {}
 
-Point2d Mesh::get_texture_coordinate(const unsigned int index) const {
+const std::pair<Point2d, double> &
+Mesh::get_texture_coordinate(const unsigned int index) const {
+  return (vertices_[index])->texture_coordinate;
+}
+
+std::pair<Point2d, double> &
+Mesh::get_texture_coordinate(const unsigned int index) {
   return (vertices_[index])->texture_coordinate;
 }
 
@@ -24,12 +30,13 @@ Point3d Mesh::get_normal_vector(const unsigned int index) const {
   return (vertices_[index])->normal;
 }
 
-std::vector<Mesh> Mesh::load_mesh(const std::string &file_path) {
+std::vector<Mesh> Mesh::load_mesh(const std::string &obj_path,
-  const auto &obj_path = std::filesystem::path(file_path);
+                                  const std::vector<std::string> texture_path) {
-  const auto &material_directory = obj_path.parent_path();
+  const auto &obj_file_path = std::filesystem::path(obj_path);
+  const auto &material_directory = obj_file_path.parent_path();
 
   objl::Loader loader{};
-  assert(loader.LoadFile(file_path.c_str()));
+  assert(loader.LoadFile(obj_path.c_str()));
 
   std::vector<Mesh> res;
   for (const auto &mesh : loader.LoadedMeshes) {
@@ -50,12 +57,17 @@ std::vector<Mesh> Mesh::load_mesh(const std::string &file_path) {
                                     mesh.Indices[i + 1], mesh.Indices[i + 2]));
     }
 
-    std::vector<std::filesystem::path> texture_path;
+    std::vector<std::filesystem::path> texture_file_path;
-    if (!mesh.MeshMaterial.map_Kd.empty()) {
+    if (!texture_path.empty()) {
-      texture_path.push_back(material_directory / mesh.MeshMaterial.map_Kd);
+      for (const auto &p : texture_path) {
+        texture_file_path.push_back(std::filesystem::path(p));
+      }
+    } else if (!mesh.MeshMaterial.map_Kd.empty()) {
+      texture_file_path.push_back(material_directory /
+                                  mesh.MeshMaterial.map_Kd);
     }
     auto material =
-        std::shared_ptr<PhoneMaterial>(new PhoneMaterial(texture_path));
+        std::shared_ptr<PhoneMaterial>(new PhoneMaterial(texture_file_path));
 
     res.push_back(Mesh(vertices, primitives, material));
   }

src/mesh.h

@@ -16,10 +16,15 @@ public:
        const std::vector<Triangle> &primitives,
        const std::shared_ptr<PhoneMaterial> &phone_material);
 
-  static std::vector<Mesh> load_mesh(const std::string &file_path);
+  static std::vector<Mesh> load_mesh(
+      const std::string &obj_path,
+      const std::vector<std::string> texture_path = std::vector<std::string>{});
 
 public:
-  Point2d get_texture_coordinate(const unsigned int index) const;
+  const std::pair<Point2d, double> &
+  get_texture_coordinate(const unsigned int index) const;
+  std::pair<Point2d, double> &get_texture_coordinate(const unsigned int index);
+
   Point3d get_normal_vector(const unsigned int index) const;
 
   const std::vector<Triangle> &get_primitives() const { return primitives_; };

src/minus_renderer.cc

@@ -83,7 +83,8 @@ MinusRenderer::calculate_barycentric_coordinate(const Triangle &t,
 void MinusRenderer::model_transform(const TransformMatrix &mtx) {
   for (auto &m : meshes_) {
     for (auto &t : m.get_primitives()) {
-      t.set_points(apply_transform(mtx, t.get_vertex_position()));
+      const auto &[res, _] = apply_transform(mtx, t.get_vertex_position());
+      t.set_points(res);
     }
   }
 }
@@ -91,7 +92,8 @@ void MinusRenderer::model_transform(const TransformMatrix &mtx) {
 void MinusRenderer::view_transform(const TransformMatrix &mtx) {
   for (auto &m : meshes_) {
     for (auto &t : m.get_primitives()) {
-      t.set_points(apply_transform(mtx, t.get_vertex_position()));
+      const auto &[res, _] = apply_transform(mtx, t.get_vertex_position());
+      t.set_points(res);
     }
   }
 }
@@ -105,9 +107,17 @@ cv::Mat MinusRenderer::render(const int resolution_width,
     for (int i = 0; i < primitives.size(); ++i) {
       auto &t = primitives[i];
       const auto &triangle_vertices = t.get_vertex_position();
-      auto tmp = apply_transform(projection_matrix_, triangle_vertices);
+      const auto &[projective_res, w] =
-      t.set_points(apply_transform(
+          apply_transform(projection_matrix_, triangle_vertices);
-          view_port_transform(resolution_width, resolution_height), tmp));
+      const auto &indices = t.get_vertex_index();
+      for (int j = 0; j < indices.size(); ++j) {
+        auto &uv = m.get_texture_coordinate(indices[j]);
+        uv.second = w[j];
+      }
+      const auto &[res, _] = apply_transform(
+          view_port_transform(resolution_width, resolution_height),
+          projective_res);
+      t.set_points(res);
     }
   }
   const auto &shading_points = rasterizer.rasterize(meshes);
@@ -131,22 +141,26 @@ cv::Mat MinusRenderer::render(const int resolution_width,
               triangle, Point2d{x + 0.5, y + 0.5});
 
           const auto &triangle_indices = triangle.get_vertex_index();
-          std::vector<Point3d> triangle_uv;
+          std::vector<Point2d> triangle_uv;
+          std::vector<double> w_coeff;
           for (int j = 0; j < triangle_indices.size(); ++j) {
-            const auto &uv = mesh.get_texture_coordinate(triangle_indices[j]);
+            const auto &[uv, w] =
-            triangle_uv.push_back(Point3d{uv.x(), uv.y(), 1});
+                mesh.get_texture_coordinate(triangle_indices[j]);
+            triangle_uv.push_back(uv);
+            w_coeff.push_back(w);
           }
-          auto projective_uv = apply_transform(projection_matrix_, triangle_uv);
           // TODO(tianlei): 推导一下为什么需要除以下面这个
-          auto w_reciprocal = alpha * (projective_uv[0].z()) +
+          // 在 screen space 对 1/w 的插值就相当于在 world space 对 w 的插值
-                              beta * (projective_uv[1].z()) +
+          auto w_reciprocal = alpha * (1. / w_coeff[0]) +
-                              gamma * (2 * projective_uv[2].z());
+                              beta * (1. / w_coeff[1]) +
-          Point2d pixel_uv{
+                              gamma * (1. / w_coeff[2]);
-              (alpha * projective_uv[0].x() + beta * projective_uv[1].x() +
+          Point2d pixel_uv{(alpha * (triangle_uv[0].x() / w_coeff[0]) +
-               gamma * projective_uv[2].x()) /
+                            beta * (triangle_uv[1].x() / w_coeff[1]) +
+                            gamma * (triangle_uv[2].x() / w_coeff[2])) /
                                w_reciprocal,
-              (alpha * projective_uv[0].y() + beta * projective_uv[1].y() +
+                           (alpha * (triangle_uv[0].y() / w_coeff[0]) +
-               gamma * projective_uv[2].y()) /
+                            beta * (triangle_uv[1].y() / w_coeff[1]) +
+                            gamma * (triangle_uv[2].y() / w_coeff[2])) /
                                w_reciprocal};
           auto &material = mesh.get_material();
 
@@ -158,8 +172,9 @@ cv::Mat MinusRenderer::render(const int resolution_width,
   return color_image;
 }
 
-void MinusRenderer::load_mesh(const std::string &file_path) {
+void MinusRenderer::load_mesh(const std::string &obj_path,
-  meshes_ = Mesh::load_mesh(file_path);
+                              const std::vector<std::string> texture_path) {
+  meshes_ = Mesh::load_mesh(obj_path, texture_path);
   spdlog::info("Mesh size: {}, the primitives size of the first mesh: {}",
                meshes_.size(), meshes_.front().get_primitives().size());
 }

src/minus_renderer.h

@@ -10,7 +10,8 @@
 class MinusRenderer {
 public:
   MinusRenderer(float near, float far, float fov, float aspect_ratio);
-  void load_mesh(const std::string &file_path);
+  void load_mesh(const std::string &obj_path,
+                 const std::vector<std::string> texture_path);
 
 public:
   cv::Mat render(const int resolution_width, const int resolution_height);

src/util/math_util.h

@@ -11,18 +11,14 @@ bool fequal(const FloatType a, const FloatType b) {
 }
 
 template <int d>
-std::vector<Eigen::Vector<double, d>>
+std::pair<std::vector<Eigen::Vector<double, d>>, std::vector<double>>
 apply_transform(const TransformMatrix &mtx,
                 const std::vector<Eigen::Vector<double, d>> &points) {
-  std::vector<Eigen::Vector<double, d>> res;
+  std::pair<std::vector<Eigen::Vector<double, d>>, std::vector<double>> res{};
   for (const auto &p : points) {
-    auto tmp_p = Eigen::Vector<double, 1 + d>();
+    const auto &transform_res = mtx * p.homogeneous();
-    tmp_p << p, 1.;
+    res.first.push_back(transform_res.hnormalized());
-    tmp_p = mtx * tmp_p;
+    res.second.push_back(transform_res.w());
-    if (!fequal(tmp_p.w(), 1.)) {
-      tmp_p /= tmp_p.w();
-    }
-    res.push_back(tmp_p.template head<d>());
   }
   return res;
 }