资料来源：https://sites.cs.ucsb.edu/~lingqi/teaching/games101.html
What’s after MVP?
Model transformation (placing objects)
View transformation (placing camera)
View transformation (placing camera)
Projection transformation
Orthographic projection (cuboid to “canonical” cube [-1, 1]3)
Perspective projection (frustum to “canonical” cube)
Canonical cube to Screen
将物体画在屏幕上，屏幕是由像素组成的，一个像素颜色由RGB三种颜色混合构成
屏幕覆盖范围(0，0)至(width，height)
像素索引从(0, 0) to (width - 1, height - 1)
像素坐标中心是(x + 0.5，y + 0.5)
无Z方向
变换到XY平面，[-1, 1]2 to [0, width] x [0, height]
Viewport transform matrix: \(\left [ \begin{matrix} width/2 & 0 & 0 & width/2\\ 0 & height/2 & 0 & height/2 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{matrix} \right ]\)
绘制屏幕上的画面，就是绘制空间中的物体，在获得屏幕空间坐标信息后，绘制物体，物体在屏幕上是由一个个点连成线，再由线绘成三角形，三角形组成物体。
在屏幕坐标中，有哪些像素是近似可以连起来成一个三角形的?
一个简单的方法，可以进行采样(采样一般指取样。取样是指从总体中抽取个体或样品的过程，也即对总体进行试验或观测的过程。分随机抽样和非随机抽样两种类型)
Sampling is a core idea in graphics.
We sample time (1D), area (2D), direction (2D), volume (3D) …
Sample If Each Pixel Center Is Inside Triangle
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for (int x = 0; x < xmax; ++x)
for (int y = 0; y < ymax; ++y)
image[x][y] = inside(tri,
x + 0.5,
y + 0.5);
Inside? Recall: Three Cross Products!
只检查在三角形内的像素，不遍历全屏幕，减少采样数量
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const Triangle& t
auto v = t.toVector4();
auto ext_pt_x = std::minmax_element(v.begin(), v.end(),
[](const Eigen::Vector4f& lhs, const Eigen::Vector4f & rhs){
return lhs.x() < rhs.x();
});
auto ext_pt_y = std::minmax_element(v.begin(), v.end(),
[](const Eigen::Vector4f& lhs, const Eigen::Vector4f & rhs){
return lhs.y() < rhs.y();
});
xMinBox = floor(ext_pt_x.first->x());
xMaxBox = floor(ext_pt_x.second->x());
yMinBox = floor(ext_pt_y.first->y());
yMaxBox = floor(ext_pt_y.second->y());
for (int x = xMinBox; x <= xMaxBox; ++x){
for (int y = yMinBox; y <= yMaxBox; ++y){
if(insideTriangle(x,y,v3f)){
Eigen::Vector3f point(x,y,1.0f);
set_pixel(point,t.getColor());
};
}
}
static bool insideTriangle(int x, int y, const Vector3f* _v)
{
Eigen::Vector3f pt;
pt << (float)x, (float)y, 0.0f;
bool isInside = isSameSide(pt, _v[0], _v[1], _v[2]) && isSameSide(pt, _v[1], _v[0], _v[2])
&& isSameSide(pt, _v[2], _v[0], _v[1]);
return isInside;
}