Triangular rasterization

The following sources ：GAMES101- Introduction to modern computer graphics - Yan Lingqi ---- Draw graphic information on the display device .

Matrix transformation from regular cube to screen

Before , We use perspective projection , Put a platform （ Field of vision ） Project to the center of the origin , Side length is 2 The cube of （ Regular cube ） in ： The camera changes AND Orthographic projection AND Perspective projection

Let's go on , How to display it on the screen ？

Let's first look at the regular cube -z The direction of the x-y Plane , Change the same size as the screen through the matrix (width Is the width of the screen ,height For the height of the screen ).

$M_{viewport}=\left(\begin{array}{cccc}\frac{width}{2}& 0& 0& \frac{width}{2}\\ 0& \frac{height}{2}& 0& \frac{height}{2}\\ 0& 0& 1& 0\\ 0& 0& 0& 1\end{array}\right)$

z The coordinates remain the same , As depth information . How to deal with in-depth information —— To ensure that the objects in front can block the objects behind , I don't know for the time being .

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Rasterize

Computer vision , Computer graphics and digital image processing , What are the connections and differences between the three ？

Computer Graphics, abbreviation CG . The input is the description of the virtual scene , Usually an array of polygons , Each polygon consists of three vertices , Each vertex includes three-dimensional coordinates 、 UVW Map 、rgb Color, etc. . The output is an image , That is, a two-dimensional pixel array .Computer Graphics Our ultimate goal is to create unreal visual perception , The key word is “ unreal ” and “ create ”, Such as 3D Special effects ;
Computer Vision, abbreviation CV. The input is an image or image sequence , Usually from the camera 、 Camera or video file . The output is the understanding of the real world corresponding to the image sequence , Such as face detection 、 License plate recognition .Computer Vision Our ultimate goal is to imitate the human eye and brain's understanding of the real things we see , The key word is “ real ” and “ understand ”, Such as face recognition ;

An image can be seen as consisting of many triangles , Each vertex of the triangle contains position information (x-y-z) And color information (red-green-blue).

How do these points form disjoint triangles , I don't know for the time being .

The reason for using triangles as basic geometry ： Triangles are the most basic shape elements , Other shapes can consist of triangles ; You can judge whether a point is inside the triangle , Enter as shown below ,AB and AP Cross product direction of == BC and BP Cross product direction of == CA and CP Cross product direction of .

Next , We consider drawing a triangle on the screen . When all triangles are drawn completely , That is to get a complete graph .

The intuitive approach is , Traverse the pixels in the range . When the pixel appears in the triangle , Namely coloring .

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Anti aliasing

Self reference video ：Antialiasing

During my undergraduate course, I took 《 Signals and systems 》, But I forgot all about it . The general logic in the video may be , In sampling ( Traverse whether the pixels are in the triangle ) front , Blur first . Blur processing is to pass the picture through a low-pass filter , Remove the high-frequency part , To reduce the overlap of frequency domain in the sampling process , So as to achieve the purpose of anti aliasing .

Implementation of low-pass filter , Is the average adjacent pixels .

MSAA The method is , Divide a pixel into smaller parts .