implenment a very simple rasterizer.

CMakeLists.txt

@@ -1,6 +1,8 @@
 cmake_minimum_required(VERSION 3.9) 
 PROJECT(minus_renderer)
 
+set(CMAKE_CXX_STANDARD 17)
+
 find_package(OpenCV REQUIRED core imgproc)
 
 set(EXECUTABLE_OUTPUT_PATH ${CMAKE_BINARY_DIR}/bin)

src/common.h

@@ -0,0 +1,14 @@
+// Copyright 2024 Bytedance Inc. All Rights Reserved.
+// Author: tianlei.richard@qq.com (tianlei.richard)
+
+#pragma once
+
+#include <opencv2/core/core.hpp>
+
+#include <Eigen/Dense>
+
+using Vector3d = Eigen::Vector3d;
+using Point2d = Eigen::Vector2d;
+using Point3d = Eigen::Vector3d;
+using BBox = cv::Rect2i;
+using PixelProperty = Eigen::Vector4d;

src/minus_renderer.cc

@@ -9,19 +9,18 @@
 #include "spdlog/spdlog.h"
 #include "spdlog/fmt/ostr.h" // github.com/gabime/spdlog/issues/1638
 
+#include "common.h"
 #include "rasterizer.h"
 #include "triangle.h"
 
 using namespace Eigen;
-using namespace cv;
 
 int main(int argc, char *argv[]) {
 
   const int width = 1280;
   const int height = 720;
 
-  Triangle t{Triangle::PointType{1, 1, 0}, Triangle::PointType{3, 1, 0},
+  Triangle t{Point3d{1, 1, -2}, Point3d{3, 1, -2}, Point3d{2, 4, -2}};
-             Triangle::PointType{2, 4, 0}};
 
   Rasterizer rasterizer{width, height};
   rasterizer.rasterize(t);

src/rasterizer.cc

@@ -6,9 +6,12 @@
 
 Rasterizer::Rasterizer(const int width, const int height)
     : width_(width), height_(height),
-      pixels_(std::vector<std::vector<int>>(
+      pixels_(std::vector<std::vector<PixelProperty>>(
           height,
-          std::vector<int>(width, std::numeric_limits<int>::infinity()))) {}
+          std::vector<PixelProperty>(
+              width, PixelProperty{0., 0., 0.,
+                                   std::numeric_limits<double>::infinity()}))) {
+}
 
 void Rasterizer::rasterize(const Triangle &t) {
   const auto &aabb = t.axis_align_bbox();
@@ -19,6 +22,41 @@ void Rasterizer::rasterize(const Triangle &t) {
 
   for (int i = x_min; i < x_max; ++i) {
     for (int j = y_min; j < y_max; ++j) {
+      auto &property = pixels_[j][i];
+      const auto &[is_inside, z_screen] = inside(Point2d{i + 0.5, j + 0.5}, t);
+      if (is_inside && z_screen > property[3]) {
+        property[0] = 1;
+        property[1] = 0;
+        property[2] = 0;
+        property[3] = z_screen;
       }
     }
   }
+}
+
+std::pair<bool, double> Rasterizer::inside(const Point2d &p_screen,
+                                           const Triangle &t) {
+  const auto points = t.get_points<3>();
+
+  const auto plane_normal = t.normal_vector();
+  const auto plane_point = points[0];
+  const auto z_screen =
+      plane_point.z() - (plane_normal.x() * (p_screen.x() - plane_point.x()) +
+                         plane_normal.y() * (p_screen.y() - plane_point.y())) /
+                            plane_normal.z();
+  const Point3d p{p_screen.x(), p_screen.y(), z_screen};
+
+  const auto v1 = points[1] - points[0];
+  const auto v2 = points[2] - points[1];
+  const auto v3 = points[0] - points[2];
+
+  const auto c1 = v1.cross(p - points[0]).normalized();
+  const auto c2 = v2.cross(p - points[1]).normalized();
+  const auto c3 = v3.cross(p - points[2]).normalized();
+
+  const auto r1 = c1.dot(c2);
+  const auto r2 = c1.dot(c3);
+  const auto r3 = c2.dot(c3);
+
+  return {r1 > 0 && r2 > 0 && r3 > 0, z_screen};
+}

src/rasterizer.h

@@ -9,7 +9,10 @@
 
 class Rasterizer {
 public:
-  using RasterizeRange = cv::Rect2i;
+  typedef enum RasterizeMode {
+    Fill,
+    Line,
+  } RasterizeMode;
 
 public:
   Rasterizer(const int width, const int height);
@@ -17,8 +20,14 @@ public:
 public:
   void rasterize(const Triangle &t);
 
+private:
+  static std::pair<bool, double> inside(const Point2d &p_screen,
+                                        const Triangle &t);
+
 private:
   int width_;
   int height_;
-  std::vector<std::vector<int>> pixels_;
+  std::vector<std::vector<PixelProperty>> pixels_;
+
+  RasterizeMode mode_ = RasterizeMode::Fill;
 };

src/triangle.cc

@@ -4,37 +4,34 @@
 #include "triangle.h"
 #include <algorithm>
 
-Triangle::Triangle(const PointType &a, const PointType &b, const PointType &c)
+Triangle::Triangle(const Point3d &a, const Point3d &b, const Point3d &c)
-    : points_({HomoPointType{a[0], a[1], a[2], 1},
+    : points_({a, b, c}) {}
-               HomoPointType{b[0], b[1], b[2], 1},
-               HomoPointType{c[0], c[1], c[2], 1}}),
-      aabb_(calculate_aabb(points_[0], points_[1], points_[2])) {}
 
 Triangle::Triangle(const HomoPointType &a, const HomoPointType &b,
                    const HomoPointType &c)
-    : points_({a, b, c}),
+    : points_({(a / a.z()).head(3), (b / b.z()).head(3), (c / c.z()).head(3)}) {
-      aabb_(calculate_aabb(points_[0], points_[1], points_[2])) {}
-
-Triangle::BBoxType Triangle::calculate_aabb(const HomoPointType &a,
-                                            const HomoPointType &b,
-                                            const HomoPointType &c) {
-  const int x_min = std::min({a.x(), b.x(), c.x()});
-  const int y_min = std::min({a.y(), b.y(), c.y()});
-  const int x_max = std::max({a.x(), b.x(), c.x()});
-  const int y_max = std::max({a.y(), b.y(), c.y()});
-  return BBoxType{x_min, y_min, (x_max - x_min), (y_max - y_min)};
 }
 
-Triangle::BBoxType Triangle::axis_align_bbox() const { return aabb_; }
+BBox Triangle::axis_align_bbox() const {
+  const int x_min = std::min({points_[0].x(), points_[1].x(), points_[2].x()});
+  const int y_min = std::min({points_[0].y(), points_[1].y(), points_[2].y()});
+  const int x_max = std::max({points_[0].x(), points_[1].x(), points_[2].x()});
+  const int y_max = std::max({points_[0].y(), points_[1].y(), points_[2].y()});
+  return BBox{x_min, y_min, (x_max - x_min), (y_max - y_min)};
+}
+
+Vector3d Triangle::normal_vector() const {
+  return points_[0].cross(points_[1]).normalized();
+}
 
 void Triangle::affine_transform(const AffineTransformType &m) {
   for (auto &p : points_) {
-    p = m * p;
+    p = (m * Eigen::Vector4d(p.x(), p.y(), p.z(), 1)).head(3);
   }
 }
 
 void Triangle::projective_transform(const ProjectiveTransformType &m) {
   for (auto &p : points_) {
-    p = m * p;
+    p = (m * Eigen::Vector4d(p.x(), p.y(), p.z(), 1)).head(3);
   }
 }

src/triangle.h

@@ -3,38 +3,40 @@
 
 #pragma once
 
-#include <Eigen/Dense>
+#include "common.h"
 #include <Eigen/Geometry>
 #include <array>
-#include <opencv2/core/core.hpp>
 
 class Triangle {
 public:
   using AffineTransformType = Eigen::Transform<double, 3, Eigen::Affine>;
   using ProjectiveTransformType =
       Eigen::Transform<double, 3, Eigen::Projective>;
-  using PointType = Eigen::Vector3d;
-  using BBoxType = cv::Rect2i;
 
 private:
   using HomoPointType = Eigen::Vector4d;
 
 public:
-  Triangle(const PointType &a, const PointType &b, const PointType &c);
+  Triangle(const Point3d &a, const Point3d &b, const Point3d &c);
   Triangle(const HomoPointType &a, const HomoPointType &b,
            const HomoPointType &c);
 
+  template <int size>
+  std::array<Eigen::Vector<double, size>, 3> get_points() const {
+    return std::array<Eigen::Vector<double, size>, 3>{
+        (points_[0]).head(size),
+        (points_[1]).head(size),
+        (points_[2]).head(size),
+    };
+  }
+
 public:
-  BBoxType axis_align_bbox() const;
+  BBox axis_align_bbox() const;
+  Vector3d normal_vector() const;
 
   void affine_transform(const AffineTransformType &m);
   void projective_transform(const ProjectiveTransformType &m);
 
 private:
-  static BBoxType calculate_aabb(const HomoPointType &a, const HomoPointType &b,
+  std::array<Point3d, 3> points_;
-                                 const HomoPointType &c);
-
-private:
-  std::array<HomoPointType, 3> points_;
-  BBoxType aabb_;
 };